In the previous study, the stationary and transient response characteristics of linear systems subjected to non-Gaussian random excitation were investigated by Monte Carlo simulation. It was revealed that the response characteristics are strongly dependent upon the bandwidth of the excitation power spectrum. Furthermore, it was also found that in the transient state, the degree of non-Gaussianity of the response caused by non-Gaussian random excitation changes periodically. These response characteristics were examined numerically. For this reason, analytical considerations (e.g. Which terms of the changing periods the response statistics consists of and which of them is dominant?) have not yet been made. Therefore, in this research, the analytical solutions of transient response statistics of a linear system under non-Gaussian random excitation are derived to investigate the response characteristics in detail. In order to derive the analytical solutions, first, the higher-order autocorrelation functions of the random excitation are obtained using the Markov property. Then, using the higher-order autocorrelation functions of the excitation, the transient response statistics are derived based on the convolution integral of the excitation and the impulse response function of a linear system. Finally, the transient response statistics are separated according to the changing periods, and the dominant term and period of the statistics are investigated.

We consider a linear system under non-Gaussian excitation and give an insight into the effect of the non-Gaussianity of the excitation on the response based on the bispectrum. A bispectrum is defined as a double Fourier transform of the 3rd-order cumulant and regarded as an extension of a traditional power spectral density. The bispectrum of the response can be written with the bispectrum of the excitation and the frequency response function of the system. Furthermore, by integrating the bispectum of the response, we can obtain the 3rd-order moments of the displacement and velocity responses. By using these properties, we can calculate the 3rd-order moments of the displacement and velocity responses from the bispectrum of the excitation. The non-Gaussianity of the response is evaluated with skewness, which is the 3rd-order moment standardized by the variance to the power of 1.5. We adopt the Cai and Lin’s model as a non-Gaussian excitation. The model includes a bandwidth parameter α. We derive the bispectrum of the Cai and Lin’s model, and calculate the skewness of the displacement and velocity responses for a variety of α. When α is small, the skewness of the displacement response is closed to the skewness of the excitation, and as α gets larger, the skewness of the displacement response gets close to 0. The skewness of the velocity response is always close to 0 independent of α. We discuss these relationships between α and the skewness of the response based on the shapes of the bispectra of the excitation and response.

This paper describes a new identification method for a nonlinear 1-degree-of-freedom systems based on the method of maximum likelihood estimation (MLE). The likelihood function of the proposed method is constructed from the analytical solution of the Fokker-Planck equation. The estimating formulas in order to obtain the unknown parameters are obtained by minimizing the likelihood function. The fundamental operation test is performed by the numerical simulation using 4th Runge-Kutta method. As the result, the identification operation is confirmed in Duffing type nonlinearity system. The examples of accuracy of un-known parameter are the case of the linear spring constant is 2.61%, the case of the nonlinear spring constant is 18.8%, the case of the ration between diffusion coefficient and damping constant is 0.91%, respectively. Moreover, dependency of number of samples is surveyed. As the result, in the number of under 100 samples, the decreasing of accuracy is observed in our proposed identification method. Also, the convergence behavior of estimation values is observed in the number of samples of over 1000 samples. Furthermore, the application to the linear system of the proposed identification method is conducted.

Reaming is a finishing process for expanding the pilot hole and improving the accuracy of roundness. In machining using regular teeth pitch reamer, a polygonal deformation phenomenon occurs in the machined hole due to self-excited vibration caused by time delay, which causes a problem of deterioration in product accuracy. In the previous studies, the authors clarify the generation mechanism of the polygonal deformation and examined the suppressive effect of the irregular tooth pitch reamers theoretically. The irregular tooth pitch reamers are available commercially and have been found to have improved roundness compared to regular tooth pitch reamers. However, the optimum design of the irregular pitch reamers has not yet been discussed. In this paper, the authors theoretically and experimentally discuss the optimum design of the irregular pitch reamers.

As the self-excited phenomenon of the acoustic pipe system, the self-excited sound of the Rijke tube, combustion vibration, thermoacoustic phenomenon, and musical sound of a leadless wind instrument such as a flute are known. These systems include a self-exciting mechanism and oscillate at the resonance frequency of the acoustic system to generate a loud sound. For these systems, research on the self-excited mechanism is being carried out for each subject. However, since heat and fluid are involved, a clear self-excited mechanism cannot be explained from the viewpoint of mechanical dynamics. In this study, firstly the wave equation of an acoustic pipe excited by a point is derived. Secondly, it is replaced with a vibration system with one degree of freedom by using modal analysis. Then, the self-excitation mechanism is investigated by positively feeding back the state quantities (particle velocity and sound pressure) of the acoustic system to the input of point excitation. As a result, positive feedback of particle velocity is equivalent to proportional control (P control) that assumes displacement output in a 1-DOF vibration system. And positive feedback of sound pressure is equivalent to the differentiated control (D control) that assumes displacement output in a 1-DOF vibration system. It is shown that the feedback path with delay time element causes negative damping and self-excited oscillation. It is also shown that the result of this calculation using modal analysis is completely in agreement with the result calculated by the cellular automaton method (CA method) which describes the solution of D'Alembert in the wave equation.

To reduce surging of a valve spring in a reciprocal engine, we design cam functions that simultaneously damp three eigen frequencies of the spring by modeling it into a series undamped 3DOF mass-spring system. The cam functions were defined from a finite-time-settling function termed vibration manipulation function (VMF), which consists of half-integer trigonal functions in an arbitrary operational period. The obtained analytical conditions of the valve spring decide the rising time of the cam. In simulations, we ascertained simultaneous suppression of the residual vibrations during translational motions of the 3DOF valve spring lifted with a designed two-dwell cam.

Brake squeal is a major vibration problem in disc brake. Among the brake squeals, in-plane squeal is a particular suppress problem, so the purpose of this study is to elucidate the mechanism of occurrence of in-plane squeal and to suppress it. In this report, we focused on the disc rotor. We experimentally investigate the difference in the effect on in-plane squeal when mass is added to the rotor and when cast iron powder is added. First, when the natural frequency of the rotor due to mass addition was investigated, it was found that the natural frequency decreased. After that, when a braking experiment was conducted, the in-plane squeal was suppressed. Next, the natural frequency and damping ratio of the rotor due to the addition of cast iron powder were investigated. As a result, it was found that the damping ratio increased even though the natural frequency did not change. After that, when a braking experiment was conducted, in-plane squeal did not occur. Therefore, when mass is added to the rotor, the effect of suppressing in-plane squeal can be obtained by lowering the natural frequency. On the other hand, it was found that when cast iron powder was added, the effect of suppressing in-plane squeal was obtained by the damping effect without changing the natural frequency.

In the automotive industry, the silence and ride comfort of the car body have been markedly improved by the development of the hybrid vehicles and fuel cell vehicles. However, the complicated fictional vibration is caused in brake system by the pursuit of a high brake performance. In this study, hot judder is modeled as self-excited vibration due to the time delay caused by heat deformation of the disc, and the fundamental generation mechanism of hot judder is analyzed by a simple three degree-of-freedom system. The pad is modeled as an elastic area with a distributed contact spring. A stability analysis for this system was conducted, consider the effect of pad length on hot judder occurrence. From the results, it was confirmed that the vibration of the braking system caused by the fluctuation of the contact force between the disc and the pad causes the fluctuation of the surface expansion of the disc, and causes a larger fluctuation of the contact force with a time delay. Also, It was found that an appropriate pad length for each number of hot spots can reduce the growth of hot judder that occurs at a specific number of hot spots.

Due to launch restrictions, lightweight structures are often used for space structures. In particular, satellites mounted inside fairings are subjected to severe axial loads during launch, which may lead to the destruction of electronic devices. The purpose of this study is to investigate natural vibration characteristics and parametric instability vibration under vertical excitation of upper-opening box structure. In the present report, we first experimentally clarified natural vibration characteristics by acoustic excitation. The test box used in this experiment was made by joining four sheets of OHP film together with cellophane tape. Three test boxes with aspect ratios (height/width) of λ = 0.5, 1.0, and 2.0 were tested with 1, 2, and 3 pieces of tape at the corners. The acoustic excitation was performed with two speakers exciteing in both in-phase and out-of-phase excitation, and the velocity response of the sides of the test box was measured using a scanning laser Doppler vibrometer to determine the vibration modes and natural frequency of the test box. As a result, the dimensionless natural frequency of the low order modes of upper-opening box structure are close to those of flat plate whose lower edge Clamped and upper edge Free, left and right edge condition Clamped and Clamped at λ = 0.5, Clamped and Simple support at λ = 1.0, and the Simple support and Simple support at λ = 2.0.

This paper theoretically investigates the localization phenomena in two pendulum vibration absorbers that are installed on a structure. It was previously reported that localization occurred in the two pendulum vibration absorbers. In order to clarify the mechanism of the appearance of localization, modal analysis is applied to examine localization from the viewpoint of vibrational modes. The equations of motion of the system are derived in the physical coordinates, and then they are transformed to the modal equations of motion. The frequency response curves for the primary harmonic vibrations are theoretically determined in both the physical and modal coordinates. It is shown that the modal equations form an autoparametric system because the first and third modes are directly excited by the external force, and the second mode is indirectly excited through the nonlinear coupling terms. Numerical results show that the two pendulum vibration absorbers can suppress the primary resonance peak, but two new peaks appear at the excitation frequency ranges lower and higher than the natural frequency of the structure. Localization occurs near the peak at the lower excitation frequency range where all modes appear simultaneously.

It is desired that the forced self-excited vibrations of structures subjected to the vortex excitation and the long-period earthquake are quenched. Therefore, this paper deals with the vibration control of self-excited system and forced self-excited system using dynamic vibration absorber. Vibration quenching is researched using characteristic roots of the system and the entrained periodic solutions obtained by the shooting method. As a result of numerical calculation using the fact that the optimum vibration control of the self-excited vibration system can be performed by the theory that omits the nonlinear term of the damping term and considers only the linear term, following was made clear: At first increase the mass ratio of the dynamic vibration absorber with the increase of the negative damping coefficient. And adopt the several percent larger natural angular frequency ratio than the optimum vibration control value of forced vibration, and adopt the several tens of percent larger damping ratio than the optimum value of forced vibration, depending on the value of the negative damping coefficient. About the vibration quenching of forced self-excited vibration, following was made clear: (1) When the non-linear damping term, which is the cause of self-excited vibration, is small and the amplitude of force is also small, optimal control is approximately performed using the optimal values of the parameters for vibration quenching of forced vibration without damping. (2) When the amplitude of the forced force is large, the vibration quenching effect is reduced if the above mentioned approximate optimal values are used. The vibration quenching effect can be improved by using the smaller angular frequency ratio.

Abstract Multiplexing dynamic vibration absorbers (DVAs) provide better vibration control compared to that obtained with single-mass DVAs; however, their structure is more complicated and thus difficult to apply in practice. This paper proposes several optimal design formulas for an electromechanical DVA in which a mechanical single-mass DVA with a piezoelectric element between the primary and absorber masses and a series LR circuit is coupled to the element. The inductor and piezoelectric element act as a virtual mass and a virtual spring, respectively, and thus the circuit works as a kind of double-mass DVA. In the present study, such an electromechanical DVA was optimized based on three design criteria (H_∞, H₂, and stability criteria) and its simple design formulas were derived.

An approximate solution of optimal parameters in the sense of H_∞ optimization for a viscoelastic dynamic vibration absorber (DVA) attached to a damped primary system is derived. The viscoelastic DVA is described by the fractional differential Voigt model, which consists of a spring element and a non-integer-order derivative element in parallel. In the previous study, we derived an approximate solution of H_∞-optimal parameters of the viscoelastic DVA for the displacement response of the primary system. The approximate solution was obtained by combining 1) a method in which the viscoelastic DVA is replaced by an equivalent viscous DVA approximately with 2) the fixed-points theory. In this paper, as the second report, we perform the H_∞ optimization for the velocity and acceleration responses of the primary system, and derive an approximate optimal solution for design parameters of the viscoelastic DVA. The validity of the approximate solution is demonstrated by comparing the amplitude magnification when the approximate solution is used with that optimized numerically. Then, by analysis using the approximate solution, it is shown that the damping performance of the optimally designed viscoelastic DVA is slightly better than that of the optimized viscous one.

So far, there have been reports of experimental analysis of vehicle dynamic models and running resistance for wheelchairs, but theoretical analysis focusing on the tires themselves has not been made. Also, comparing wheelchair tires with automobile tires , the structure and shape are different, and the conditions such as operating speed are also different.

Therefore, in this study, I considered the model of tire deformation and the tire contact characteristics for wheelchair tires, and applied the theory of existing automobile engineering to predict the rolling resistance of wheelchair tires going straight on flat ground. I measured rolling resistance by experimental device and compared with the theoretical value.

Some of the fluid particles in Rayleigh-Benard convection with perturbed velocity field may be transported chaotically in the Lagrangian description, even when the velocity field seems to be stable in the Eulerian description. In this study, we measure the two-dimensional velocity field of the perturbed Rayleigh-Benard convection by Particle Image Velocimetry (PIV) and detect the invariant manifolds called the Lagrangian coherent structures (LCSs) in order to clarify the chaotic structures of the convection. Especially, we show that LCSs entangle with each other as homoclinic tangles and create some lobes, where fluid particles in the lobes are transported in accordance with the lobe dynamics. In addition, we show that a figure-eight structure appears in the middle of each cell, and that two types of cells with qualitatively different structures appear alternately in the layer when the integration time of the LCSs is increased. Further, we propose a novel perturbed Hamiltonian model that represents some of the experimental results qualitatively.

In this study, analysis is conducted on behavior of an electromagnetic reciprocating vibratory swing compressor. The governing equations of the swing compressor are derived in terms of motions of piston with coil and motor assembly and current induced in the electric circuit. Electromagnetic coupling is also considered between the vibrations of a spring-piston system and the electric circuit which consists of a coil and a resistance. First, the analytical model is introduced with the vibration system with two degrees of freedom. The expansion and compression processes of refrigerant are assumed as polytropic processes. The polytropic indices are estimated by experiments. The parameters such as damping and hysteresis loss of iron core are obtained and identified by preliminary experiments. Next, the numerical results are compared with the experimental results to verify the analysis presented in this study. Good agreements are found between numerical and experimental results which verify our analysis.

Nonlinear characteristics of two DOF Duffing oscillator are investigated. In our previous study, mass and stiffness proportional dampings were used separately, and the nonlinear characteristics appeared only near the first and second resonance frequency, respectively. To investigate nonlinear properties of both natural frequencies, the case that mass and stiffness proportional dampings exist simultaneously is considered. Two combinations of stiffnesses that have same natural frequencies are used. The frequency response curves calculated by harmonic balance method show that the nonlinear characteristics moves from the first resonance frequency to the second one as the mass proportional damping increases. The frequency response curves of the elongations of springs are also considered. For the system that has the same stiffness characteristics for both springs, the larger deformed spring is changed by the order of the natural frequency.However, for the system that has the different stiffness characteristics, the larger deformed spring is unchanged.

Noise and vibration performance is common requirement for engineering structure. Furthermore, such engineering structures need to employ the bio-based materials for reusability. This paper proposes elastic metamaterial made of pulp-steel composite structure whose periodic shapes prohibit the wave propagation in the frequency ranges referred as to band gap. As the molded pulp can manufacture the periodic shapes with low cost and low environmental burden, it has the potential to apply the elastic metamaterial for the mass-production. Wave propagation within the elastic metamaterial is modelled by wave finite method which provides dispersion curves of the elastic metamaterial. The calculated dispersion curves suggest that the elastic metamaterial made of pulp-steel composite structure can form the band gap related to the flexural waves. To demonstrate the vibration suppression in the band gap frequency, the frequency response of elastic metamaterial is measured using the those consisting of the four-unit cells, resulting that the frequency response is significantly reduced in the band gap frequency.

Recent advances in 3d printer technology have made it possible to perform 3d printing using CFRTP (Carbon Fiber Reinforced Thermo Plastics). 3D printed CFRTP plate made by Mark Two (Markforged). The 3D printed CFRTP plate is made of by nylon resin including continuous carbon fiber. Our object is to reproduce vibration mode of the 3D printed CFRTP by the FE model in this research. The FE model has local coordinate systems along the fiber direction in the plate. The X direction of a local coordinate system fit to the direction of carbon fiber. The effect of the selection width of the diagonal elements on the vibration characteristics is investigated. When the selection range was large, the natural frequency was calculated to be high. But the vibration modes were not change. Comparing the experimental results with the analytical results, the best agreement was obtained when there was no coordinate conversion.

This research deals with a new analytical procedure on bending vibrations of a thin plate. The plate is divided into finite number of non-orthogonal segments. The mode shape function is introduced with the product of higher power series or power series and trigonometric function. The unknown coefficients of the mode shape function are substituted by the deflection and its higher derivatives at each node of segments, which enables to satisfy both continuity and boundary conditions at the node of segment. The collocation method is used to satisfy the continuity of the derivatives of the deflection at the side of segments. Discretized equations of motion of the plate are derived with Galerkin method. Natural frequencies and modes of vibration are calculated with and without collocation method. By using the collocation method, continuity of space derivative of deflection between two adjacent segments are satisfied, which enables to obtain good agreement between the present results of natural frequencies and the exact ones.

Laminated composite plates are known as tailoring materials, since structural characteristics can be designed by properly placing fiber orientation angles in the layers. The objective of this work is to study three types of optimization problems on in-plane vibration of symmetrically laminated angle-ply rectangular plates. It considers the maximization of the in-plane lowest first frequencies, secondly minimization of the first frequency, and thirdly maximization of the difference between the first and second frequencies. In numerical experiments, some interesting observations are found, and discussions are made to make effective use of the findings for vibration design.

This study discusses identification of material constants of Single-Layer CFRP thin plate using vibration analysis with general purpose FEM code and differential evolution method. This identification method is a method to select material parameters to match the vibration characteristics of the experiment and the vibration characteristics of the analysis. In the method, a general-purpose FEM code calculates vibration modes and natural frequencies of thin CFRP plate using material parameters which are selected by differential evolution method (DE). Some simulation data are used to probe the validity of the identification method. As a result of validation, this method is found to be no different from the conventional method and was found to be valid. Using the simulated data, this method can identify three elastic coefficients of CFRP plate without error.

The aim of this study is to design an optimum CFRP lattice structure for application to a morphing wing. The ground structure based topology method is adopted as the optimization method, and the results are validated by experiments. In this study, to confirm the effectiveness of the optimization method, a simple hook shape was optimized and its stiffness and strength was compared by tensile tests. A 3D printer capable of laminating thermoplastic CFRP was used to fabricate the specimen. The results of tensile tests showed that the optimized specimens exhibited higher stiffness and strength than the reference model, confirming the effectiveness of the proposed method.

In this study, we apply the sequential approximate multi-objective optimization (SAMOO) to an open-hole laminated plate with partially different lay-up configurations for assuming fabrication by the AFP equipment. The SAMOO is a method to search for the optimal design with a small number of evaluations of the objective function while adding appropriate sample points to the response surface. When the optimization problem deals with many objective functions, it becomes difficult to visualize the design candidates and to understand the relationship between the objective functions. Thus, the self-organizing map (SOM) which displays multi-dimensional data in two dimensions is employed for visualization and clustering of obtained non-dominated solutions. Numerical results showed that the trade-off relationships among the three objectives were clarified and design alternatives could be explored according to the design tastes, and it was confirmed that the SOM was effective for the present optimization problem.

In this study, we focus on the bouncing ball system with a periodically oscillating boundary. In the system, it is known that chaotic behavior arises. The bouncing ball system have application in various engineering systems. We have studied the system and found that the maximum value of ball height is changed stepwisely varying increase of the periodically oscillating boundary’s frequency. The purpose of this study is to clarify the mechanism arising the stepwise bifurcation. In this paper, we measure the displacements of the ball before and after the bifurcation point, and investigate the change of dynamics by Poincaré maps. Moreover, it's clear that the number of cycles of the boundary during a single bouncing is close to an integer value just before the height of the ball is maximized when stepwise bifurcation is occurred.

This research deals with a vibration suppression problem occurring in a viscoelastic damper system modeled with a fractional-order differential equation using a fractional-order linear quadratic regulator (LQR) as a typical modern control. In the previous report, the fractional-order LQR was configured with a state feedback style. However, ordinary sensors cannot measure a fractional-order state in practice, because a fractional-order state is composed of displacement, velocity and acceleration. Therefore, a state observer is required to estimate all of the states including fractional-order states. This report aims at realizing the fractional-order LQR with an output feedback style by constructing a state observer in order to estimate fractional-order states.

Overhead cranes are widely used and play a significant role for mass transportation in factories. One of the main problems in operating an overhead crane is the residual vibration which often decreases efficiency and safety of the operation. In order to deal with this problem, the authors proposed a new type of open-loop control method for suppressing the residual vibration by eliminating natural frequency component. This method is based on the fact that residual vibration is completely suppressed in a linear undamped system excited by an external force that does not contain the natural frequency component 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. This paper proposes a new method that can reduce computational cost compared with conventional methods, examining its effectiveness numerically and experimentally.

This paper presents time-suboptimal vibration-free reference trajectories for position control of 1-DOF undamped linear oscillatory systems. By applying the frequency-domain shaping technique to the design of reference acceleration trajectory for a positioning system with an elastically coupled mass, the vibration-free reference trajectory is analytically obtaioned based on its mathematical model. In the frequency-domain shaping, the authors partly solve time-optimal problems with given maximum values of the acceleration and the velocity. As a result, the deterioration of the resulting trajectory in travelling time is minimized and the difference from the so-called time-optimal trajectory is kept small. The traveling time is also comparable to, i.e., sometimes shorter and sometimes longer than, that of UM-ZV (unity-magnitude zero-vibration) shaper. Implementation issues which arise when discrete-time controllers are used to generate the reference trajectory are also investigated. The proposed vibration-free reference trajectories are used in a real linear positioning system and the performance is verified in experiments as well as numerical simulations.

In this paper, we specifically examine a point-to-point (PTP) motion task of a flexible manipulator with macro fiber composite (MFC) and present a feedforward control technique for suppressing the residual vibration. We use a MFC attached to one side of the flexible manipulator that has one revolute joint as an actuator. In the control technique, we attempt to express the joint angle by the combination of cycloidal and polynomial functions. On the other hand, the input voltage profile of the MFC is expressed by Gaussian functions. The trajectory of the joint angle and the input voltage profile are dependent upon the coefficients of the polynomial function and the Gaussian functions, respectively. To cancel the residual vibrations, the trajectory and the input voltage profile are optimized simultaneously by tuning the coefficients using the particle swarm optimization (PSO) algorithm. We perform experiments to verify the validity of the vibration control method based on an off-line simulation. Results obtained from simulations and experiments demonstrate the effectiveness of the proposed method for suppressing the vibration.

A rational dimension reduction method based on a new type of complex modal analysis is developed in order to accurately analyze nonlinear vibrations generated in large-scale structures with local strong nonlinearity, non-proportional damping and asymmetric matrix at low computational cost. In the proposed method, first, the linear state variables are transformed into modal coordinates using complex constrained modes obtained by fixing nonlinear state variables. Next, a reduced model is derived by selecting a small number of modal coordinates that have a significant effect on the computational accuracy of the solution, and coupling them with the state variables of nonlinear state variables expressed in physical coordinates. In that process, the remaining modal coordinates that have little effect on the computational accuracy are appropriately approximated and integrated into the equations of motion for nonlinear state variables as correction terms. Furthermore, by using a method of estimating the effect of higher order modes from lower order modes, the computation of higher order eigenpairs becomes unnecessary. In this report, a method for determining the number of low-order modes is proposed to improve the practicality of the method, and its effectiveness is confirmed for thin plate structures.

In order to estimate the vibration damping characteristics of the elevator rope, a basic experiment using a silicon rope was conducted. There are three causes for rope vibration damping. The first is viscous damping, which is proportional to the vibration velocity to the 1.5th power. The second is vortex damping, which is proportional to the square of velocity, and the third is structural damping. The loss coefficient was obtained by changing the vibration excitation amplitude and measuring each displacement transfer function. When the vibration amplitude is large, the velocity square damping becomes dominant. We also proposed the CA method as a vibration analysis method for strings with varying lengths.

The analysis result by the CA method showed a value close to the approximate analysis solution.

Cavitation is a formation of bubbles in liquid with high-speed, where a phase transition from liquid phase to gas phase occurs when the pressure of the liquid is reduced to the saturated vapor pressure. The Rayleigh-Plesset equation is well known mathematical model of a spherical single cavitation bubble. However, there have not been proposed an appropriate mathematical model of such a single bubble including the shock wave phenomenon associated with the collapse of the bubble. In this study, we propose a coupled model of the Rayleigh-Plesset equation and the wave equation associated with pressure. In this model, these equations are combined by a bubble surface boundary condition, which is defined by solutions of the Rayleigh-Plesset equation. Further, by using our coupled model, we make a numerical test of the rebounding behavior of the single bubble in an ultrasonic field and the shock wave emission. As a results, we show that the shock wave phenomenon associated with the collapse of the bubble, namely, an intensive pressure on the bubble surface and the shock wave propagation are reproduced.

The natural angular frequencies and natural vibration modes of the three-dimensional orthotropic rectangular parallelepiped are investigated. A lot of studies have been done on the orthotropic laminated composite materials, but few studies have been done on the materials that are not made of layers. Previously, we studied the case that all the mode orders at each axial direction were same. In this report, the case of the different mode orders each other is studied. Same as our previous reports, in the relationships between dimensions and natural angular frequencies, there are ranges where the natural angular frequencies vary linearly, they are almost constant and the intermediate range between them. In the relationships between the length and the natural angular frequencies, the entire curves move in the increasing direction of the length by a factor of the modal order in the length direction when only it is changed. When both the mode orders in the thickness and width directions are changed in the same manner, the curves move in the decreasing direction of length by the reciprocal of the mode orders. The eigenvectors are unchanged in the range of the natural angular frequencies varying linearly and the range of them being almost constant.

When particles placed in an acoustic tube are resonated using a speaker, the particles start to move and rise against gravity, forming a fold-like pattern. Since the interval and height of patterns change depending on experimental conditions such as the magnitude of sound pressure and resonance frequency, it is sometimes used in sound visualization demonstration experiments. However, although it has been studied since the discovery of this phenomenon, the mechanism of its occurrence has not been fully elucidated. This paper considers the acoustic radiation force acting on the sphere and the force acting on the particles in the acoustic tube proposed by L.V.King. In particular, using the actual specifications, after calculating the acoustic radiation force, the inclination of the thread that suspended the particles was calculated and compared with the experimental value. Furthermore, consider an experiment in which the tube was narrowed by clay in the middle of the acoustic tube. Finally, the acoustic radiation force was calculated based on King's theory, with the pattern in the middle as an obstacle.

This paper shows a fundamental study to apply the principle of metamaterial to solid waves. A method of making the stiffness apparently negative and an effect of the apparently negative stiffness for a lumped parameter system in which the governing equation is isomorphic to the central difference approximation formula of the wave equation are investigated from the viewpoint of vibration isolation. The results are as follows: 1) It was shown that the stiffness of the mass/spring system can be made apparently negative by using a rotational inertia damper. 2) By inserting a system with apparently negative stiffness between the excitation source and the target, the system acts as a high-cut filter and reduces the input from the excitation source to the target. 3) It was shown that the cutoff frequency and cut level of the high-cut filter can be controlled independently by the rotational inertia of the rotational inertia damper and the degrees of freedom of the system whose stiffness is apparently negative.

In order to deflect the radiated sound waves by an array of sound sources, temporal phase differences between the adjacent sound sources are necessary. Usually, the sound can be deflected by electronically providing the phase-shifted driving signal to sound sources comprising the array. In this study, we propose a new method for deflecting sound emitted from a linear array of sound sources whose driving frequency, amplitude, and phase characteristics are all consistent. Instead of directly changing the phase of the driving signal, the dynamic characteristics of the vibration systems installed in front of the emitter are adjusted to cause a physically phase-shifted response. Such an indirect phase difference caused by the vibrator array achieves the deflection of the interfered sound waves. Firstly, numerical calculations are performed by assuming different natural frequencies to the vibrators composing an array so that the radiated sound could be deflected at angles of θ = 20°, 30°, 40°, 50°, and 60°. It was found that the desired deflection angle could be obtained under all conditions. Secondly, experiments were conducted to verify the numerical predictions. Thin resin plates with different elastic moduli were manufactured that mimicked vibrators. We confirmed that the sound wave could be deflected for all deflection angles at the sound source frequency of 4 kHz.

In this paper, we propose a virtual sensing technology combined with model order reduction. The virtual sensing is a simulation technology that integrates a numerical model and sensor data with a Kalman filter. In addition, the virtual sensing enables to perform various analysis using the estimated states. However, since the virtual sensing is computed in the time domain, the use of finite element models with large degrees of freedom increases the computational cost. This issue can be solved by the model order reduction which is a technique to reduce the computational cost by reducing the degree of freedom of the finite element model while maintaining the analytical accuracy. The proposed methodology is validated experimentally by which the states are estimated by the virtual sensing using the finite element model reduced by the model order reduction and the actual vibration measured by a small number of sensors when a motor is driven. The virtual sensing estimates 3-axis acceleration accurately. Then, the Mises stress map in the piping is calculated by using estimated vibrational displacement.

Owing to aging of distribution main, the accident such as leakage and explosion are occurring. To prevent above accidents, it is essential to maintain and manage the system through appropriate renewal and repair. For efficient maintenance and management, it is important to quantify the condition of main by Non-Destructive Inspection (NDI) and reflect it in renewal and repair plans. One of method to maintain the main efficiently, deterioration diagnosis method for distribution main using the eigen frequency of in-plane bending mode in circular cylindrical shell is already suggested. The eigen frequency of in-plane bending mode is expected to have high accuracy in detection of deterioration, because the eigen frequency is proportional to pipe thickness. However, actually main is subjected to ground soil elastic force because of buried situation. In this paper, the in-plane bending oscillation in cylindrical shell which is subjected soil stiffness is systematically considered.

In this study, we propose a matching method for a variety of the magnetostrictive vibration power generation device that are suitable for respective ambient vibrations by using the Self-organizing map (SOM). SOM is a kind of clustering methods that can classify the given data without any external criteria. The ambient vibration data are converted into the input signal for SOM by way of filtering and linear prediction processes. The data are then used to train SOM by which the data are grouped according to their similarity. Subsequently, the vibration responses of the generators were put through the trained SOM in order to determine into which cluster the data were grouped. The results showed the possibility of clustering ambient vibration data and matching the power generators to the appropriate vibration sources by using SOM. However, the classification accuracy was not enough due to the bias of the dominant frequency components in both the ambient vibration data and the generators. The natural frequency and its harmonic components were significant in the latter case. It is necessary to introduce the additional data with dominant frequencies that are not covered by the environmental data employed in this study, and to create variations of generator which do not overlap in response frequencies.

Behavior of equipments with a gap exsisting in an industrial plant has not been clear for high-frequency excitations. In this paper, the authors investigated the effect of the gap by conducting vibration tests with a simple test piece, in which two cases of high-frequency random waves were used. The first case of wave is a narrow band randam wave with only high frequency components, and the second case of wave is a wide band random wave with low frequency to high frequency components. While the gap was increased in the test, the test piece slipped and did not respond to the excitation of the first case, whereas a strain decreased and an acceleration increased for the second case. The displacement of the first wave was so small that the test piece moved inside two gaps without impacts. On the other hand, the contact occurred against the second wave. Therefore, the acceleration, which is more sensitive to high frequency compared to the strain, increased due to higher frequency components caused by impacts. As the results, we clarified the behavior with a gap for the two typical cases of high-frequency waves.

This paper describes the results of a series of seismic analyses conducted to clarify how plastic deformation of a pipe and its support structures affect the seismic response of the entire piping system. The first analyses include; plasticity is considered for (1)none, (2)the piping only, (3)the support structure only and (4)both the piping and the support structure. The second analyses are parametric survey of yield load and post yield stiffness of the restoring force characteristics of support structures.

The results of the first part analyses have revealed important implications on the seismic design of piping systems by elastic-plastic response analysis. First, the piping response, i.e., elbow strain typically, is significantly reduced when plasticity is taken into account in the piping support. On the contrary, it seems that the piping support response is not so much affected by the consideration of piping plasticity.

As the results of the second analyses, the yield load of the support structure has a large effect on the response of the piping system, while the post yield stiffness does not have much effect compared to the yield load.

In order to investigate the effect on the seismic response of the piping system when considering the elasto-plastic behavior of the piping support structure or the main body of the piping system, an elasto-plastic time history response analyses were conducted on a piping system model having multiple support structures. From the analysis results, it is confirmed that the response acceleration can be reduced by introducing the support stiffness, because it decreased the natural frequency of the piping system and it resulted in increasing the frequency ratio. The response of piping system can be further suppressed by introducing the inelastic behavior of support structures. However, the analytical results shows that the response displacement of the piping system tends to increase when the yield load of the support structure is fairly small. Therefore, when elasto-plastic deformation of the support structure is allowed, it is necessary to assess the effect on the overall response of the piping system and to give an appropriate elasto-plastic characteristics to the support structure.

In this study, inelastic energy absorption factors are investigated for the equipment installed in the nuclear building. The elastic-plastic response spectra were evaluated using synthesized base layer wave of the Japan Building Center of Japan, BCJ-L1 and BCJ-L2, and actual observed seismic ground motions, and the inelastic energy absorption factors were calculated and compared. As a result, it was found that the inelastic energy absorption factors tended to be underestimated for equipment with a period longer than the building's natural period and overestimated for equipment with a shorter period. It was also found that the factors varied greatly depending on the type of seismic ground motion used in the calculation, although the overall trend did not change much when the installation position or the second stiffness of bi-linear restoring force of the equipment were changed. Therefore, that there are some issues in the calculation of inelastic energy absorption factors based on the energy conservation because it varies depending on the seismic ground motion.

In this study, we present the issues and proposals to use the elastic-plastic response spectrum method for seismic design of piping systems. First, we showed the idea of converting a piping system model with elastic-plastic vibration into a single-degree-of-freedom (SDOF) system model by applying the modal method in the elastic-plastic region. Next, the equivalence of elastic-plastic vibration response between the piping system model and the SDOF system model was examined. In previous studies, the equivalence of the vibration response has not been sufficiently discussed. Hence, the elastic-plastic seismic response analysis was performed using the piping system model and the SDOF system model, and the similarities and differences in the vibration response were investigated. For the piping system model, the basic response characteristics were examined using a straight pipe that does not have the effects of flexibility characteristics and stress indices. It was shown that the maximum responses for both models were almost the same in the small input, but the response of the SDOF system model was further larger than that of the piping system model in the large input with large plasticity. This result suggests that the scope of application should be limited when the elastic-plastic response spectrum method is used for piping systems. In addition, we found that the square root of the sum of squares (SRSS) method popularly used to calculate the maximum response in the response spectrum method is also effective in the elastic-plastic region. Finally, based on the above results, we proposed the modeling and calculation methods when using the elastic-plastic response spectrum method for the piping system.

Regarding seismic design of plastic region of ductile equipment, the application of a simple static seismic design method is studied, based on the concept of required yield strength spectrum using Japanese recorded earthquake motion waveforms. As a result, especially in the high frequency region, and in the case to allow the target ductility factor to be about 3 to 5 or more, the equivalent static seismic design method by setting the ZPA considering the high-cut filter used for JMA measurement seismic intensity calculation as the design seismic coefficient is possibly effective.

Mechanical snubbers and inertia mass dampers are known as vibration control devices that have inertia mass elements and generate the inertial resistance force. By adding the devices with the inertia mass elements to piping systems, we aim to reduce various responses of piping systems subject to seismic disturbances. In this study, we propose a design method to optimize design parameters of inertia mass dampers installed on 3-dimensional piping systems that consist of some tangent and curved pipe elements (beam finite element model) to achieve good dynamic responses while maintaining the structural integrity of the piping systems and the inertia mass dampers. A performance index considering various specifications related to mitigation of responses of the piping system for earthquake disturbances and the economic cost for installation of the devices with some inequality constraints is defined. Design parameters to optimize the performance index are the number and the model size (capacity) of the inertia mass dampers, the value of its inertia mass, and its placement (node and attitude) on the piping system of the inertia mass dampers. The performance index is optimized with a genetic algorithm. The problem formulation of a simulation example is described to confirm the feasibility of the optimum design.

Suppressing earthquake damage to tall structures such as distillation columns in chemical plants, Tuned Mass Damper (TMD) is added to control the vibration of the structures. In order to design parameters of TMD efficiently, this paper propose a risk-based design method to determine parameters and installation position of TMD. Specifically, based on the probability of earthquake occurrence by the seismic hazard curve at the location of the structure, the seismic response analysis and fragility curve indicating the probability of damage to the target structure are calculated. From these results, the mean annual frequency of exceeding a certain damage state of the target structure for each parameter of TMD is calculated. comparing the damping performance and the cost of the equipment, risk-based design method is helpful when considering the adaptation of the equipment.

The seismic design is important for the SFR(:Sodium-cooled Fast Reactor). Not only the decrease of the horizontal seismic load but also the decrease of the vertical seismic load is necessary in the severe seismic condition. Accordingly, the three-dimensional seismic isolation system is developed for the SFR. This system was designed with a horizontal natural frequency of 0.294 Hz and a vertical natural frequency of 3 Hz. This system consists of thick rubber bearings, coned disc springs, and oil dampers. The static test in these elements of this system was carried out. The investigation of seismic PRA in the SFR with this system is necessary. In this study, the analytic examination on the vertical response behavior during severe earthquake is carried out. In this report, the analysis model with the mechanical characteristic, which is provided in the element test, is investigated. The time history response analysis with this model is carried out during severe earthquake. The response of components is approximately linear in the input seismic load. The extreme response increase of components hardly is confirmed. As a result, the reliability of this system is confirmed.

In nuclear power plants, seismic reinforcement has been done after the Fukushima accident. For dynamic equipment, such as pump and valve, it is difficult to increase the seismic capacity, so the reduction of seismic force is important issue. Since installation of seismic isolation system to entire building is not rational for existing structures, seismic isolation floor would be a one of promising strategy. In this study, the effect of introducing seismic isolation floor is investigated both deterministically and probabilistically. Then the effect of reducing the seismic risk of the parallel system with diversity is also examined. In the deterministic analysis, the response acceleration cannot be reduced unless the eigen period of equipment is longer than 0.8[s], however the displacement is increased in the longer period range, that is the risk of damage due to the displacement increases. According to the probability evaluation, we found that the seismic risk was reduced even at about 0.4[s], and the risk of damage due to displacement is in the acceptable range even at a longer period. With the system with seismic diversity, the damage risk can be reduced by both acceleration and displacement by adding seismic diversity.

The purpose of this study is to identify natural frequencies and modes of a base-isolated building by modal analysis using finite element method. In general, multi-degree-of-freedom models are often used to analyze vibration properties of multi-story buildings; however, this modeling is hard to represent spatial behaviors of the buildings such as torsional vibration, and must be considered carefully in case to apply it to base-isolated buildings. In this study, we modelized a base-isolated RC building located in Meiji University as a frame structure combined with floor slabs and aseismic rubbers on the foundation, and computed the natural frequencies and modes of horizontal and torsional vibrations. The primary and secondary natural frequencies of the numerical models agreed approximately with those given by measurements of ambient vibration and seismic waves. In addition, the natural modes demonstrated that the aseismic rubbers restrained large deformation of the buildings and worked effectively for seismic isolation.