In this paper, authors proposed a new method to add damping to Tuned Rotary-Mass Damper(TRMD). New TRMD developed by the authors uses a cylindrical mass and a polygonal slope for adding to damping characteristics.by inelastic collision. And this new method will realize adding damping characteristics at low cost, because the damping coefficient can be designed by the number of sides of the polygonal slope.

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The damping effect of a dynamic vibration absorber (DVA) with granular material in a horizontally vibrating system is studied both experimentally and analytically. Different from the conventional DVA, granular materials are placed into the cavity attached to the absorber mass. The principle behind the damping is the removal of vibratory energy for the absorber mass through losses that occur during impact of granular materials which move freely within the boundaries of the cavity. By using the suitable granular material as a damping element, it is expected to obtain a stable vibration damping effect without being affected by temperature change. Therefore, it can be applied in extreme temperature environments, where most conventional DVA would fail. The behavior of granular material was analyzed using the discrete element method. This method makes it possible to consider the effect of granularity on the damping effect. Granular materials used in the experiment were copper balls and were uniform size. It is shown that it is possible to obtain high damping effect. It is also found that the resonance frequency decreases with increasing the mass ratio. In addition, the validity of analytical model of a DVA with granular materials is examined by comparison with experimental results.

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Regarding the two different seismic design requirements with the same design limit to keep elastic behavior under seismic loadings due to, (first) “Elastic Design Earthquake Ground Motion” whose acceleration response spectra are assumed to be one-half of those by ” Standard Earthquake Ground Motion”, and (second) static seismic force based on “Static Seismic Coefficient” adopted in the seismic design of Nuclear Power Plants in Japan, elastoplastic response analysis by the one-DOF bilinear model and comparative evaluation was carried out using the observed seismic motion 48 waveforms of the Japan Meteorological Agency seismic intensity 7 and 6-Upper. Response ductility factor was proposed as damage assessment index to evaluate the reliability of seismic capacity against ductile failure modes of mechanical components due to seismic inertia force. As a result, it was clarified that by setting the static seismic intensity to about 0.6 to 1.2, the static design based on the static seismic coefficient may be able to substitute the dynamic design based on the seismic motion for elastic design.

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In order to clarify the seismic damage of machines and equipment, and influence on the industrial facilities in the 2016 Kumamoto Earthquake, the seismic damage investigation mainly based on the questionnaire survey was conducted under the Japan Society of the Mechanical Engineers. From the result of the questionnaire survey, the failure at the fixing or the support of machines were reported, and it seems that the most of the seismic damage observed in the 2016 Kumamoto Earthquake were due to the large seismic motion. 46% of the questionnaire respondent prepared the emergency manual for the seismic events, and most of them said that it was useful in the 2016 Kumamoto Earthquake. Some future issues for the improvement of the seismic safety in the industrial facilities are discussed based on the questionnaire survey, as well as the investigation method for the seismic damage of the industrial facilities.

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Japan is an earthquake prone country among the world. Especially, the Southern Hyogo prefecture earthquake occurred in 1995 hit by enormous damage. Thus, structures in Japan are desired high safety. Against such a background, seismic technologies have been actively studied and developed. Seismic isolation system is one of the seismic technologies. Seismic isolation system isolates the structure from the ground. Thereby, acceleration input to structure can be reduced. However, seismic isolation structures are few compared to the total number of structures. Consequently, seismic observation records of seismic isolation structures are few in number. In order to improve seismic safety, seismic observation record of the structures obtains to important in earthquake. In this study, we deal with a seismic isolation structure of Tokyo Denki University, we conducts seismic observation since December 2011. In this paper, we investigate relationship between the intensity of the earthquake in construction site and the natural frequency of the target structure by using seismic observation record of the target structure. And, analytical model in constructed by using the above relationship. After that, analysis result by the analytical model and seismic observation records are compared. Thereby, the reproducibility of the analytical model is evaluate.

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In recent years, from the purpose of environmental impact reduction and earthquake-proof improvement, even if it carries out an industrial apparatus pair not only in a building, the earthquake-proof performance attracts attention. So the electrical machinery apparatus maker is tackling the earthquake-proof improvement in industrial apparatus. In this research, the FEM analysis model of cast resin transformer was built, and comparison verification of the analysis accuracy was carried out with the experiment.Since it united and the technical point required for earthquake-proof improvement was considered, the result is shown.

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A simplified analysis was conducted, and it was explained that the response spectrum of the cumulative fatigue damage value of the cantilever pipe with concentrated mass attached to the tip markedly decreases with increasing natural frequency. In addition, the validity of the analysis was shown by response analysis using actual earthquake motions in the first part of this paper. By the way, in same case it is said that there are cases where the response to high frequency acceleration is a problem for the piping system at the earthquake. Therefore, using the above concept, it is shown that the response of the cumulative fatigue damage at the resonance frequency for the sinusoidal excitation can remarkably decreases with increasing the vibration frequency of the excitation acceleration in the second part of the paper.

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Piping systems supported by multiple support structures are excited by different floor response for each support position. Seismic response of piping systems can be calculated accurately by independent time history analysis (ITHA) in considering multiple excitations. On the other hand, the uniform response spectrum analysis (URSA) is commonly used in seismic design of piping systems of nuclear power plant owing to its advantages of simplicity and conservativeness. The floor response spectrum at the center of gravity of piping systems is generally applied in the URSA. In order to check the accuracy of URSA with the floor response spectrum at the center of gravity of piping systems, a comparison of ITHA and URSA was carried out. The actual piping systems of nuclear power plant spreading largely in vertical direction was selected as analysis object model so that the difference of seismic excitation for each support structure is relatively large. In the seismic response analyses, horizontal floor response of two directions and vertical direction was input. As a result of comparison, piping stress calculated by URSA is larger than that of ITHA at most of piping nodes including the point where the maximum stress is generated. It was confirmed that piping stress can be evaluated conservatively by URSA with the floor response spectrum at the center of gravity of piping systems.

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Time history analysis with multiple excitations is an analysis method that can perform reasonable evaluation. However, the analysis method which is common to be used to evaluate seismic performance of nuclear power plants is not time history analysis with multiple excitations but modal analysis under covers all floor response spectra all supporting response so far. Therefore there are few examples quantitatively showing how much evaluation can be rationalized by time history analysis with multiple excitations. Time history analysis with multiple excitations can be expected to have a large reasonable effect on long laid pipe like a secondary heat transfer system of loop type FBR. In this report, when a time history analysis with multiple excitations is used for aseismic evaluation of pipes which is long laid in the vertical direction and horizontal direction, as an example the secondary heat transfer sysytem of MONJU, how much rationalization effect is obtained compared with the modal analysis under covers all floor response spectra all supporting response. As a result, it was confirmed that the reduction effect of 30% or more in the long laid pipe in the vertical direction, and the reduction effect of 18% in the long laid pipe in the horizontal direction.

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In general, Nuclear Power Plants (NPPs) are designed for a postulated earthquake event. Two conceptual stress limits which are Primary stress limit and Primary plus Secondary stress limit are required to meet in the design codes for seismic loads on essential structures such as a piping induced by the seismic event. The past researches proposed an interpretation that seismic response of structure is comprised of load-controlled load and displacement-controlled load, whereas most design codes consider the seismic response corresponds to load-controlled load which should be limited with the Primary stress limit to prevent a plastic collapse.Although these limits are considered to qualify two independent loads which consist of load-controlled load and displacement-controlled load, all of design codes for NPPs give weight at qualifying the load-controlled load since the load-controlled load, the pure Primary Stress components, is believed to govern a plastic collapse on structures, whereas no plastic collapse has ever occurred on any experimental tests. Past researches proposed an interpretation where seismic response is comprised of load-controlled load and displacement-controlled load. An interpretation of the each term in the equation of motion was proposed in the former researches PVP2015-45287 which found a structure excited by a lower frequency than the natural frequency which is considered as an excitation at Rigid condition could result in plastic collapse because of a minimal recovering force counteracting the deformation. This result implies that the current design codes which assume elastic-behavior may include significant over-conservatism to ensure the adequacy of structures under seismic condition. As many experimental results are showing, very large seismic loads which excessively exceed the design limit barely caused failure in piping components. This paper investigates the relationship between inertia forces and element forces on a single mass cantilever model applying a bi-linear material property against several random time-history loads which are adjusted to represent the said excitation conditions. This paper also clarifies the correlation between deformations due to the excitations and the inertia/element forces observed on the models.

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Current seismic evaluation method widely used based on the dynamic analysis considers the elastic and plastic deformation of materials, excluding the fracture of them. On the other hand, much larger earthquakes are considered for the seismic design of steel-frame structures through the 2011 Tohoku Earthquake or the 2016 Kumamoto Earthquake. Under these severe ground motions, the fracture of structural members could be occurred. If member fracture occurs during earthquakes, there are considered to be many effects on the vibration property and the seismic performance of the structure. Therefore, the fracture of members is preferably taken into account in the seismic performance evaluation for these large earthquakes. In this paper, the dynamic seismic analysis method considering member fracture developed by the author and the ordinary method not considering member fracture are applied to the steel-frame structure model. By comparing each result, the effects of considering member fracture are discussed.

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Limit state of braced frame steel structure under sinusoidal shaking was clarified in this study. The load-displacement relationship of the braced frame steel structure was obtained from high acceleration vibration test by using resonance shaking table of CRIEPI. The resonance frequency of the resonance shaking table is 10 Hz, and the natural frequencies of test specimens were set to low, high or equal relative to 10 Hz. In the all cases, a fatigue crack occurred at heat-affected zone of the base near fixed end. The shapes of hysteresis loop became swell and was inclined to the horizontal axis when the load amplitude was exceeded 20kN. The crack initiation and propagation is considered to cause the shapes to change. On the other hand, the buckling or local deformation were not occurred in the all cases.

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Vibration effect analysis was carried out in order to investigate environmental vibration of the resonance shaking table introduced for high acceleration shaking tests. Based on past ground survey results and design information of shaking table, a detailed three dimensional analysis model was created and wave propagation analysis was performed. The analysis result agreed with the vibration level data measured at the trial operation of the resonance shaking table. The acceleration distribution in the surrounding ground was visualized by volume rendering, the environmental vibration behavior of the surface wave and the body wave was clarified. These results would be utilized for the solution of vibration problems occur in the future.

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Research on seismic isolation technology was also a question of how much restoring force can be reduced. Seismic isolation rubber with thin film like rubber and metal plates stacked in multiple stages to reduce the restoring force has achieved great success. However, research to date has shown that rocking movement has become a major obstacle when trying to construct a three-dimensional seismic isolation using it. This research is an effort to further minimize the restoring force, to eliminate obstacles to three-dimensionalization and make the three-dimensional seismic isolation more realistic. Vibration test of a prototype of a newly developed three-dimensional seismic isolation mechanism were carried out using a real scale 3 dimensional seismic wave by E - defense excitation device. The developed 3-D seismic isolation mechanism consists of an air levitation mechanism that isolates horizontal vibration and a spring link mechanism that isolates vertical vibration. The prototype showed unprecedented high performance of about 20 dB of anti-vibration capability at 1 Hz for both horizontal and vertical, and the effectiveness of this mechanism was verified.

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At present, there are many types of isolation system, but many of them are designed for the short-period ground motion. And the long-period ground motion has recently attracted the attention, but the isolation system for the shortperiod ground motion does not have an ability to suppress the vibration due to the long-period ground motion. In this study, a new isolation system is proposed for not only the short-period ground motion but also the long-period one. The basic concept is that the dynamic property, which is the natural frequency, is changed by adding a spring when the amplitude of isolation table exceeds a threshold value. The validity of the method is checked by the numerical simulation using a single-degree-of-freedom system. As a result, it is shown that the resonance can be suppressed by the proposed method. Then the applicability is checked by using the experimental setup. As a result, the system can suppress the resonance phenomenon, so that it was concluded that the proposed system has a sufficient ability to suppress the resonance due to the long-period ground motion.

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We have ever applied PFT-ELS (Equivalent linear system using the restoring force model of power function type) method to analyze the nonlinear vibration characteristic of seismic isolation laminated rubber. However, the restoring force characteristics cannot express shapes like experimental values in the PFT-ELS method. Therefore, in this research, we apply PFT-HYS (Hysteresis system using the restoring force model of power function type) which can accurately express the restoring force characteristics more than the PFT-ELS for the nonlinear vibration analysis of the seismic isolation laminated rubber. Then, the analysis results of PFT-HYS method is compared with the PFT-ELS method.

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Many earthquakes have occurred in Japan and Japanese design seismic wave for several plants have become more severe after strong earthquakes. Especially, since vertical seismic conditions have became more severe, it is difficult to ensure the safety margin of the seismic evaluations in industrial facilities. As a way to ensure the margin of seismic evaluations, it is effective to adopt the vertical seismic isolation system. When the vertical frequency with the vertical isolation system becomes low frequency range, the rocking vibration will occur. By using the seismic isolation system of approximately 3 Hz in vertical frequency, the response in vertical direction is reduced without large rocking vibration. However, variations of a specification in seismic isolation system may occur in actual isolation device. Therefore, in this paper, the vibration characteristic including the rocking vibration is discussed, and also an analysis method is evaluated in consideration of the variation of vertical stiffness. Then, using the proposed analytical method, the tendencies of the vertical frequency variation and the rocking vibration response are confirmed. The rocking vibration occurs because of the deviation between the center of gravity and center of stiffness. Therefore, it is necessary to control the decentering between the center of gravity and rigidity.

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In recent years, an elevator becomes larger capacity and higher speed to cope with high-rise building. For example, a large capacity elevator capable of taking up to 90 passengers or a high speed elevator having a maximum speed of over 1000 m / min can be cited. Along with this change, safety and comfort are regarded as more important. However, it is problem that vibration and noise occur in a machine room and neighboring rooms by vibration growing big because of traction machine getting bigger. Presently, base of supporting traction machine and against vibration devise was set to solve this problem, but the method of anti-vibration design has not been clarified. As a result, excessive design is causing cost problems. From such a background, the object is to propose a member configuration that is simple in configuration and can exhibit high vibration damping effect. In this study, I model an elevator actual machine to use modeling method of preceding study and examine the protection against vibration design. In this paper, we report improvement of accuracy by improving the modeling method used in the previous research, and propose the possibility of vibration reduction by changing the mass of the members of the traction machine base.

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Elevators are essential for means of vertical transportation. In recent year, Elevators to be installed in high-ride buildings are long travel, thus the elevator rope. High-rise buildings have longer natural period than conventional buildings. As elevator ropes become longer, the natural period of the elevator ropes become longer and get closer to the natural period of the building. Consequently, the elevator ropes are hooked to the equipment of well wall when the elevator ropes vibrate by an external force, such as a strong wind and earthquake. Secondary damage such as containment of passengers and elevator service stop may occur. It has become a problem. For example, The Great East Japan Earthquake in 2011, 2215 cases of problem such as catch and damage of elevator ropes have been reported. However, operations of elevators after earthquakes are required. Therefore, in this research, we aim to construct a vibration reduction method for elevators that can operate even after the earthquakes. In this report, we examine effectiveness of lifts using intermediate transfer floors for damage reduction of ropes. In the analysis, the maximum displacement of the main rope and the number of collisions were examined when the lifting travel is divided from 2 to 4. As a result of the analysis, it was confirmed that dividing the lifting travel reduces the displacement amount of the rope and the number of collisions.

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In the 2011 off the Pacific coast of Tohoku Earthquake, four fall accidents of the escalators confirmed. In these accidents, the escalator connected on the third floor from second floor dropped at commercial facilities of the steel-frame building. In general, the escalator is set on beams of buildings with one side of the leg or both sides as non-fixed style in order not to restrict motion of the escalator. As a cause of the fall, the escalator came off from the beam of building by layer deformation more than expected. After the escalator fall accident, the new standard was defined. According to this standard, the layer deformation angle was considered more than before, and possibility which comes off the beam of building becomes short. However, it is considered that a non-fixed part collides with the beam of building by the earthquake; the collision may give compression and residual displacement to the escalator. From the above-mentioned background, the purpose of this study is to grasp behavior of response and collision of an escalator at earthquake. In this paper, behavior at an earthquake for an escalator against huge earthquake that could occur in the future was examined.

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The damping characteristics of a square pipe packed with steel balls and silicon oil can be improved by a combination of large balls and high viscosity oil and a combination of small balls and low viscosity oil. However, the reason for those has not been made clear yet. In this paper, the ball behaviors in impulsive excitation experiments are observed using a high speed camera, and the drag acting on a ball in silicon oil in a square pipe is numerically analyzed under the condition of the first vibration mode of the pipe when the square pipe vibrated are analyzed by ANSYS CFX software. It is shown that the ball behaviors are different from one combination of ball size and oil viscosity to another and that a high damping capacity is obtained when the contact between the balls and the square pipe frequently takes place.

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In this study, influence that the torque properties of the rotary particles damper received from applying magnetic field were investigated. Steel balls of 0.8 mm in diameter were prepared as the particles. A coil was attached outside of the rotary particles damper to apply magnetic field to the particles. Strength of magnetic field that was applied to the particles was changed by adjusting an electric current. The torques of the rotary particles damper were measured under condition that the forced angular displacement of amplitude of 30 degrees was given to the rotary particles damper. The torque properties of the rotary particles damper under non-magnetic field was same as a torque properties of general friction damper. On the other hand, when the magnetic field was applied to the particles, the torques increased as the angular displacement of the damper was increased. The maximum torques were changed depending on magnetic field strength.

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We have studied the damping mechanism of a granular material damping system applied to reducing vibration in structures that have a high natural frequency and small vibration displacement. We considered the damping mechanism based on the vibration energy. We calculated the movement of the all granular materials and the container, the work by the collision, and the work by the friction. The work by the collision between the granular materials and the container has a big influence on the damping mechanism when the total mass of granular material is small. On the other hand, the influence of the work by the friction is increased in accordance with increase of the total mass of granular material. In this report, as a study for high attenuation of the granular material damper, we report the result of examining how the characteristics (density and friction coefficient) of the granular material affect attenuation characteristics of the granular material damper by calculation.

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Damping material is used to provide structures and machines with damping characteristics. Damping material is applied to part of the product in order to reduce noise and vibration. The improvement of damping properties is important and viscoelastic material/particle composites are focused on. Many studies have reported vibration damping characteristics of viscoelastic materials are improved by particle composite process. However, it is not clear that the relationship between the vibration damping characteristics and the conditions of the particle compounding. Hence, it is difficult to predict the damping performance by compounding condition. In this study, we investigated the effects of blending of particles on the loss factor by PET particle/natural rubber composites. Evaluating dynamic viscoelasticity was performed. As a results, it is found that loss factor of composite materials have strain amplitude dependence. We built dynamic model for composite materials. This model includes equivalent stiffness, damper and friction mechanism due to the effect of surface between particles and matrix. And we assumed that dynamic frictional force is proportional to the square of the strain amplitude. Results show that analytical values of loss factor nearly correspond to experimental data.

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Magnetorheological fluid is known as one of functional fluids, whose rheological properties can be controlled by the applied magnetic field strength. By using this property, brakes, clutches, dampers and various engineering applications have been studied. However, sedimentation of the magnetic particles of MR fluid will result in unsteady dynamic behaviors of the MR devices. In order to overcome this problem, we propose a new magnetoresponsive material named as the MR compound. The basic properties of MR compound have not been elucidated, which is thought to intermediate between liquid and solid. The purpose of this study is to characterize the magnetic field response properties of the MR compounds and to evaluate the transmissibility characteristics of the vibration isolator incorporating the compound. The effects of the magnetic field strength and the shear rate on the resultant viscosity change of the MR compound were investigated experimentally. Also, magnetic particle sedimentation behaviors in both MR compound and MR fluid were compared by the long-term observation. Additionally, the vibration transmission characteristics of a variable viscous vibration isolator incorporating the MR compound was evaluated. Experimental investigations showed that the proposed vibration isolator is able to suppress the vibration in a wide range of frequency band in comparison to the conventional passive isolators.

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There are two type modeling methods for describing dynamical behavior of viscoelastic materials; the Simo’s model and the fractional derivative model (or the fractional model). The Simo’s model is based on the generalized Mawxell model in which a number of Maxwell model with different decay constants are connected in parallel. One of the mathematical expressions of the Simo’s model is the Prony series in which the individual Maxwell models are given in integral form. The fractional derivative model can be defined as a limit of generalized Maxwell model with continuous distribution and an infinite range of decay constants. Owing to these properties of fractional derivative and the Prony series, one can evaluate the accuracy of the Prony series for the Simo’s model. In this paper we show how the accuracy of the Prony series is estimated quantitatively as the model of viscoelasticity including the viscoelastic dampers. We also show that the accuracy of the fractional models for viscoelastic materials can be estimated with the use of the Prony series.

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The models that include fractional derivatives are known to describe the characteristic behaviors of viscoelastic materials. However, due to their calculation costs for numerical estimations of fractional derivatives, the application of fractional derivative model (or fractional model) have to be limited to theoretical works or numerical works in small time steps. Recently, the present authors proposed an algorithm that reduces the calculation cost. In this paper, this algorithm is applied to the fractional differential equation for viscoelastic damper. The speed and the accuracy of the algorithm are investigated through numerical integrations of the equation. The present algorithm is applicable to nonlinear responses to large strain as well as linear responses to small strain. By the present algorithm, one is able to perform long term simulations of responses to oscillatory forcing with wide range of periods such as earthquakes including the Tohoku earthquake.

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The plumbing vibration can cause the noise and the damage. To solve these problem, you may control plumbing vibration by attaching viscoelastic materials as damping materials around the plumbing. However, you cannot predict the detailed vibration reduction effect in a design stage because the evaluation of the damping performance is generally carried out experimentally. Therefore, it is possiple that you cannot get an effective control on vibration effect or that the amplitude increases even if you attach a damping materials. In this report, we suggest a vibration analysis model of plumbing that viscoelastic damping materials are attached to to make it possible to predict the vibration reduction effefct beforehand. By this suggestion technique, we model the influence that damping materials give for plumbing vibration as added mass and added damping, and incorporate these in a 1-dimensional plumbing bendng vibration analysis model. By this method, we succeed in reducing calculation load than a calculation by the general 3-dimensional model while keeping the calculation precision. In other words, you can easily predict the damping effect of viscoelastic materials with high accuracy and suggest the most suitable design guidance.

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A rational method of dimensional reduction is developed in order to analyze accurately a nonlinear vibration of a large-scale system with nonlinearity. Almost nodes without strongly nonlinear excitation are transformed into the modal coordinates by using the complex constrained modes that is obtained by fixing the nonlinear nodes. And a small number of modes whose effect on computation accuracy of the vibration analysis is significant are extracted. On the other hand, the remaining modes are appropriately approximated and are eliminated. The low-dimensional model is constructed by these procedures. Furthermore, by applying an efficient method to eliminate higher-order modes, the low-dimensional model is constructed without computation of higher-order eigen pairs. Effectiveness of this method is verified by computational result

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It is important to consider the bifurcation caused by the journal bearing at the design stage of the rotor system. In this paper, nonlinear approximate modeling of fluid film force of a finite length model of the journal bearing is performed by discretizing the Reynolds equation using the finite difference method. Bifurcation analysis considering the influence of the bearing shape, such as oil inlet and groove, will be possible by using this model. In this model, the fluid film coefficients considering up to the third order are numerically calculated. In order to achieve compatibility between calculation cost and calculation accuracy, the relationship between the mesh number (mesh size) of the finite difference method and the accuracy of the fluid film coefficient is investigated, and an appropriate number of mesh is examined. Bifurcation analysis of the flexible rotating shaft system supported by the journal bearing is performed. The analytical results of the proposed model is compared with the analytical results of the fluid film force model using infinitesimally short journal bearing model applying the half-Sommerfeld boundary conditions, and its usefulness is validated.

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An audible warning device (AWD) is a device which sounds by impact vibrations. The behavior of AWD is a kind of self-induced vibration in which the suction behavior in AWD depends on its own motion. In specific condition, period doubling bifurcation occurs and behavior of AWD becomes unstable. Therefore, the bifurcation behavior is investigated by a simple model. First, a simple analytical model consists of a shaft, a pole, and a resonator of AWD is introduced, which is 3 degree-of-freedom system accompanied by impacts, and suction force between the pole and the shaft is modeled as a ramp function which starts to increase from zero-value at the time of an impact. Then, a map from state variables of an impact to those at the next impact is derived. Fixed points of the map and their stabilities are numerically calculated, and arc-length continuation method is used to obtain those. It was found that the saddle-node bifurcation occurs when time duration from an impact to the next impact coincide with a natural period of the mode that the resonator mainly vibrates. Furthermore, the bifurcation of impact behavior is drastically influenced by the phase of the vibration of the resonator at the time of impact.

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Hunting of a railway vehicle is the self-excited oscillation, which is unfavorable for the running stability. Therefore, a lot of research on it has been done. The authors have conducted hunting tests using two different bogies under the condition of the half rolling stock on the roller rigs. The bogies were basically the same as for the structure except for the wheel profile. The result showed that the different types of oscillation occurred depending on the bogie when peripheral wheel speed reached the critical speed of hunting: one is small amplitude oscillation which was generated by the supercritical hopf bifurcation and the other is large amplitude oscillation which was generated by the subcritical hopf bifurcation. As the result of the wheel-rail contact analysis of the two bogies, it was confirmed there was relatively huge difference in their nonlinearity and that could affect the type of hopf bifurcation.

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In aircrafts and space structures, there are many structural components that can be considered as flexible beams. Vibrations can be harmful to the performance of such structures. In this study, fractional calculus was applied to the vibration suppression of a flexible beam, and the controller parameters were designed. The tuning of the controller parameters has been performed in some previous studies using a trial-and-error approach. However, this tuning process is time-consuming, and there is a risk of destabilization. As an alternative tuning method, a function that implements an optimization algorithm (e.g., the “fmincon” function in MATLAB) has been used in some studies. However, this complicated algorithm can place a heavy load on the computer. Therefore, in this study, a fractional-order controller was designed as an alternative non-trial-and-error approach that is simpler than previously implemented optimization algorithms. This paper proposes a fractional-order controller design method for the vibration suppression of a flexible structure. First, the process of designing a controller to meet the specifications of the Nyquist diagram is explained. An improvement to the design method that allows the attenuation level of a resonant peak to be treated as a specification is then discussed. Numerical simulations performed in this study demonstrate that the proposed fractional-order controller is more robust against spillover instability than the integer-order controller.

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In this study, vibration characteristics of a single-degree-of-freedom linear oscillator with the fractional order derivative are examined in terms of the relationship between the order of the derivative, the damping coefficient of the equation of motion and a critical damping over the wide range of the order by using numerical analysis. Two types of critical dampings proposed in the previous studies are considered. No critical value of the damping coefficient is observed in some range of the order. We explain analytically the reason why the impulsive response of the system always vibrates when the order is 1/2. It is also shown that the difference of the existence of the critical damping between the order 1/3 and 2/3 is mainly caused by the change of the characteristics of the roots of the characteristic polynomial of the oscillator. The response characteristics are classified into three cases in the view of the existence of the two types of critical dampings. The relationship between the order of the derivative, the coefficient of the motion equation and the resonance frequency is also obtained by using numerical calculation and is compared with the classical mass-spring-damper system. The relationship between the order, the coefficient and the peak value of the frequency response function is also investigated.

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In order to obtain statistical moments up to the 4th order of the response of narrow-band non-Gaussian randomly excited systems readily, equivalent non-Gaussian excitation method is extended. The narrow-band non-Gaussian excitation used in this paper is governed by an Ito stochastic differential equation determined by the dominant frequency, bandwidth and probability density function of the excitation. Moment equations which govern the response moments are generally not closed form due to the complex nonlinearity of the diffusion coefficient in the stochastic differential equation expressing the excitation. To make the moment equation closed form, equivalent non-Gaussian excitation method is used. Equivalent non-Gaussian excitation method, which makes the moment equation closed form by approximating the diffusion coefficient to the equivalent diffusion coefficient expressed by a quadratic function, was proposed to calculate the moment equation of systems under non-Gaussian random excitation with zero dominant frequency. In this paper, by proposing new equivalent diffusion coefficient, equivalent non-Gaussian excitation method is extended to apply to the systems under non-Gaussian random excitation with nonzero dominant frequency. In order to assess the validity of the present method, a single degree of freedom linear system under two types of narrow-band non-Gaussian random excitations are considered. By comparing the kurtosis of responses calculated by this method and Monte-Carlo simulation, the validity of this method is demonstrated. Finally, in order to discuss the accuracy of the method, the statistical moments of the equivalent non-Gaussian excitation are investigated.

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In this research, the effectiveness of higher order spectral analysis is presented for vibration system with viscous damping and Coulomb friction characteristics. First, we approximated the Coulomb friction characteristics. Coulomb friction characteristics were approximated by using "sigmoid function". Representation of many attenuation characteristics including “one-side” damping is possible. And, we modeled the power polynomial in velocity in the damping characteristics combined viscous damping and approximated Coulomb friction. Finally, the higher order frequency response function was defined using Higher Order Spectra (HOS), “Bispectrum” and “Trispectrum”. We formulated high frequency response function in nonlinear attenuation characteristics and numerical simulation analysis and presented the effectiveness of these.

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Although state-space representation has provided advanced and mathematical analysis in modern control theory, existence of non-autonomous input vector prevents a simple expression of vector-matrix product in state equation. It is because non-autonomous external force cannot be expressed as a function of merely a state vector. In this study, we decompose an arbitral non-autonomous intermittent function of an external force for a 1DOF oscillator into vibration manipulation functions, which represent internal forces in a closed Hamilton system of three vibro-impact oscillators designed for Grover algorithm. Through the sequential decompositions and their unsmooth joints, each piecewise input vector is taken into a new state-space representation of a simple product of an extended state vector with state matrices of Grover operators. From this point of view, we could regard the intermittent change of the state vector with piecewise input as a manipulation of coherent phonons under the control of quantum algorithm in the intermittently closed Hamiltonian system with discrete impulsive interactions from environment. This might suggest an answer of an inverse problem in Newtonian mechanics, which pursuits isolated systems from dynamics with non-autonomous force.

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This paper proposes an identification method of symmetry nonlinear system using Fokker-Planck equation. The proposed identification method will be derived from the least square estimation based on probability density function of Fokker-Planck equation. In order to estimate the probability density function, response of target nonlinear system is supposed to be subject to a constrained Gaussian Mixture Model, which has a constraint about symmetrical distribution. The estimation algorithm will be derived by using a method of maximum logarithmic likelihood, i.e. ExpectationMaximization algorithm. In a numerical simulation based on a nonlinear one degree-of-freedom system subjected to white random excitation, the estimation result of probability density function shows good agreement with the ground truth. In addition, relationship between restoring force and displacement shows good agreement with the ground truth.

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When structure is subjected to excess loading, its response is beyond elastic limit. In such a case, restoring force and displacement relation has hysteresis loop characteristic. If initial load exists, hysteresis loop characteristic has asymmetrical characteristic. In this case, plastic deformation grows up in one direction and displacement response grows up in one direction. In this paper, response of structure having asymmetrical hysteresis loop characteristic is examined. Structure is assumed to be subjected to seismic excitation. The effect of asymmetrical hysteresis loop characteristic on random response of structure is examined.

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The response distribution of a SDOF linear system subjected to non-Gaussian random excitation is investigated. The excitation is modeled by a zero-mean stationary stochastic process prescribed by the non-Gaussian probability density and the power spectrum with bandwidth and dominant frequency parameters. In this paper, we use bimodal and Laplace distributions for the non-Gaussian distribution of the excitation. The excitation is generated numerically by using the Itoˆ stochastic differential equation. Monte Carlo simulations are carried out to obtain the stationary probability distributions of the system displacement and velocity. It is shown that the shape of the response distribution changes depending on a difference in the shape of power spectral density between the excitation and the response. Then, in order to evaluate the difference of the spectral densities quantitatively, a new index is defined. We find that when the index is close to 0, the shape of the response distribution looks like the shape of the excitation distribution. For the index around 0.6, the response distribution becomes the middle shape between the excitation probability density and a Gaussian distribution. In the case of the index greater than 1.2, the response distribution is nearly Gaussian. We also discuss the relationship between the present difference index of power spectra and another index which the authors used in the previous study to investigate the response distribution of a non-Gaussian randomly excited system. The difference index of power spectra between the excitation and the response can be calculated readily from the frequency response function of a linear system and the excitation power spectrum, regardless of the excitation probability distribution. This index enables us to predict roughly the shapes of the probability distributions of the displacement and velocity responses without Monte Carlo simulation.

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In this paper, we extend an analytical method via complex fractional moment (CFM) for the response of a system under combined Gaussian and Poisson white noise excitation. CFM is a quantity which is considered as the extension of the order of the moment to a complex number and related to a Mellin transform of a probability density function (PDF). We deal with both linear and nonlinear systems. In order to obtain the PDF of the response of the system, we need to solve a generalized Fokker-Planck (FPK) equation, which includes infinite terms. So we truncate the terms of the fifth or higher order, which are considered as negligibly small. Then by applying a Mellin transform to this truncated generalized FPKeq and using the characteristics of CFM, we can calculate the CFMs of the response. Finally, applying an inverse Mellin transform to the CFMs, we can obtain the PDF of the response. The effectiveness of this method using CFM is demonstrated by comparing with the Monte Carlo simulation results. The influence of parameters of the systems and the excitation upon the accuracy of the present method is also considered.

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The approximate analytical method combined with equivalent linearization and equivalent non-Gaussian excitation method is proposed to estimate the statistical moments up to the 4th order of the stationary response of a Duffing oscillator subjected to non-Gaussian random excitation. These moments contain information on the mean, the variance, the asymmetry and the tail heaviness of the response distribution. In the previous study, the equivalent non-Gaussian excitation method was applied to a linear system. It was shown that the moments up to the 4th order of the response can be accurately obtained by this method. On the other hand, many of real structures have nonlinear restoring force. Therefore, in this research, equivalent non-Gaussian excitation method is applied to a nonlinear system. In order to obtain the moments, the moment equations for the response, which are derived from the equation of motion of the system and the stochastic differential equation governing the excitation, are used. However, they are not generally closed form due to the complex nonlinearity of the diffusion coefficient of the stochastic differential equations governing the excitation and the nonlinear term of the equation of motion of the system. Therefore, using non-Gaussian excitation method and equivalent linearization, the diffusion coefficient is replaced with the second order polynomial and the nonlinear parameter of the system can be replaced with a linear term, and then the moment equations can be closed. By solving these equations, the moments up to the 4th order can be obtained. Using these obtained moments, the skewness and the kurtosis of the response are also determined. In the analysis, various non-Gaussian distributions, and a wide range of the excitation bandwidth and nonlinearity of a Duffing oscillator are considered. To demonstrate the effectiveness of the method, the results of the proposed method are compared with those of Monte Carlo simulation.

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An overhead crane is widely used at factories, and it plays an important role in the mass transportation system. The main trouble in operation of the overhead crane is that the residual vibration of a cargo often occurs at the end of motion. In addition, the development of the automatic operation system is desired for an efficient and safe transportation. In this research, a new type of open-loop control method has been proposed for suppressing the residual vibration. This method is based on the dynamical property that the residual vibration does not occur in a linear undamped system when it is excited by an external force which does not contain any component of natural frequencies of the system. The authors have applied this property to a nonlinear damped system and developed an efficient method to derive an adequate trajectory of the trolley of the overhead crane which enables complete prevention of the residual vibration of the cargo. Also, in order to reduce the rapid velocity change of the trolley and large swinging of the cargo during transportation, the authors optimized the trajectory of the trolley by using the method of Lagrange multiplier. This paper deals with a 2-dimensional overhead crane and design routing path for obstacle avoidance, then applies the vibration control method. The results show that the trolley moves along the path planned in advance, preventing the residual vibration.

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Overhead traveling cranes are widely used at ports and factories, and they play an important role in mass transportation systems. The main problem in operation of overhead traveling cranes is that the residual vibration of a cargo often occurs at the end of transportation. At present, prevention of the residual vibration depends on proficient skills of operators. Therefore, the automatic operation of overhead traveling cranes is strongly desired for an efficient and safe transportation. In our previous paper, a new type of open-loop control has been proposed which is based on the concept that the residual vibration does not occur in a linear undampede system excited by an external force which does not contain the component of natural frequency. This control is also applicable to system with strong damping and nonlinearity by regarding associated terms as part of the external force. This paper improves the robustness against an inevitable estimation error in natural frequency, combining an optimization method in order to reduce the swing motion of the cargo during transportation.

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This study develops an Active Wheel Damper (AWD) which can be attached easily to flexible structures such as the boom sprayer. The AWD also achieves lightweight and higher inertia by using the flywheel, and can realize sky-hook control easily because the absolute angular velocity of the flexible structure is measured by the gyro sensor. For achieving higher vibration suppression performance, disturbance cancellation control has been combined with the sky-hook control, and the Sky-hook with Disturbance Cancellation (SWDC) control has been applied to the AWD controller. Generally, a low cost microcomputer, which commonly has limited I/O port resource, is used to construct such control device. Our previous study supposes low resolution controller (minimum resolution is 2 bit), and shows that performance of the AWD can be kept by applying the dynamic quantizer to the controller. However, the control performance is changes according to the sampling period and the actuator torque per bit (TPB) of the controller, and ‘Impulse Resolution’ introduced in the previous study can realize simple evaluation of control performance. This study shows the difficulty in deciding the sampling period and the TPB, and using the ‘Impulse Resolution’ makes this problem simple to understand. So, the index ‘Impulse Resolution’ is useful for realizing those controllers.

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In this paper, we propose an energy saving high-speed position control of a flexible manipulator to suppress residual vibrations in point-to-point (PTP) motion. In the proposed method, the trajectory profile of the PTP motion is generated through a cycloidal function whose input is the output of a polynomial function. The obtained trajectory is dependent upon the coefficients of the polynomial function. To achieve the suppression of the residual vibrations as well as the operating energy of this PTP motion, the coefficients are tuned by a particle swarm optimization (PSO) algorithm. To accomplish the minimization of not only the driving energy but also the residual vibrations consisting of first and second vibration mode amplitudes in the high-speed positioning, we define the sum of the driving torque as the objective function for the PSO. Numerical simulation shows that by minimizing the sum of the driving torque, the optimal trajectory suppressing not only the first vibration mode but also the second vibration mode can be generated for the high-speed positioning. The optimal trajectory also reduces the operating energy. In the experiments, we demonstrate that the feedforward vibration control can be achieved by driving manipulator along the optimal trajectory. Results obtained from simulations and experiments prove the effectiveness and feasibility of the proposed vibration control technique.

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In a previous report, the author proposed a new damping device, called switched mass damper, SMD. The SMD consists of a mass m_a connected to the primary system by a spring and another mass m_b. The mass m_b is connected to the mass m_a through clutch mechanism, which is switched on and off depending on the displacement of the mass m_a. Numerical simulation was performed to check damping performance of SMD in the previous report to find that SMD suppress vibration of the primary system such that the resonance peak of the primary system is cut away. In this report, experiment is conducted to confirm the results of the numerical simulation, and verify the damping performance of SMD experimentally.

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In asymmetrical shaft system which has asymmetry in shaft stiffness, it is known that unstable vibration appears near the major critical speed by parametric excitation. In this paper, we propose use of dynamic damper for preventing unstable vibration in asymmetrical shaft. Firstly, equation of motion of asymmetrical shaft system with dynamic damper is derived, and steady-state solutions are obtained. Then, stability analysis of steady-state solutions is conducted. It is found from numerical examples that unstable vibration is suppressed by selecting appropriate parameter of dynamic damper. Experimental analysis is also conducted, which confirms the validity of theoretical analysis.

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Various typed impact and vibration isolation devices have been widely used to protect the objects particularly in the field of medical, biology, or any precision device industries. These devices are mainly composed of the spring, damper, and actuator. On the other hands, this paper proposes another new simpler method to insulate the impact disturbance by using principle of center of percussion (COP). In the Experiment, the pendulum typed hammer gave impulsive force to a horizontal one-link arm to measure the impact force reduction performance. When the position of the rotational axis of the one-link arm and the impact point satisfies the condition of COP, the effect of the impulsive force by the hammer is suppressed. However, the one-link arm is needed a rotational spring to prevent from free rotational motion. This paper discusses the performance of the impact force reduction dependent on the presence or absence of spring via the several simulations and the experiments.

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Expanding degrees of freedom in vibration systems is thought to be an effective way to improve the power generation efficiency of energy-harvesting devices from the vibrating source, since the system becomes responsive for a wide frequency range due to the appearance of multiple resonant peaks. A magnetostrictive-type vibration energy harvester using an iron-gallium alloy (Galfenol) has received much attention in recent years. The device consists of two beams of Galfenol combined with iron yokes, coils, and a bias magnet. A bending force applied at the tip of the cantilever yields a flux change due to tensile or compression stress, and the flux variation leads to the generation of voltage on the wound coils. This energy harvesting technology has advantages over conventional types, with respect to size and efficiency, and it is extremely robust and has low electrical impedance. In this study, the differential evolution (DE), known as a kind of global optimization techniques, was introduced for the parameter design of the harvester that constituted a two-degree-of-freedom vibration system. Using DE, we numerically explored the best combination of spring constants and masses of the vibration system that maximized the electric power generation. We show that an appropriate set of parameters can easily be found within the design space

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