This paper presents a numerical method to investigate the frequency response of a rectangular plate. When we use the transfer matrix method to calculate frequency response of plates, exciting force is limited to a line force and applicable object is also restricted. To expand the range of application of the transfer matrix method, we propose a method to calculate modal parameters from free vibration analysis by using the transfer matrix method. Modal mass is calculated by numerical integration from modal vectors. We have applied this method to calculate the frequency response of plates. Comparing the results obtained from the proposed method and finite element method, characteristics of the frequency response of both methods agree with each other. Calculation process of the proposed method has an advantage of computational efficiency. As a result, it is possible to be a powerful way to execute parametric studies.

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A new design method is proposed here to maximize the fundamental frequency of laminated composite plates reinforced by curvilinear fibers. Spline functions represent arbitrarily shaped fibers and Ritz solutions generate frequency equations. The optimum curvilinear shapes are searched for the maximum fundamental frequencies using genetic algorithms, and the increments of data points which define the spline shape are used as design variables under the limited range of undulation. Comparison of the present analysis method gives good agreement with the finite element method in terms of natural frequencies and vibration modes, and the optimized results show that the present plate with optimally shaped curvilinear fibers gives higher or equal fundamental frequencies than those of the conventional plate with optimally oriented parallel fibers.

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Experimental results are presented on chaotic vibrations of a rectangular plate with an in-plane elastic constraint. Opposite edges of the plate are clamped and the other edges are simply supported. One of the clamped edges is connected with elastic springs and is movable to an in-plane direction. The simply-supported edges are composed with adhesive elastic thin films. Under the specified in-plane compressive force, the plate shows the type of a softening-and-hardening spring. Moreover, the plate has the condition of the two to three internal resonance between the second and third modes. Under periodic lateral excitation, non-periodic responses are obtained in specific frequency regions. The non-periodic responses are examined with the Fourier spectra, the Poincare projections and the maximum Lyapunov exponents. It is found that two types of chaotic responses are generated from the internal resonances dominated by the first mode and higher modes of vibration. Appying the Karhunen Loeve method, contributions of vibration modes on the chaotic responses are confirmed. The first mode contributes to the chaotic responses dominantly. The higher three modes including the second, third and fourth modes have 10 to 20 percent of contribution. As exciting amplitude increases, the lower frequency region of chaotic response with large amplitude shifts to the higher frequency range owing to the hardening nonlinearity of the plate, while the higher region of chaotic response with small amplitude shifts to the lower frequency range.

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Experimental resuls are presented on chaotic vibrations of a simply supported circular plate with initial deformation. The plate is excited by lateral periodic excitation. In typical frequency range, non-periodic response is observed. The amplitude of response shows the irregular movement with amplitude modulation. The response is examined by the Fourier spectra, the maximum Lyapunov exponent and the Poincare projection. The response is found to be the chaotic response and that is generated from internal resonance condition of one to four. Time responses at the five points of the plate are measured simultaneously within long time interval. Applying the principal component analysis on the response of long time interval, it is found that three lower modes of vibration are generated in the chaos. The lowest mode of vibration contributes to the chaos dominantly. The second mode with one nodal diameter and the third mode with two nodal diameters contribute with small amount. The principal component is calculated with every short time intervals, the large amplitude of the chaotic response the contribution of the lowest mode of vibration predominantly. When the amplitude of the chaotic response decreases, the contribution of the lowest mode is decreased by 10 percent while the higher modes increase.

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This study presents experimental results on chaotic vibrations of a shallow cylindrial shell-panel with clamped and simply-supported boundaries. Both opposite sides of rectangular boundaries are clamped by blocks and the other opposite sides are simply supported by flexible films. First, to find fundamental properties of the shell-panel, the linear natural frequencies and the characteristics of restoring force of the shell-panel are measured. The characteristic of restoring force of the shell-panel shows a type of a soften-hardening spring. Then, the shell-panel is excited with lateral periodic acceleration. In typical ranges of the exciting frequency, non-periodic responses are generated. These responses are examined with the Fourier spectra, the principal component analysis, the maximum Lyapunov exponents and the Poincare projections. The responses are found to be the chaotic responses. The chaotic responses accompany with sub-harmonic resonance responses of the order 1/2. The chaotic responses are generated from internal resonances dominated by the lowest mode and higher modes of vibration.

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This paper deals with response analysis of collision vibration in continuous system excited by periodic displacement with arbitrary functions. A system of steady vibration in a cantilever beam having an attached mass at free-end is considered. The cantilever beam has structural damping in the beam, and it is being put in the viscous fluid with hydrodynamic drag. The attached mass collides elastically with the coil spring clamped on asymmetrical faces when the amplitude of mass exceeds the clearance between the coil spring and the attached mass. Then, the restoring force is assumed to be an asymmetric piecewise-linear system. For such a system, the beam undergoes a nonlinear vibration when the attached mass collides with the coil spring. In order to analyze harmonic, superharmonic and subharmonic resonances for the system. Fourier series method is applied to obtain an exact solution for resulting vibration. Next, the numerical calculation is performed to obtain the resonance curves. The numerical results show effects of the mass ratio, the amplitude ratio of excitation, the spring constant ratio, the structural damping ratio and the external damping ratio on the resonance curves. The numerical experiments are also carried out to verify the numerical results.

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This paper presents a computational method of random vibration of the turbine blades using the multi-degree of freedom spectrum analysis. This computational method is applied to the cyclic symmetry method to the spectral analysis and enabled a large-scale calculation of the steam turbine blades. Also, the random vibration examination by a simple blade model was done, and the problems of the calculation condition were clarified. Both modal damping and random excitation PSD (Power Spectrum Density) are most important factors of the calculation. The calculation results were corresponding to the measurements well, and the validity of the computational method was confirmed.

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This paper presents an analytical method to investigate the three-dimensional elastic vibration problems on a railway carbody. The carbody is modeled as a simply-supported non-circular cylindrical shell without end plates. Transfer matrix method is applied to the analysis model. The model has an advantage of the matrix size for calculation. Therefore we have applied this model to simulate the effect of the rigidity of the connecting part between roof and side panel. As a result, it is found that amplitude ratio of floor to roof can be reduced when we set the rigidity of the connecting part between roof and side panels to higher value. And it is also found that the natural frequencies become higher at the same parameter changing.

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Modal property estimation of railway vehicles by using a linear prediction model is studied in this paper. The relation between input (excitation force or axlebox accelerations) and output (carbody accelerations) of an actual railway vehicle obtained by stationary or running test is expressed by means of an ARX (Auto-Regressive eXogenious) model. The procedure to extract modal properties is described in detail. Determination of appropriate model order (order of prediction coefficients of the ARX model) is especially discussed from the view of practical use. To employ average prediction errors for two different parts of analyzed data is proposed and their effectiveness to determine the model order is evaluated. The availability for the MIMO (multiple-input multiple-output) problem is also described. It is shown that detailed modal characteristics can be identified successfully by using proposed method from measured data for both of stationary and running test.

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In order to improve the riding comfort for passengers on railway vehicles, it is effective to suppress the vibration of the vertical bending mode. Therefore, the primary suspension damping force control system with variable axle damper is under development, which enables to control its damping force continuously. This paper reports how the relationship between the natural frequencies of the primary suspension and that of the first bending mode of the carbody influences the vibration reduction performance of this system. Numerical simulations and running tests have been carried out, and the results have indicated that the efficiency of vibration suppression is dependent on that relationship. More concretely, a velocity feedback of the vibration of truck frames, i.e. a skyhook control low, has been effective when the both natural frequencies are close. On the other hand, model-based control lows such as an LQG control should be introduced if the natural frequency of the bending vibration of the carbody exists apart from those of the vertical bouncing and pitching motions of the truck frames.

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Recent reports imply that railway vehicles could be derailed solely by the ground motions of earthquakes without fatal damages of vehicles or tracks. Based on the reports and facts, we believe that we should further study the derailment mechanism of a high speed railway vehicle excited by large seismic motions, to pursue to minimize the risk of railway system safety against large earthquakes. We improved our original planar vehicle dynamics simulation model to a model to allow yaw motion of wheel-set, which enable to estimate the influence of the attack angle of wheel/rail and steering effort of the wheel contacting to rail at flange and yielding large radial difference. Through the analyses based on the new model, the following outcomes were obtained. (1) Most of derailments are brought as the result of the rocking motion of a vehicle by track excitations underneath. The excitation amplitudes for derailment are influenced by vehicle speed particularly in lower input frequencies. (2) Wheel climb derailment is not observed. We attribute it to the negative attack angle of wheel/rail during wheel/rail flange contact. (3) At the moment just before derailment when wheel is contacting on rail at flange top, the steering effort of wheel-set, which may contribute to avoid or delay derailment, is not observed.

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This paper is concerned with the vehicle property using the camber angle of a tire. The purpose of using the tire camber angle is to improve the cornering ability and to save energy. Then a new method of turn using the camber angle of a tire is proposed. First, five types of turn for the cornering ability and the conservation of energy is selected. The scaled vehicle is used for the purpose of a fundamental research in this paper. Drive and steering system of the scaled vehicle are 4WD and 4WS using 12 motors. The tire force of a scaled vehicle tire is measured by tire testing machine. Then the map of the tire force was made. The cornering ability and the energy saving are investigated from the results of the step response test and cornering performance test. Therefore we confirmed that the new method of turn is effective for improvement of the cornering ability and the conservation of energy.

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In this paper, a control system for an active stabilizer is designed in order to not only reduce the roll angle during cornering but also suppress the rolling vibration on a rough road concerning the ride comfort. A full vehicle model which has a suspension system with the active stabilizer is derived. The active stabilizer has an actuator which can actively generate the torque at the center of a stabilizer bar. In order to balance competing goals for the roll reduction and the improvement of the ride comfort, the control system for the active stabilizer is obtained using the linear quadratic control theory. It is verified that the control system designed can settle the rolling vibration on the rough road more quickly than the vehicle model of a normal suspension while reducing the steady roll angle during cornering to the same level as that of a passive stabilizer, and control the roll motion by the control torque which is lower than the reaction torque of the passive stabilizer.

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In this paper, we design a control system to stabilize a motorcycle which is in the state of steady-state circular turning at the low speed by using an assist actuator of the front steering. The nonlinear dynamical model of a rider-motorcycle system is derived taking into account of leaning of the rider, and is linearized around a certain equilibrium point to perform the eigenvalue analysis and the frequency response analysis. A reduced-order model that can be used to design the control system is derived on the basis of the frequency response analysis. The attitude stabilization control system is designed by using H_∞ control theory. It is verified that the H_∞ control system designed can stabilize the attitude of motorcycle against a front-steering torque disturbance during steady-state circular turning.

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This paper proposes SSM (Sensor Steering Mechanism) for lateral guided vehicle with rear wheel steer mechanism. Author demonstrated the geometry of SSM for the front wheel steer type and the reverse phase four-wheel steer type one. SSM presents a stable lateral guiding performance for automated vehicle which follows a straight and curved path created by guideway. The other hand, SSM is not established for a rear wheel steer type vehicle. Rear wheel steer vehicles are forklifts and backward moving of the conventional motor vehicles of which steering wheels are located at the front. SSM for the rear wheel steer vehicles enables a forklift to automated moving on every spaces, if the control method by SSM is established. This paper leads SSM relation for a rear wheel steer vehicle and constructs an experimental robotic vehicle with proposed SSM. Simulated and experimental data show the advantages of proposed SSM.

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These days, the searches for sustainable Personal Mobility Vehicle (PMV) are ongoing worldwide. The authors proposed the two-wheel vehicle which has two transformable modes; a two-wheel steering and two-wheel driving (2WS/2WD) bicycle and a stabilized parallel two-wheel vehicle. This paper investigates the 2WS/2WD bicycle and proposes the stabilization control. It shows that by steering rear wheel to the negative phase to the front and by driving rear wheel to the negative phase to the front, it cancels back and forth movement and reduces the roll angle amplitude.

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Bump foil journal bearings are prospective applicants for machine elements that can support a small-sized rotor of high-speed rotary machinery. The authors have proposed two models to the bearing, one of which corresponds to the bearing with an excessive static friction between the top and the bump foils and the other to the bearing without the friction. The variation of predicted maximum load capacity of the bearings with respect to the assembly preload was in qualitatively good agreement with the measurement. This study aims at predicting the effect of the design variables of the bearing on the stability threshold speed of the horizontal rigid rotor supported in the model bearings. The modified stability charts show that the effect of two of the variables, the attached angle and the angular extent of top foil, is noticeable, the other two variables, the rigidity of top foil and the equivalent spring constant of bump foil, is modest and the rest of the variables, the density and the thickness of top foil and the pitch angle of bump foil, is negligible. It is also found that the models have to be modified, considering that the top foil is detached from the bump foil.

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The head positioning accuracy of the hard disk drive (HDD) should be improved to meet today's increasing performance demands. Vibration suppression of the arm in the hard disk drive is very important to enhance the servo bandwidth of the head positioning system. In this study, the smart structure is introduced into the hard disk drive to suppress the vibration. It has been expected that technology of smart structure will contribute to the development of small and light-weight mechatronics devices with the required performance. First, modeling of the system is conducted with finite element method (FEM) and modal analysis. Next, the actuator location and the control system are simultaneously optimized using genetic algorithm (GA). Vibration control effect with the proposed vibration control mechanisms has been evaluated by some simulations.

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A new control device to suppress horizontal vibration in an elevator cabin, mainly caused by irregularity of a guide rail, is presented. The proposed control device consists of two rotary electric motors with eccentric masses. The one motor produces torque to rotate the eccentric mass according to the command signal from the controller, while the other motor rotates the mass to terminate the unwanted vertical force. The performance of the proposed system is examined through the numerical simulations considering the nonlinear characteristics of the rotating masses and the experiments with a miniature elevator cabin carrying the proposed actuator. The results indicate the proposed control device reduces the vibration without producing the unwanted vertical vibration.

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This paper describes a new zero power control strategy for a hanging type maglev system. In this maglev device, a permanent magnet generates the levitation force, and a Voice Coil Motor (VCM) maintains the device stably in an equilibrium-levitated position. In order to realize zero power control, a spring is installed in the maglev device so as to counterbalance the force of the actuator on the mass gravitation, and a current integral feedback loop is used in the controller so as to adjust the actuator current zero in the balance state. A prototype of the maglev system was constructed; a theoretical model was developed; a zero power controller was designed and constructed; and numerical simulations and experiments were performed. The results shown here suggest that this zero power control strategy is feasible and effective for the hanging type maglev system using a permanent magnet and VCM.

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This paper presents a control system for active magnetic bearings (AMBs) considering the motions of the stator. AMBs require active control for stable support of the rotor. Many control methods for AMBs have been proposed. Most of them are designed assuming that the stator is fixed on the base. However, in some applications, the stator moves with the object in which the AMB is mounted. In this paper, the transmittance from the stator motions to the relative motions of the rotor to the stator is investigated both theoretically and experimentally. Remarkable influences of stator motions have been observed at a low frequency range. As the gyroscopic effect becomes larger, they extend to higher frequency range. In addition, estimated signals from a disturbance observer are used to cancel the influences caused by the stator motions. It is shown that the effect of the cancellation depends on the estimation speed of the observer.

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CP control of a two-link planar flexible manipulator is studied. The method to derive the optimal trajectory of the state variables and the computed torque wherein the tip position of the manipulator follows an arbitrary continuous path accurately is proposed. The exact trajectory of the state variables for an arbitrary tip position path can not be obtained because a flexible manipulator is a redundant and underactuated system. The dimension reduction feature of subspace control is used. In subspace control, the state space is separated into the control subspace and the complementary subspace. The proposed method consists of the calculation of the approximate trajectory of the state variables using the control subspace and the correction of the trajectory using the complementary subspace. Also, the availability of this method is confirmed by numerical simulation. The tip position follows desired trajectory accurately in both cases of the linear and circular desired trajectory.

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This paper discusses the minimum number of inputs for orientation control of a freely rotating body under conservation of angular momentum by means of internal motion of the system. Two models are considered as the analysis models for rotating body. One consists of a rigid body with a pair of particles symmetrically located around the center of mass. The other has a symmetric rotor instead of moving particles. Analyses based on differential geometry show that three dimensional attitude is locally reachable with only one control input. Some exceptional conditions are disccussed from the view point of mass arrangement and initial condition of motion.

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In order to stabilize the inherent unstable system like the inverted pendulum on a cart, severe judgment of situation is required. Accordingly, it can be expected that the human operators exhibit a complex behavior occasionally. This paper tries to identify the individual difference of human operator's behavior from time series data by using fuzzy inference and acquire individual skill of human operator. It also investigated the chaotic behavior of human operator and the possibility of the formation of complex system in the learning process of the human operator with difficult control objects. The operators in the experiment are skilled to some extent in stabilizing the inverted pendulum by training, and the data of ten trials per person were successively taken for an analysis, where the waveforms of pendulum angle and cart displacement were recorded. The maximum Lyapunov exponents were estimated from experimental time series data against embedding dimensions. It was found that the rules identified for a fuzzy controller from time series data of each operator showed well the human-generated decision-making characteristics with the chaos and the large amount of disorder. And the individual difference of chaotic and complex human operation can be identified with fuzzy inference.

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Active noise control (ANC) in a three-dimensional sound field (e.g., in an office) is investigated in this paper. Since the size of the controlled area generally depends on the wavelength of the target noise, it is difficult to control the noise in a whole room using ANC. Instead, noise control method in the vicinity of a subject's head (referred to around-head control) is investigated in this paper. To realize around-head control, an evaluation point that mimics head movement is required. However, movement of the evaluation point during control has not been considered in conventional ANC. Authors have proposed control with filter map in order to solve this problem. In this method, the controlled space is subdivided into small grids. A filter map is produced by storing and updating filters in each grid. A new method for updating the map is proposed in this paper. A reliability index is calculated and used in this updating method. The effectiveness of proposed method is shown by numerical simulations using acoustic properties measured in an anechoic chamber.

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Recently, demands not only for quiet sound design but also for comfortable sound design arise. Therefore it is necessary to predict radiation sound in time domain at a design stage. In this paper, we apply CIP (Cubic Interpolated Propagation) method for time domain analysis of acoustic and elastic vibration problems to examine the transient behavior. By using that, we verify the process of excitation of acoustic mode in an enclosure and the adequacy of frequency response characteristics of elastic plate by comparing with FEM results. Adding to that, we have achieved to predict radiation sound from the vibrating structure (elastic plate) in time domain by using elastic and acoustic CIP analysis together. The radiation sound pressure from vibrating plate is calculated from the beginning of vibration to the steady state. This CIP vibro-acoustic analysis will be a basis of virtual audition system of radiation sound of mechanical structure in design stage.

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Pressure wave propagating in a tube often changes to shock wave because of nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computation cost. In order to overcome the problem of computation cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of connecting nonlinear spring is derived from the condition of adiabatic change of fluid, and the equivalent mass and the equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in cylindrical tube. Pressure waves generated in a hydraulic oil tube, in a sound tube and in a plane-wave tube are analyzed numerically by using the proposed model in order to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the phenomena that the pressure wave with large amplitude propagating in the sound tube and in the plane tube change to shock wave are numerically reproduced. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.

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Dynamic property of polyurethane foam is investigated experimentally. Polyurethane foam is loaded periodically with various amplitudes and various frequencies, and load, deflection and velocity of the polyurethane foam are measured. Using non-parametric identification technique in time domain, dynamic property of polyurethane foam is modelized as a function of velocity and deflection of polyurethane foam. Then we proposed a new model of dynamic property of polyurethane foam. Experiments are conducted with various conditions of size and compressibility, and the validity of the proposed model is confirmed. Difference of dynamic property by size and compressibility is investigated.

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A coupled inverted pendula model of competition and cooperation is proposed to obtain a purely mechanical implementation of dynamics comparable with the Lotka-Volterra competition dynamics. It is shown numerically that the proposed model can produce the four equilibria that can be compared to ecological coexistence, dominance, and scramble. It is also shown that the proposed model exhibits fractal dependence on initial conditions. The result implies that selection of the equilibria will be uncertain under finite accuracy of knowledge on initial conditions.

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Tripod Constant Velocity Joint is used in driveshafts. The thrust force of the joint causes lateral vibration in front drive vehicles. To analyze the thrust force, we construct a detailed model based on multibody dynamics approach. This model includes all main parts of the joint as rigid bodies and considers all force components of contact and friction acting among these parts. In this model, we utilize a new contact modeling method of needle roller bearings for both more precise analysis and faster computation. By comparing the computational results with the experimental ones, we verify this model and clarify the main factors of 2nd and 3rd rotating order components of the thrust force. Moreover, we show the influence of the skew of needle rollers on the thrust force and evaluate the contribution of friction forces at each contact region to the thrust force.

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Continuous operation of rotating machinery with a rotor crack is a risk condition since the rotor crack grows rapidly and may fail causing a catastrophic accident. This paper develops the finite element model of the rotating shaft with an open crack. The analytical method for the calculation of the natural frequencies of such a rotor system with an open crack is investigated, and the modeling of the open crack element is discussed. The natural frequency of the experimental system is measured for various positions and depths of the open crack. By comparing both the theoretical and experimental results of the natural frequencies, the accuracy of the developed finite element model of the rotating shaft with an open crack is clarified.

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Noise components in measured signals usually are assumed as statistically stationary. But if the sources of the noise are vibrating, the intensity of the noise is expected to vary periodically. In this study, the noise with the fluctuating intensity is modeled as the product of envelope function and white noise. The autocorrelation functions of the modeled noise and white noise are not distinguishable. But the autocorrelation function of the absolute value of the product of envelope function and white noise theoretically coincides with the autocorrelation function of the envelope function, except at the point of τ=0. From these properties, the method to analyse the envelope function using the absolute value function is proposed. In the numerical examples, the proposed method and the wavelet autocorrelation function which is proposed in our previous paper are applied to the noises with sine envelope function and chirp envelope function. The present method successfully analyse the frequency characteristics of the envelope functions.

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Differential pressure transmitter with an orifice is widely used as a major field flowmeter. A major drawback of this flowmeter at operation site is blockage of an impulse line, which connects a differential pressure transmitter with an orifice tap. By conducting experiments at a water line, the diagnostic method based on the pressure fluctuations in the impulse line can diagnose the blockage in the steady state. However, there is a possibility of making a wrong diagnosis in the transient state in this method. This paper investigates the cause of this problem by comparing the experimental results at an air line with at the water line. In addition, the effectiveness of a diagnostic method based on the phase difference between orifice upstream and downstream pressures is clarified even in the transient state. Through experimental investigations, the following results are derived: 1) The long-term pressure change has a harmful effect to diagnose the blockage with the pressure fluctuations. 2) The diagnostic method based on the phase difference can diagnose the blockage even in the transient state; however, this method can not diagnose the severe blockage in an air line. Therefore, the method based on phase difference has to be improved.

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An online model-based performance monitoring of a heat exchange process using water and steam, which is one of the key components of distributed energy supply systems, has been developed based on a static input-output model of the process. This performance monitoring first estimates output process variables and heat exchange performance of the process in response to the variation in measured input process variables. These estimated values are then compared with the measured ones for online performance monitoring. This paper examines effectiveness of the performance monitoring under transient state with irregular changes in water and steam flow rates by the numerical analysis. The result shows sufficiency of the estimation accuracy of the output process variables and heat exchange performance and the detection capability of the deterioration of the heat exchange performance under transient state.

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Transfer Path Analysis (TPA) is a key technology for tackling with the noise and vibration problems, and the precision of the identification influences the result of contribution analysis. For the identification of input force, the matrix inversion method is commonly used as an indirect method where the pseudo-inverse of the FRF matrix is multiplied to the response spectra to estimate the input force spectra in a least-square sense. This paper presents a new approach to improve the accuracy of the input identification by the matrix inversion method. To avoid the inversion of the ill-conditioned matrix, the apparent-mass matrix (force/acceleration FRF matrix) is directly estimated in a vibration test. In this paper, the accuracy of two identification methods are compared by applying two approaches to FEM analysis and a vibration test. And it is shown that the identification accuracy by the apparent-mass matrix approach is superior to the matrix inversion method.

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Colloidal damper is a dynamic damper which uses a principle of difference of surface extension force, which is occurred by the direction of movement of surface. Some characteristics of the colloidal damper was investigated by our group. So this paper presents a damping characteristics of colloidal damper for the amount ratio of silica gel and water, volume of cylinder and pre-pressure of the cylinder by changing exciting frequency and displacement of a piston. As the results it is known that optimum amount of ratio of silica gel and water exist for cross section of cylinder, damping characteristics increases as increase of pre-pressure of the cylinder and the optimum volume of the cylinder is exist for a given damping force or capacity.

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The present paper discusses the estimation of the road friction coefficient based on the brush model. This popular tire model is reanalyzed beginning from the conventional simple physical model, and intrinsic expressions are derived. The grip margin, which is defined as the residual tire force normalized by the radius of friction circle, can be estimated using three components of the tire forces and the self-aligning torque. A cubic equation is obtained as a grip margin equation for the isotropic model. The anisotropic model yields a quintic equation. The solutions of these equations are approximated by Chebyshev polynomials. The estimation method is verified by numerical simulations using CarSim, which is a popular vehicle simulation software application. The estimated friction coefficients agree well with the assumed values for the cases of smaller grip margins, especially under lower-friction conditions.

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This paper presents a method for quickly analyzing drop impact on mobile devices at an early design stage. Drop impact response analysis is one of the most important analyses for producing reliable products. Many parts depending on the know-how of experts now take lot of time and money to analyze. To reduce the development lead time and cost, an efficient analysis method is proposed. First, after drop transformation shapes were carefully observed, a drop impact response analysis using modal analysis was derived. Second, the natural frequencies and mode shapes of the mobile device were measured for the proposed analysis method. The modal parameters of the mobile device were acquired precisely for a broadband frequency with a scanning laser doppler vibrometer. A simple plate model can be used for this analysis model instead of a complicated model converted from a computer aided design. The accuracy of the proposed method is almost the same as that of finite element analysis by an explicit method using a complicated model.

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