Free vibrations are analyzed for a flexible spinning disk / spindle system with axial translation and rigid-body tilting.Considering the effects of the rigid-body motions of the disk / spindle system, the coupled equations of motion are derived by using Hamilton's principle based upon the Kirchhoff plate theory and von Karman strain theory.The coupled equations are solved by the Galerkin approximation method in order to obtain natural frequencies of the disk / spindle system with axial translation or rigid-body tilting.This study puts a focus on the effects of the rigid-body motions such as axial translation and rigid-body tilting which are coupled with the flexible modes of the disk.

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High-speed railway noise arises from vibration and aerodynamic noises.Rolling noise from rail and wheel vibration and aerodynamic noise generated under the car body can be minimized with noise barriers constructed along the rails.Thus, noise radiated from current collectors becomes the dominant noise source, and it must be controlled to reduce noise emission from high-speed railways.A pantograph cover is a useful and effective apparatus that reduces aerodynamic noise from a conventional pantograph when the operating speed does not exceed 300 km / h.At speeds over 300 km / h, however, the conver does not reduce aerodynamic noise enough to meet Japanese noise regulations, and its lift also becomes quite large.A new concept for a low-noise current collector has been developed.This current collector uses a delta-wing shape for the collector and has a pair of insulators on a hydraulic mechanism covered by a streamlined dome.The noise level of the new collector is expected to be 19 dB(A)lower than that of the present pantograph.

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Using a narrow annular passage between a tapered outer cylinder and a tapered axisymmetric body, we analyzed the moment of the fluid-dynamic forces acting on the body, which vibrates harmonically in the rotational mode.The moments were divided into those of inertia, damping, and stiffness.The following conclusions were obtained by study of these coefficients.When the pivot is situated downstream of the passage inlet, intense dynamic instability due to negative damping and static instability due to negative stiffness occur when the passage is divergent.If the pivot is situated at the passage inlet, the instability does not occur.When the angles of the wall surfaces of the axisymmetric body and outer cylinder to the body axis are varied respectively, the boundary of negative damping is approximately given by the straight line.It was found that negative damping is caused by the effect of steady flow.

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We present analytical and experimental studies on the stability of an axisymmetric body which vibrates with one degree of freedom of rotational motion.The leakage types are tested for three divergent passages of which the tapered abgles of the outer cylinder are negative, zero and positive, and one parallel passage.When the flow rate of water is gradually increased, the damping ratio and Reynolds number at the stability boundary are measured.It is determined that the most influential parameter on the stability of the system is the position of the pivot.When the pivot is situated downstream of the outlet, dynamic instabilities due to negative damping occur in the case of the divergent passages and static instabilities due to negative stiffness occur in the case of the parallel passage.Reynolds number at the stability boundary increases linearly with increasing natural frequency.The theoretical values correspond well with the experimental results.

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This paper presents the numerical method for dynamic problems involving fractional operators.Based on Liouville-Riemann's definition of fractional derivatives, the algorithm is developed by incorporating one-step schemes of well-known Newmark types into our own formula.The scheme has the merit of excellent operational characteristics and the simplicity of application.Numerical experiments were given to show the superiority and effectiveness of the algorithm.

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This paper deals with a discrete adaptive state feedback control method based on the concept of strict positive realness and its application to a liquid transfer system.First, we propose a basic construction of the adaptive control system taking into account the stability of the system and feasibility of the adaptive algorithm.Second, the proposed control method is applied to a liquid transfer system control problem.Control performances are examine from the point of view of experiments.It is shown that the adaptive state feedback control is valid for the liquid transfer system receiving the change of liquid mass.

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A disturbance cancellation controller for the active dynamic vibration absorber is modified to follow the frequency of disturbance without any complicated adaptive algorithm.The original compensator has an internal model of a sinusoidal disturbance.When the frequency of disturbance varies, the dynamics of the model must also be altered to be identical to those of disturbance for perfect regulation.In the modified compensator, control input is generated by calculating a convolution integral instead of solving the corresponding state-space equation;exogenous signals synchronized with the actual disturbance are used in the convolution.The performance of the designed controller is experimentally studied.

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A connection is made between time-optimal control and the popular proportional and derivative(PD)control for second-order servo systems with input constraints.It is shown that time-optimal control can be achived using PD algorithm provided that the ratio between the proportional and the derivative gains is adjusted according to the initial condition.A closed-form tuning formula is derived.Compared to the conventional time optimal control algorithm, the proposed method requires simple on-line computation and is easy to implement.The method is applied to a DC servo motor and comparisons are made with fixed-gain control algorithms.Since high-gain PD control is closely related to slinding-mode control, the relations between the proposed scheme and sliding-mode control are also investigated.It is seen that whether a high-gain PD algorithm has time-optimal or sliding-mode responses is determined by the ratio of proportional to derivative gains.

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In this paper, a new approach combining the state variable feedback control and the grey forecasting is presented for the position control of a servohydraulic cylinder.In industrial implementations, it may be interesting to minimize the number of sensors because of cost considerations.Therefore, for our servohydraulic positioning system, only one position sensor will be employed and the other necessary states(that is:velocity and acceleration)are obtained through numerical derivation of the position signal.Applying the method of numerical derivation, which is the simplest way for the acquisition of velocity and acceleration signals, does not require a known system mathematical model.Disadvantages, however, are the phase-lag problem of the derived signals and the consequent overshoot of the output response.Owing to the predictive property of the introduced grey forecasting, the experimental results show that both the phase-lag of the derived signals and the overshoot of the response curve are effectively compensated.

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Computational experiments are performed with the simple genetic algorithm(SGA)for a wide range of intron lengths, crossover rates, mutation rates, and replication rates.The best-adapted species emerges widely with a critical intron length proportional to the overall crossover rate in an environment of discontinuous evolution(quasi-macroevolution).This result coincides with the relation between the intron length and mating rate observed in actual Eukaryotes.On the basis of this knowledge, a method for optimizing the crossover rate in the SGA is proposed for the purpose of accomplishing artificial macroevolution in engineering problems.

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Evolution strategies(ESs)are search algorithms which imitate the principles of natural evolution as a method to solve parameter optimization problems numerically.The effectiveness and simplicity of ES algorithms have lead many people to believe that they are the methods of choice for difficult, real-life problems superseding traditional search techniques.However, the inherent strength of the ES algorithms largely depends upon the choice of a suitable crossover and mutation technique in their application domains.This paper discusses a new ES in which both a subpopulationbased arithmetical crossover(SBAC)and a time-variant mutation(TVM)operator are used.the SBAC operator explores promising areas in the search space with different directivity while the TVM operator exploits fast(but not premature)convergence with high precision results.Thus, a balance between exploration and exploitation is achieved in the evolutionary process with these combined efforts.The TVM also acts as a fine local tuner at the converging stages for high precision solutions.Its action depends upon the age of the populations, and its performance is quite different from the Uniform Mutation(UM)operation.The efficacy of the proposed methods is illustrated by solving discrete-time optimal control models which are frequently used in the applications.

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This paper presents an H∞ pole placement method, under a weighted mixed sensitivity problem, to design robust axis controllers in which the selection of weighting functions is investigated according to the relaxed performance measure.The objective is to independently design motion controllers using the notion of relaxed performance measure to reduce the dynamic contouring error, i.e., the cross-the-path error, in multiaxis servomechanisms.Experimental results from a biaxial servomechanism show that the H∞ pole-placement method for axis controller design can effectively reduce contouring error by matching axis delay times and hence achieve good contouring accuracy.

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A new optimal digital-redesign approach for the input time-delay continuous-time cascaded system is proposed in this paper.It shows that the states of the sampled-data system with the digitally redesigned control law closely match those of the original cascaded continuous-time closed-loop system with analogue control law at any instant between sampling periods.Moreover, the developed digital control law can be implemented using low-cost microcomputers with a relatively longer sampling period.Also, it utilizes the innovative one-duration description of input time-delay sampled-data system, that it suitable for any value of input time delay, even larger than one sampling period.An illustrative example is presented to demonstrate the effectiveness of the proposed design methodology.

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A redundant manipulator can achieve multiple tasks using the degree of redundancy.In this paper, a redundancy resolution problem is formulated with multiple criteria into a local equality and inequality constrained optimization problem.To achieve multiple tasks, the task with the highest priority can be performed by optimizing a corresponding objective function.The forward kinematic relation and the other tasks with higher priority are performed by satisfying an equality constraint and a set of inequality constraints, respectively.The solution of the path planning is then obtained using an optimization procedure.Different to the conventional approach, the inverse of the Jacobian matrix is not used in the proposed method.The proposed method also provides a unified approach to solve motion planning problems with multiple tasks.

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Understanding actual ball motion in a ball bearing is important for tribological analysis.In earlier studies, a search coil method was used to detect ball motion, however, three-dimensional ball motion could not be obtained.Recently, the Hall element method has been developed to detect three-dimensional ball motion.In this method, in spite of the fact that the radial components of the magnetic flux were measured through contact points, a fixed Cartesian coordinate system was used regardless of the contact condition.In this study, the direction of the contact points was taken into account to calculate the Hall voltage and to estimate the error in angular velocity.If the effects of contact point change are not considered, some errors may occur.The results show that the direction of the contact points considerably affects the angular velocity calculations.

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The formulas for displacement and velocity analyses are derived for the RSCR spatial four-link mechanism and the velocity of the coupler link is geometrically determined by instantaneous screw axes.The condition for limit positions of the driving-link motion is obtained on the basis of the force transmissibility from the coupler link to the driven link and the deteminant, which is composed of the coefficients of simultaneous equations for velocity analyses.By geometrically investigating the conditional function, a quantity is proposed in order to evaluate motion and force transmission characteristics.The parts of the functional relationship between input and output angles divided by the limit positions of the driving link, which are called branches and correspond to the composition loops of the mechanism, are identified by means of two newly established rules.

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The surface geometry of the roller-follower cam mechanisms are derived as the cam makes contact with the roller on their instantaneous screw axis.These surfaces, such as cam surface, follower surface, surface of action, and pitch surface, are ruled surfaces.With the restrictions of the geometric characteristics of a hyperboloidal roller, the relative locations of the axes of these cam mechanisms have to satisfy certain relation and the kinds of roller-follower cam mechanisms synthesized in axode contact are verified.The angular velocity of the roller and the screw pitch of the cam pair are derived, and the types of the contact surfaces, the pressure angle, and the purerolling cam pait are also discussed.

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Crack closure in epoxy resin plates with embedded shape memory(SMA)wires as an actuator in intelligent structure members was investigated as a function of the length of crack, duration of the supply of electric current to the SMA wires and the volume fraction of the SMA wires under tensile loads using photoelastic experiments.The effect of heat generation due to the SMA wires in the plate was also investigated.The crack closure was evaluated by the stress intensity factor obtained from photoelastic fringes generated near the crack tip.The results showed that the closure strongly depended on the crack length and duration of the current supply.The closure was not found in the plate with a crack which did not pass through the SMA wires.A complete cessation of the supply caused the disappearance of the closure with time.Continuous current supply resulted in change in quality of the epoxy matrix and separation of the SMA wires from the matrix.The intermittent current supply prevented the separetion and maintained the closure.

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In structural design, the stiffest structure is considered optimal.However, flexibility can provide structures with certain advantages in terms of structural performance or additional function such as mechanical function, if flexibility mode can be specified.Compliant mechanism is a new breed of mechanisms which uses the design concept of structural flexibility to achieve a specified motion.In this paper, an integrated structural optimization method to implement flexibility in the mechanical structure is proposed, and applied to the compliant mechanism design.First, structural flexibility is expressed using mutual energy, and a new multi-objective function incorporating the maximum flexibility and minimum compliance is formulated.Next, a design procedure is constructed using the homogenization design method and image based approach.Finally, some examples of designing compliant mechanisms are presented, which confirm that the method presented here can be applied to the compliant mechanism design.

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Free surface profiles of aluminum sheets under equi-biaxial tension are examined by employing three kinds of fractal analyses, i.e., the zeroset, power spectrum and box-counting metods.With an increase in plastic strain, long-wavelength components of the surface profiles become dominant, and their fractal structure tends to become constant beyond a certain strain.It is found that both surface roughness and fractal dimensions depend on the equivalent strain, independent of the stress ratio.A method for simulating the surface roughening behavior is presented by utilizing the power spectrum method.

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The purpose of the present work is to develop a simple and economical method of punching and forming processings of intractable AFRP(aramid fiber reinforced plastics)laminated composites by improving conventional press working technique.An aramid plate is tightly restrained around the formed region as well as the bottom of the plate, and subsequently it is punched by a specially designed hollow punch.The present improved technique of press working named strong restraining shear processing(SRSP)has led to an excellent processing of intractable AFRP composites, which has never been achieved by any other technology such as water jet cutting or vibration press.

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A new griding method of ultra-high efficiency and high precision for ceramic balls is introduced.The principle of the grinding method is described and the grinding characteristics for Si₃N₄(Hot Isostatically Pressed, HIP)balls was investigated at grinding loads ranging from 2-40 N and drive shaft speeds ranging from 200-5000 rpm using diamond wheels of various grit sizes from 2μm to 100μm.Experimental results show that the method has a material removal rate as high as 29μm / min.The sphericity was improved and reduced from 43μm to 6μm within a very short grinding time of 6 minutes when a SD200 wheel was used.A sphericity of 0.12μm was obtained by using a SD8000 diamond wheel.

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Methods for the study of weakly nonlinear continuous(distributed parameter)systems are discussed.Approximate solution procedures treating reduced-order models of systems with quadratic and cubic nonlinearities obtained with the Galerkin procedure are constrasted with direct application of the method of multiple scales to the governing partial-differential equations and boundary conditions.By means of several examples and an experiment, it is shown that low-order reduced models of nonlinear continuous systems can lead to erroneous results.A method for producing reduced-order models that overcome the shortcomings of the Galerkin procedure is discussed.Treatment of these models yields results in agreement with those obtained experimentally and those obtained by directly attacking the continuous system.Convergence of the reduced-order models as the order increases is also discussed.

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The steady-state responses which the damped Duffing oscillator with a softening spring property under a harmonically stimulating force exhibited in the main resonant frequency region have been analyzed by using both an approximate analytical procedure;that is, the harmonic balance scheme, and a numerical procedure.With regrad to the structure which the system reveals in this region, there exists another branch which seems to be caused by bifurcation from the resonant branch at a certain frequency as well as to the usual resonant and nonresonant branchs.It has been verified that many kinds of periodic solutions exist in the frequency region of interest between this new branch and the resonant one.In addition to the traditional harmonic solutions;that is, resonant and nonresonant solutions and the new branch, there appears a third harmonic solution branch.However, it is absolutely unstable.This unstable solution enables us to explain reasonably the constitution of attractors in this resonant frequency region.Furthermore, an approximate stability analysis of these new branches, including the usual resonant and nonresonant branches, has been developed and has revealed stability problems of all these branches.It has also been shown that chaotic phenomena, which are related to the fundamental harmonics in the region of interest, arise dur to period doubling bifurcation and develop only along the path of the second new branch.

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We consider a pendulum subjected to feedforward and feedback control with periodic desired motions.The pendulum is assumed to be driven by a servo-motor with a small time constant.Here we concentrate on the case in which the desired motion is globally or locally asymptotically stable when its amplitude is zero.Using the averaging method and Melnikov's technique, we show that the desired motion becomes unstable at several bifurcations and chaotic motions occur for the nonzero amplitude case.Numerical simulations are also given and compared with the theoretical predictions for periodic and chaotic motions.

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For a parametrically excited cantilever beam the effect of the tip mass on the nonlinear characteristics of the frequency-response is theoretically presented.The equation of motion governing the system is formulated by Hamilton's pronciple, taking into account the inertia and curvature nonlinearities and a quadratic damping effect of the beam.Using the method of multiple scales and center manifold theory, the bifurcation points of the frequency-response curve are analyzed.It follows that there are two transcritical bifurcations, and in addition to these bifurcations there are two saddle-node bifurcations, in the cases when the tip mass is relatively light and heavy, respectively.Experiments are also performed and the results show good qualitative agreement with the theoretical ones.

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Experimental results are presented on chaotic oscillations of a post-buckled reinforced beam subjected to lateral excitations.The beam is partially reinforced and is clamped at both ends.One end of the beam is arranged to move to an axial displacement by an elastic spring.The beam is deformed to a post-buckled configuration by the axial constraint.Under the post-buckled condition of the beam, chaotic responses are generated in specified regions of exciting frequency.The chaotic responses are examined by the Fourier spectrum, the Poincare projection and the maximum Lyapunov exponent.It is found among other tings that the chaos of the reinforced beam is mainly generated with the lower modes of vibration.The instability regions of chaos as well as the effect of inertia in the axial direction are also examined.

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This paper describes a convenient method of identification of nonlinear vibration system by a neural network using time series data.The neural network with suitable selection of system imputs and outputs are applicable for system identification of nonlinear vibration by learning of response.Learning only time series data of impact response of piecewise linear system, it ispossible to predict both forced vibration response and impact response in time domain by the neural network.Also, by learning only time series data of periodic response in coexisting regions of chaotic and periodic response of Duffing system, it is possible to predict both chaotic and periodic response of forced vibration by the network, for given predicting conditions chosen nearby the learned condition.The effectiveness of the method is demonstrated by numerical simulations for piecewise linear system and Duffing system.

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This paper describes statistical mechanical results of the gear dynamics with and without the effect of shaft stiffness.For this purpose, we use statistical mechanical analysis by means of dynamical structure functions.We have already applied this method to several mechanical chaotic vibrations and shown numerically and experimentally that a series of peaks arising in the dynamical structure functions characterize the chaotic vibrations near bifurcation points.However, the method have never been tested on systems with the backlash.Terefore, statistical mechanical properties of chaotic dynamics arising in the gear system have not been fully understood.This paper studies this point by means of the dynamical structure functions, the Poincare map, and bifurcation diagrams.The chaotic bifurcation of the gear system is characterized by our method.

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It is a very difficult problem to determine the stability of the periodic steady-state vibrations generated in a large-sized nonlinear system with multi-degree-of-freedom.In order to overcome such difficulty, a new pratical method to accurately analyze the stability of the periodic solutions obtained from the method of harmonic balance is developed for a nonlinear structure connected in series.The present method is mainly based on the argument principle and is applicable to the stability analysis of any multi-degree-of-freedom system excited parametrically.By introducing the same treatment as that of the incremental transfer influence coefficient method into the computation process of the present method, the computation speed is improved and the memory size required in the computation is considerably reduced.The validity of the present method is confirmed by the results of numerical computation for some examples.

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Nonlinear forced oscillation of a rotating circular disk excited at a point fixed in space is considered.For theoretical analysis, modal equations are derived from the govering partial differential equations.Then, based on these modal equations, the characteristics of oscillation induced by a harmonic excitation are investigated.Numerical calculation is conducted for a typical case in which the excitation frequency is near the primary resonance points of the forward and backward traveling wave modes.It is shown that near the primary resonance point of the backward traveling mode, the forward traveling mode oscillation occurs in addition to the backward traveling mode oscillation, and conversely, near the primary resonance point of the forward traveling mode, the backward traveling mode oscillation occurs in addition to the forward traveling mode oscillation.An experimental analysis is also conducted, which confirms the validity of the theoretical analysis.

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The Jeffcott rotor is the most widely used theoretical model in the analysis of rotor systems.This model satisfies the condition of 1:(-1)internal resonance, and we clarified the effect of this internal resonance on nonlinear steady-state oscillations at the major, twice the major and three times the major critical speeds in previous papers.In this study, we investigated nonstationary oscillations during acceleration through the major critical speed in the Jeffcott rotor and other rotor systems which almost but not exactly satisfy the 1:(-1)internal resonance relation, and investigated the influence of internal resonance.The following are clarified theoretically and experimentally.(a)Nonstationary oscillations of the Jeffcott rotor and other rotor systems whose natural frequencies almost satisfy the 1:(-1)relation are influenced by the internal resonance.(b)It is easier to pass the major critical speed of a rotor system with internal resonance than that of a rotor system with no internal resonance.(c)When the system has slight discrepancies among critical speeds, that is, almost satisfies the relation of internal resonance, the rotor can pass the major critical speed very easily with small amplitude even if the acceleration is small.

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As a fundamental study on the squeal of a railway wheel running on a rail with roughnesses, a rod was rubbed against the circumference of a thin stationary steel disk in its axial direction under random excitation.The disk serving as a railway wheel was clamped centrally with a free periphery.White noise excitation was applied to the disk on the assumption that external forces due to surface roughnesses of the rail are random.The measurements and analyses of the frictional vibration of the disk revealed that squeals with only a single mode occur at the low random excitation level and squeals with multiple modes occur more frequently than those with a single mode as the random excitation level increases.

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The objective of this paper is to analyze chatter vibrations in an automotive wiper assembly which consists of two blades driven by a direct current motor via one link.For this purpose, first, the characteristics of the chatter vibrations in a currently used wiper are examined experimentally.Then, by assuming that the wiper is modeled by a two-degree-of freedom system, the equations of motion are derived.They are solved for practical wiping speeds.By comparing the results with the experimental results, it is found that the derived equations well predict the experimental results.Based on the equations it is concluded that the chatter vibration is mode-locked motion.Finally, the equations of motion are solved for lower wiping speeds.It is predicted that for these speeds, chaotic motion as well as quasi-periodic and periodic motion can occur.

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This paper describes theory and experimental verification of a self-excitedvibratory system which can excite lower mode of the original passive system of a flutter wing mechanism as a hypothetical model of insect wings.In order to realize a self-excitation system of natural mode of vibration, we proposed two kinds of positive velocity feedback with nonlinear negative damping:Van der Pol(VDP)type and negative Coulomb friction(NCF)type.In order to drive only the lower mode, a low pass filter and cross feedback methods were proposed.It was found that the analytical results were in good agreement with the experimental ones, and that the NCF type can excite the limit cycle motion more rapidly than the VDP type.Robustness of the selfexcited flutter motion to the change to mass parameter was also demonstrated.

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Elastic yarns in the winder system of a textile machine are deformed into a certain convex polygon in the process of winding at an operating speed of the bobbin holder rotating viscoelastically in contact with the drive roll.The polygonal deformation inceases and develops into a serious vibration of the machine.This paper presents a model and a theoretical analysis to investigate the mechanism of this vibration phenomenon which is regarded as instability due to the time lag.The bobbin holder and the drive roll are both modeled by the one-mass one-shaft system.From the numerical computations using parameters obtained experimentally, the analytical results showed a good agreement with the phenomenon generated in the actual machines.

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The nonlinear vibrations of a structure coupled with water sloshing in a circular cylindrical tank are theoretically and experimentally studied.For the purpose of vibration control the liquid tank is installed on the structure subjected horizontally to a sinusoidal excitation.In the theoretical analysis, the only nonlinearity of fluid force due to large sloshing amplitude is considered.The theoretical resonance curve for the harmonic oscillation is presented when the water surface is in a state of planar motion(i.e., when the excitation is small).When the excitation is comparatively large, the resonance curve is obtained by a swept sine test in a numerical simulation.As a result, it is found that the resonance curve changes from a soft spring type to a hard spring type as the water level decreases.In the case of a large excitation, a swirl motion of water surface and an almost periodic oscillation of the structure appear in certain regions of the excitation frequencies.Also, a super-summed-and differential harmonic oscillation can occur at the tuning frequency due to the nonlinearity of the fluid force.These theoretical results agreed quantitatively well with the experimental results.

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Flow-induced vibration of a vertical cantilevered pipe with an end mass, is examined theoretically and experimentally under the supercritical condition that the fluid velocity of an axial flow in the pipe is slightly over its critical value.As the fluid velocity is increased above the critical value of the fluid velocity, i.e., the critical velocity, the planar or nonplanar pipe vibrations are self-excited due to the internal flow.In this paper, the effect of the end mass is discussed with the nonlinear coupled equations governing the nonplanar pipe vibration.Moreover the experiments were conducted with a silicon rubber pipe conveying water, and the spatial behaviors of the pipe were observed by means of the image-processing system.

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This paper deals with the experimental and analytical study of seismic response behavior of piping systems in industrial facilities.In industries, Piping systems are generally supported on hangers, rod restraints, friction supports etc.A three dimensional mock-up piping supported on rod restraints and friction support is excited by large scale(15m×15m)shaking table.At the friction support, two dimensional nonlinear sliding motion is observed between the piping and friction support due to simulated earthquake excitation.Free vibration analysis is carried out using FE model of the piping system.A modal analysis procedure is evolved to calculate the responses of the piping supported on friction support.Maximum responses and dissipated energy at the friction support obtained analytically are compared with those obtained in experiments.A good agreement is observed between the experiment results and those obtained analytically.

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This paper presents the dynamic analysis of curving behavior of railway vehicles.Curving simulation of vehicles running at low speed is important from a point of view of safety.It haven't often been done and results of simulation usually differ from measured them.Though the influence of leveling valves and differential pressure valves can be generally ignored in the case of simulation of vehicles running at high speed, the effects of them must be considered at low speed.Therefore we improved A'GEM which is multibody dynamics software to add non linear air suspension elementswith leveling valves and differential pressure valves.The results of curving simulation were compared with experiments with good agreement.

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Phenomena such as singing flame or Rijke tube are heat-induced vibrations of air column in a tube, which are coupled with heated fluid motion.In this paper, computation of air column vibration with local heat input is carried out to the extent that amplitude of pressure variation is fully increased and amplitude growth rate is saturated.Computed amplitude growth rates are compared with those obtained by experiments for a vertical tube and computational validity is assessed.From the computational results, it appears that both the fluid behavior around the heater and the energy dissipated by viscosity influence the amplitude growth rate of pressure variation.The energy of driving or damping air column vibration is estimated and discussed for explaining the mechanism of air column excitation.

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