This paper is concerned with a vibration control method for a nonlinear multi-degree of freedom system using an active mass damper(AMD). The sliding mode control theory has robustness for uncertain and nonlinear systems. In this paper, a five degree of freedom structure model with nonlinear stiffness which subjected to fundamental excitation is considered. The equation of motion for the structre is presented in modal coordinate. A mode synthesis method is apllied to the structure and an AMD. A fuzzy sliding mode controller is applied to control vibrations of the system with the AMD which is mounted on the top of the structure. In numerical example, the relative displacements and the velocities of masses can be reduced by the controller. The effectiveness of the proposed procedure with the AMD is demonstrated for suppression of vibrations of the system.

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Recently, the demand for motion simulators used as testing devices has been increasing. For example, driving simulators is important for the observation and grasp of human's operation characteristic under various run conditions, development of vehicles design, and operation support system. When motion simulators are used as testing devices, the motion simulators cannot obtain the reliable experimental data without the running reproduction performance of real motion. Although, hydraulic servo system is often used for the simulators, the hydraulic system has the fault that acceleration distortion arises by friction between cylinder and piston under conventional displacement proportional control. In this study, control technique that improves acceleration tracking performance is proposed, based on dual model matching, for Parallel Link Type Motion Simulator with the hydraulic servo system. Then the effectiveness of the technique is verified through experiments.

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This paper deals with a human body response in sitting on a wheelchair on a shaking table. Moreover, the human body model made by the computer simulation was created on the basis of a sinusoidal wave vibration experiment data and level difference experiment data. The wheelchair-human body model was created using DADS which is rigid body analysis software. In consideration of characteristics at joints of the human body, the passive and active moments were generated by constructing control systems. As a result, the simulation model reproducing a human body response was created.

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In this paper, the extended reduced order physical model, which is developed to represent dynamics of flexible structures in multibody systems, is implemented to general multibody formulations. The elastic deformations are described using vibration modes associated with the rigid bodies that are effectively defined using dynamic properties of the system in this reduced order modeling method. The augmented formulation are used to develop the constraint equations associated with the connections between the reference body and the several rigid bodies in the modal representations used to modal elastic deformations. For this purpose, the modal constraint is developed for the recursive formulations, while these constraint equations are transformed into the form that is suitable for the augmented formulation using the singular value decomposition or QR decomposition. The use of the formulations in this paper allows for the implementation of the extended reduced order physical model into the commercial multibody codes such as ADAMS and DADS.

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Prediction of dynamic performance will become very important in vehicle design to shorten development period, because counter-measures for component performance can be reflected into design drawings, and then validation period for a prototype can be shorten as much as possible for development of distribution vehicle like forklift truck. In this paper, we introduce a design methodology to apply multi-body dynamics, being coupled with mathematical power-line model, to engine-type forklift, and examine prediction accuracy for typical application, that is, traveling, lifting, tilting and combined working pattern. As a result, important design information for mobility, stability, working cycle time, can be simulated by this methodology, and the possibility for more effective development is confirmed.

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A simulation model of a hybrid excavator has been developed for the estimation of the fuel consumption and the optimum design of the hybrid system dynamics in the practical operation of the hybrid excavator. The hybrid excavator consists of a hybrid power train system with power electronics devices such as converter, an actuator system driven by electro-hydraulic system, and linkage system of a front attachment with the boom, the arm, and bucket. The simulation model enables us to analyze these systems totally. In this paper, the power electronics system is modeled to second order differential equations of motion, and the total system equations are established with considering the coupling with the power electronic system, the hydraulic system, and linkage system. The boom system is picked up for the operability design for the residual vibration, and the energy saving effect is estimated for the boom system.

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Recently, in the viewpoint of environment problems, the improvement of the efficiency of the construction machinery such as excavator or crane is demanded. For this purpose, it is investigated that the hybrid system used in the automobile is adapted into the construction machinery. In the previous study, the control method, which derives the operating property close to the present hydraulic system, is proposed. In this study, the simulation model of the swing system of the hybrid construction machinery is proposed and the efficiency of the hybrid system is compared with the hydraulic system by simulation. Consequently, the fuel consumption of the engine in the one cycle of the swing operation of the hybrid system is proved to be 30〜37% of the hydraulic system. This is caused by the effect that the hybrid system can be operated by the more compact engine than hydraulic system and kinematic energy can be recovered by the regeneration of the motor.

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Dynamics of a moving body restrained on a 3-D trajectory considering resistance to forward motion is investigated. The equation of motion of the moving body is derived by using differential algebraic equation (DAE). By using this equation, the time history simulation analysis is performed. Also, the vibrational experiment have been performed using the actual roller coaster in site. The accelerations in simulation are compared to those in experiment. Both show a good coincidence qualitatively.

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In this report, we analyze the twist motion in salto backward motion performed by a horizontal bar exercise robot. Although there are many robots capable of acrobatic motion in the air, conventionally at least two active joints are used to generate the twist motion. However, in our previous experiment, we have reported that twist motion is caused by action of only one joint. Thus, we construct a 3D model with consideration of asymmetry mass distribution and demonstrate the twist motion by simulation. We also analyze twist angular velocity in view point of controllability of 3D posture by one actuator.

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This paper describes a new control method that realizes a giant swing motion of a 3-DOF link horizontal bar mechanism. Trajectory of free giant swing motion represented with respect to the wrist joint-angle is utilized as a reference-trajectory in the configuration based control that was proposed in our previous study. Tracking performance is investigated minutely in cases of the continuous- and discrete-time configuration based controls. Additionally,we introduce a set of wrist joint angle-variant feedback gains to decrease the tracking error in case of the discrete-time configuration based control using a digital controller. The validity of proposed control method was shown by computer simulations.

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This paper deals with suitable configurations of a robot manipulator that pulls weeds out by the roots. The weeding robot manipulator, which works outside, should take away weeds in an energy-conserving way. Moreover, the weeding robot manipulator is required to generate a large force to pluck out weeds, because some weeds have roots spreading deeply and tightly. In this paper, the suitable configurations for a weeding robot manipulator are defined as configurations in which these requirements are fulfilled. In order to find such a configuration mathematically, we formulized this problem as a constrained optimization problem and then solved the problem using Sequential Quadratic Programming.

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Electroaerodynamic investigation has been carried out in a pin-to-plate gas discharge system to clarify the mechanism of repulsive force generation between the pin and the plate electrode at corona discharge. Numerical calculation has been conducted by two steps. At the first place, corona discharge field was calculated to deduce volumetric force and then in-duced ionic wind was calculated. Calculated pressure distribution on the plate electrode was in the order of 10 Pa that was in good agreement with the measured. Calculated velocity at the center was several m/s that is confirmed by a time-of-flight experiment and the velocity distribution near the pin electrode also agreed with the measured with a laser Doppler velocimeter. These results confirm that the ionic wind is the cause of the repulsive force at the corona discharge.

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Insects are the most prosperous creatures on the earth. They have many abilities, such as the ability fly, which are interesting to many researchers because their mechanisms may have future engineering applications in, for example, micro-robots. In this study, the behavior of wing flapping of bees was investigated by measuring the displacement of the bees' back. The force generated during flapping was measured using a simple force sensor and the correlation between the force and the acceleration of the wing was discussed. The dynamic characteristics of bee's wings ware investigated under forced vibration.

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We produced flywheel energy storage system, using a CFRP flywheel and a newly designed motor/generator. The flywheel consists of high-modulus graphite/epoxy filament wound composites, which are designed for better stress distribution. This allows the flywheel to rotate at higher speed. The motor/generator mounted inside the flywheel provides high efficiency energy transfer into and out of the system because it has no core in the coil. The regenerative efficiency was evaluated under an atmospheric and vacuum condition. In the evacuated shroud the efficiency was over 85%. High speed FW system must be attended evacuated shroud with the adaptable equipment for reduced aero resistance. We propose the new theory to floating shrouds that we had being the study, several years ago, recently we had the experimental evaluations to effect for reduced aero resistance only by floating shrouds. This paper describes the problems of evacuated shroud and the effect of floating shrouds.

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This paper presents the way to improve the effect of dynamics education for mechanics majors by using their mental models. Mental model is the images reminded in the first stage in learning first matter. Students have experienced many phenomena related to dynamics in their everyday life. Under the suitable guidance based on their mental models, they could obtain a right and essential understanding of dynamics. In order to improve their mental models, we used bodily sensation type teaching materials and visualization of phenomena.

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In case of destruction test on shaking table, the energy, dissipated in the process of collapse, is employed as one of indexes to grasp the test structure strength. In general, for the vibration systems, internal dissipated energies are equal to externally supplied energies. Considering the shaking table and test structure as one vibration system, the input energy generated by actuators of shaking table can be used to estimate the dissipated energy during collapse of the test structure. This paper describes the computation method of energy and numerical simulation results.

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This study has been examined about a 3-dimensional measurement method that can measure a position and an attitude of test object without any contact. Fundamental hardware and software in measurement system has been constructed until now. Moreover, the fundamental dynamic measurement accuracy and effectiveness of the proposed measurement system has been confirmed from the several shake table tests in elastic region. This paper describes the effectiveness of the proposed system by the destructive experiment which used the full scale wood houses and method of evaluating camera coordinates data .

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This study has been examined the 3-dimensional measurement method for dynamic displacement of real scale test model on shake table tests. This system can measure 3-dimensional dynamic behavior of test model without any contact by applying an optical motion capture technique and image processing technique. The system therefore is the most suitable measurement system for an evaluation of complex 3-dimensional behavior of test model. This paper describes the dynamic measurement accuracy, the effectiveness of the proposed system from the results of shake table tests using the collapse building model and the inverted pendulum model.

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The synthesis process is most important for such new creative development. It is effective to combine the graphical / sensitive design process, the function designs process and also the structure design process, using the Parallel Approach with "Visual Thinking" and "Thinking CAE". The usual prediction technology by forward CAE is poor at a creative process. Visual Thinking creates the imagination to new structure design. Thinking CAE pulls the added value out of new developed structure. The digital engineering method to digitalize directly the visual information of new image, as virtual reality, enhances this approach.

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It has been clearly shown that a can or PET bottle made by origami technique can be crushed with much smaller force. Furthermore, this structure is desirable to absorb more crash energy during automobile light collision or vehicles-pedestrian accidents. Thus, in this research, to minimize average crashing force of the origami structure, the shape of the structure and the angle of polygonal folding lines are optimized by the method of MPOD, one kind of Response Surface Methods based on Holographic Neural Network (HNN).

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This paper proposes a robust optimum design technique for Surface Acoustic Wave (SAW) filters. The frequency characteristics of SAW filters are governed primarily by their geometrical structures, namely, both of the configurations and the arrangements of Interdigital Transducers (IDTs) fabricated on piezoelectric substrates. For deciding optimal structures of SAWfilters, traditional design techniques estimate their frequency characteristics based on the equivalent circuit mode of IDT. However, they have rarely considered the reliability of the equivalent circuit mode of IDT even though it may be spoiled by the scattering of parameters' values. In the robust optimum design of SAW filters, the proposed design technique employs a penalty function method combined with a variable neighborhood search and counts errors due to inaccuracy of the equivalent circuit mode of IDT. Computational experiments conducted on an optimum design of a practical three-IDT type SAW filter demonstrate the usefulness of the proposed design technique.

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This paper studies the topological optimization of cantilevered beam-type, extruded aluminum structures subjected to various loadings by genetic algorithm. In optimization, maximum deflection of the structure is minimized under the constraint condition, where total number of ribs within the structure is kept to be constant, by selecting the locations of ribs. The deflection of the structure is evaluated by using the finite element program developed for two-dimensional elasticity in this study. In numerical calculations optimal design solutions are obtained for the structures subjected to bending, shearing and stretching loadings.

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Recently, in order to improve performance of gas turbine's compressor, the thickness of compressor blade has become thinner. Therefore, for the purpose of increasing reliability, the blade's natural frequencies should be predicted precisely. In the compressor blade design, many natural frequencies must be tuned so as not to resonate with the frequencies of the excitation force under the constrained conditions which come from the requirements of manufacturing and performance. In this paper, an effective auto-tuning technique of the blade's natural frequencies is presented by combining Taguchi method with optimization method under constrained conditions and its application is shown. The new optimal technique in this paper is very useful in such blade design because the blade frequencies are automatically optimized, and at the same time the expected frequency deviations due to manufacturing tolerance are minimized. The calculated results show this method proposed can be applied to robust design of actual compressor blade.

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In this paper, we present a solution to shape optimization of plate and shell structures for a natural frequency problem. The weight is minimized under a natural frequency constraint. The designed boundaries are assumed to be movable only to in-plane directions. Optimized structures are discretized by the plane elements based on the Mindlin-Reissner's plate theory. A non-parametric, or a distributed shape optimization problem is formulated and the shape gradient function is theoretically derived using the material derivative method and the Lagrange multiplier method. The traction method, or the shape optimization method developed by authors is applied to obtain the optimal shape in this problem. The validity of this numerical solution to minimize the weight of plate and shell structures is verified through simple and practical examples.

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The objective of this paper is to present a concept of structural dynamic design considering controllability for smart structures. A smart structure is composed of the piezoelectric film sensor and actuator in order to reduce the structural vibration. H_2 controller is designed with the reduced order model of the smart structure which is obtained by finite element and modal analyses. The control force is applied by the piezoelectric film actuator and the feedback signals are detected by the piezoelectric film sensor and the accelerometer in the system. The structural topology is optimized to achieve an enhanced vibration control performance. The structural optimization problem is defined based on the structural frequency response and the density of each finite element is employed as design variable. It is verified that an enhanced performance on vibration suppression can be achieved by the presented optimal design method.

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This paper deals with impact vibration in a mass-spring system for two-degree-of-freedom excited by periodic force with arbitrary functions. The analytical model is steady impact vibration for two-degree-of- freedom having two masses in which one mass is subjected to an exciting vibration. Then the restoring force, which has characteristics of an unsymmetric piecewise-linear system, collides elastically to anather mass when amptitude of the mass increases farther than clearance. In order to analyze resulting vibration for the main resonance, the Fourier series method is applied and is analyzed for this system. Next, following the theoretical analysis, numerical calculations are performed, and the resonance curves are made by using resulting vibration. Effects of amplitude ratio of excitation, stiffness of clamped spring and mass ratio on the resonance curves are shown by numerical results. For verification of the analytical results, analog experiments are performed by using simulator, and numerical results are compared with analog results on the resonance curves. The analytical results are in a fairy good agreement with the simulated ones.

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This paper deals with impact vibration in continuous system excited by periodic force with arbitrary functions. The analytical model is steady impact vibration for a fixed-simply supported beam. The beam collides elastically to clamped spring of symmetric faces at an arbitrary midpoint of span. In order to clarify the main resonance of the system subjected to excitation by displacement, the resulting vibrations are analyzed by applying the Fourier series method for this system. Following these theoretical analyses, numerical calculations are performed, and the resonance curves are made by using the resulting vibration. Effects of the stiffness of clamped spring, the collision position ratio and the amplitude of excitation on the resonance curves are shown by numerical results. For verification of the analytical method, experiments are performed. The numerical results are in a fairly good agreement with the experimental ones.

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This paper deal with two-degree-of-freedom forced system composed of main system and an impact damper which has been analysed by many researchers. Periodic solutions, bifurcations, chaos, and the vibration control are discussed. A shooting method for impact systems presented by authers before are used in numerical calculation. As a result, the followings were made clear. (1) Unsynmetric periodic solution with 4 collisions per period and many subharmonic vibrations with many collisions were found. (2) The discontinuities in the stability of the periodic solutions caused by impact were shown using characteristic multiplier. (3) There were two routes to chaos, namely, period doubling route and torus doubling route were found. (4) Hyper chaos was found for the first time in the impacting system. (5) The design using synmetric periodic solutions with two collisions per period is not enough in the design of the impact damper.

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In the previous reseach, we have proposed the open-loop motion control method for an underactuated manipulator in order to swing up free link and to stabilize that at the upright position without observing the state of free joint. In this paper, we investigate the reachable area of the underactuated manipulator, which is moving in the vertical plane. Applying the proposed method more globally, we realize the positioning of the manipulator and carry out the stabilization of those cofigurations. The reachable and stabilizable positions of the tip of the unactuated link are theoretically and experimentally shown.

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This paper presents the optimal trajectory planning for a one-link flexible manipulator to suppress the residual vibration. In the trajectory planning, we express the joint angle by cubic spline function, and then use genetic algorithm to find an optimal trajectory. The optimal trajectory thus obtained has minimum vibration requirement. The manipulator is modeled by considering axial inertia, nonlinear curvature and inextensibility condition. The Lagrangian approach in conjunction with the assumed modes method is applied to obtain the equation of motion of the manipulator that is used in the trajectory planning. In the numerical calculation, we verify the effectiveness of the trajectory planning and investigate the effect of nonlinear curvature on the dynamics.

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The vibration supression becomes very important for designing the helicopter blades to ensure the comfortability and safety. Now-a-day, the pendulum absorbers and others are adopted for the purposes to reduce the vibration of the rotor blades. But, the drawback is that the dimension of the pendulum absorbers is determined by the anti-resonance concept based on the linear theory, and also its characteristics are not analyzed completely. In a Helicopter, periodic forces act on the blades due to the influences of the air thrust. These periodic foreces act on the blades with their integer multiple of the rotational speed of the rotor. We have proposed a two-degree-of-freedom model of the rotor blades and the pendulum absorbers, and it clarifys the vibration-proof effect of the pendulum absorbers on these forces.

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When the system is subjected to excess seismic load, the response is beyond yield point. On the other hand, it is well known that the response is reduced due to absorbed energy by hystersis loop characteristic caused by plastic deformation. In this paper, relation between the first excursion probability of the system subjected to filtered white noise and absorbed energy by hysteresis loop characteristic is examined. Reduction of the maximum response is also examined. It is found that the first excursion probability and the maximum response decrease with the increase of absorbed energy by hysteresis loop characteristic.

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The lattice Boltzmann method has been applied to calculate the probability density function of a nonlinear system subjected to white noise excitation, because of its advantage that the algorithm of the lattice Boltzmann method easily satisfies the both conditions that probability is non-negative and total probability equal to one. The probability density function is governed by partial differential equation known as the Fokker-Planck equation. The local rule of the lattice Boltzmann method is obtained by assuming Fokker-Planck equation as a kind of diffusion-drift partial differential equation. The probability densities of a Duffing and a Van del Pol oscillator are calculated and compared with exact solution or Monte Carlo simulation results.

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Using multigrid, an efficient method to calculate the stationary probability density function of a single DOF nonlinear system subjected to white noise excitation is proposed. Under white noise excitation, the probability density function of the system is governed by a linear partial differential equation called as the Fokker-Planck equation. An improved scheme has been proposed for the Fokker-Planck equation in the previous paper. In this study, multigrid which is known as an efficient numerical method for the elliptic partial differential equations is combined with the scheme. In numerical examples, present method shows same accuracy of solution and less computational effort compared with usual method.

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The response characteristics of the nonlinear oscillator to the harmonic excitation with the random perturbation and those to the narrow-band random excitation are compared. The Fokker-Planck equations governing the probability density functions of the responses to these two types of excitations are derived and solved by the finite difference method. The numerical examples for the Duffing oscillator are shown and compared with corresponding Monte Carlo simulation results. The relation between the jump phenomenon in the sample function of the displacement response and the multiple peak of the probability density function of the response is considered.

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This paper deals with 1/2-order subharmonic oscillations in a nonlinear two-degree-of-freedom system where the natural frequencies are comparatively close. The first-order approximated equations of the subharmonic oscillations are derived by using the multiple time scales method. The results of the bifurcation analysis are then compared with the results of the numerical simulation of the original equations of motion. As a result, the approximate solutions of 1/2-order subharmonic oscillations bifurcate into combination resonance when the excitation frequency is close to the sum of the two natural frequencies. In addition, as the two natural frequencies get closer, the subharmonic oscillations may change to chaotic vibrations.

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In this research, we consider a 2-DOF nonlinear system in which the masses are connected by means of a weakly linear stiffness. We show nonlinear normal modes in this system using the method of multiple scales. It is shown that the bifurcation and the stability of the modes depend on the coupling stiffness and the amplitude of the masses, respectively. We indicate that the bifurcations of the frequency response curve are characterized from those in the nonlinear normal modes. Furthermore, we investigate the occurrence of mode localization depending on the coupling stiffness.

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This paper is a numerical study about the Duffing's equation with pulsating external force. Our previous paper about vibration cutting showed that chaotic motion arised in cutting system turned into cyclic motion by the addition of pulsating cutting force. Therefore, we assume that the pulsating force is able to suppress chaotic vibration in nonlinear systems. In this paper, we change the continuous external force in Duffing's equation into the pulsating external force, and show that the chaotic behavior turns into cyclic behavior just as in the case of the vibration cutting system. Moreover, we add the pulsating force to the continuous external force, and show that the similar effect occurs. These result suggests that there is a possibility that the adding pulsating force is the effective method to control chaotic behaviors.

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We consider a problem of constructing a spacecraft transfer trajectory with low cost and moderate flight time from the Earth to the Moon. We adopt as the spacecraft model the planar circular restricted three-body problem or its perturbation due to the solar gravitation, and reduce computation of optimal transfers to a nonlinear boundary value problem. Using a computer software called AUTO, we solve it and continue its solutions numerically to obtain the optimal transfers. Especially, we find a transfer trajectory having about 15% lower cost, compared to the traditional Hohmann transfer.

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The behaviors of chaotic waves calculated by the different map function have been investigated and the following results have been obtained. The values of amplitude and also power spectrum become small in the case that the different chaotic waves are added. The sum of the power spectrum of each independent chaotic wave is larger than the power spectrum of added chaotic wave. The wave and the power spectrum of the same two chaotic waves become entirely same. The chaotic waves for the changed initial value show the same behaviors as the case of different chaotic waves . The values of power spectrum becomes small even in the case that the sine waves and the random wave are added.

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The method of normal forms is applied to the nonlinear equations of the liquid motion in a rectangular tank. The basic idea underlying the method of normal forms is the use of local coordinate transformations so that the dynamical system can take the "simplest form". In this study, the 1st and 2nd modes are considered, and the transformed equations of O(1) are obtained. It can be explained from these equations that the mean value of the 2nd mode takes the negative value. Comparison with the direct numerical integration of the original nonlinear equations of motion shows the validity of the present analysis.

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In this report, the validity of nonlinear vibration analysis by applying a reduction model is checked. Applying a ordinary non-linear vibration analysis method directly to a periodic steady-state vibration analysis of a system with large degrees of freedom, there are many cases that calculation becomes impossible because dimensions of treated matrices become huge. Therefore, in the most case, a vibration behavior of a large-scale system is estimated from analysis result of a reduction model obtained by applying the concept of modal analysis to a large-scale system. In this report, on the basis of such present way, the efficiencies of the method using a reduction model and the Incremental Transfer Stiffness Coefficient Method, which algorithm involves no approximate process without modeling process, are validated by comparing the computational result obtained by both methods.

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In this paper, we consider analytical formulation method of an impact oscillator system which is typical piecewise linear System, from a viewpoint of integrable system. First, global representation of general solution of the target system that is preveously proposed by present author can be regarded as rigourous discretization by means of unequally spaced difference scheme in relation to impact times. This means that dynamics of the impact oscillator as continous-time dynamical system is doublly prescribed by nonlinear difference equation governing impact times transcendentally and linear diference equation with regard to time evalution between impact states. Finaly, it is shown that piecewise linear system is exact solvable chaotic generating system that is included different important category, self reference system, hybrid system, and integrable system.

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When verifying the measure against control of the squeal in a car disk brake, the manufacturers have investigated using the actual car and using the dynamo which took out only the brake unit. In this paper, in addition to two experiment dynamos installed a brake unit by the different method, it experiments in squeal using the actual car, and these common features and differences are clarified. Moreover, the measure against control of the squeal common to these is verified experimentally, and the validity is shown by proposing the general measure against control of the squeal in a different vibration characteristic.

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This paper examines the separator plate vibration in wet friction systems. Wet friction systems have been widely applied to diverse machines. Occasionally, noise and vibration occur during an engagement in these systems. Authors had reported that the torsional vibration of the input shaft, in-plane and out-of-plane vibration of separator plate occurred in a developed test apparatus. In this study, separator plate vibration was noticed and investigated in detail. It was clarified in-plane vibration of separator plate was observed as a damped free oscillation during a stick-slip motion of input shaft. From the experimental results, separator plate vibration phenomena were clarified.

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This study is concerned with the identification of chaotic vibration by wavelet transform technique. The time histories to be examined are from numerical simulation of the responses of a non-linear vehicle model. The results of continuous wavelet transform of the time histories with 4 types of mother wavelet, Harr, Mexcan Hat, Meyer and Morlet, are discussed. It is found that, the Morlet mother wavelet is most suitable for the identification. It is concluded that the selection of mother wavelet is necessary for the identification of chaos and with the results of wavelet transform, chaotic vibration can be identified more easily than with that of power spectra analysis when the time history has multi-frequency components.

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Experimental results are presented on chaotic vibration of a thin lead valve with impacts. A model of the valve composed of a cantilevered beam is excited laterally by an exciter. Chaotic responses involving impacts of the beam are examined by the power spectrum and the Poincare projection. The maximum Lyapunov exponents of the responses are calculated. The mode contribution to the chaos is inspected by the principal component analysis. The chaotic responses by impacts are accompanied with higher modes of vibration. Increasing exciting frequency, the maximum Lyapunov exponent of the chaos increases and the generation of the 2nd mode of vibration becomes obvious. As exciting amplitude increase, contribution of the 2nd mode to the chaos becomes higher.

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The self-synchronized phenomena between two metronomes fixed on a pendulum-like horizontal plate are investigated by applying the improved shooting method. It is clarified from the analysis of several models with different values of system parameters that the metronome system has self-synchronized solutions at various frequency ratios of two metronomes and the plate. In addition, alternative formulation of variations to analyze a system with impulsive effect by the improved shooting method is derived in the differential form.

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It is confirmed from the previous experiments that a two-degree-of-freedom system, which consists of two blocks with rotating masses and a connecting element of a spring and a dashpot between two blocks, moves on a floor due to unsymmetrical characteristics of friction force. The unsymmetrical characteristics of friction force results from the centrifugal force of rotating mass driven by DC motor mounted on each block. This report investigates the effect of system parameters on the self-synchronized phenomenon and the moving performance of the system by applying the shooting method. In addition, it shows that the stick-slip motion sometimes occurs in the moving process of blocks and the self-synchronization with the stick-slip motion may improve slightly the moving performance of the system.

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