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丸山, 真一 ; 小野里, 直樹 ; 永井, 健一 ; 山口, 誉夫
概要:
application/pdf<br />Journal Article<br />Experimental results are presented on nonlinear vibrations of a cylindrical shallow shell-panel with a rectangular platform. Opposite cylindrical edges of the shell-panel are clamped and the
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other opposite straight edges are simply supported. One side of the clamped edges is connected with elastic springs and is movable to an in-plane direction. The simply supported edges are supported by adhesive elastic films. Under the in-plane compressive force over the buckling load, the post-buckled configuration is obtained. In the specific compressive force, the shell-panel has the conditions of internal resonances. By exciting the shell-panel with periodic lateral acceleration, nonlinear periodic and non-periodic responses are observed in specific regions of the excitation frequency. These responses are examined with the Fourier spectra and the principal component analysis. Non-periodic responses are evaluated by the maximum Lyapunov exponent. Under the smaller magnitude of the compressive force, the principal resonance and the sub-harmonic resonance of 1/2 order corresponding to the lowest mode are obtained. Furthermore, the combination resonance dominated by the higher modes of vibration is also obtained. Under the larger magnitude of the compressive force, the chaotic response is generated from internal resonances close to the lowest natural frequency. Applying the principal component analysis, dominant modes of vibration and their contributions are confirmed on the combination resonance and the chaotic response.
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山口, 誉夫 ; 永井, 健一 ; 丸山, 真一
概要:
application/pdf<br />Journal Article<br />It's difficult to clarify deformation patterns in chaotic vibration of a beam, because multiple modes are generated simultaneously. This paper describes identification of spatial modes in a
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chaotic vibration for a buckled beam. KL (Karhunen-Loeve) method was applied to the identification. Using this method, time histories are decomposed into components which have no correlation each other. Contribution of the components to the original time histories can be estimated as eigenvalues of covarriance matrix of the time histories. Moreover, we used the corresponding eigenvectors to identify spatial modes in the chaos. We focused on chaotic motion of the beam involving a dynamic snap-through phenomena. The time histories for the identification were given from numerical analysis. The identified eigenvectors were compared with the natural modes of vibration. As a result, effectiveness of KL method was revealed.
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永井, 健一 ; 鈴木, 央 ; 山口, 誉夫 ; 丸山, 真一
概要:
application/pdf<br />Journal Article<br />Analytical result is presented on chaotic oscillations of a buckled beam under an axial spring. The beam with a concentrated mass is clamped at both ends. The beam is compressed to the
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post-buckled configuration by the axial spring. The beam is subjected to periodic lateral acceleration. Introducing a mode shape function to a basic equation, nonlinear ordinary differential equations of multiple-degree-of-freedom system is reduced to by the Galerkin procedure. Changing a stiffness of the axial spring, an internal resonance condition of one to two is selected. First, steady-state resonance responses are calculated by the harmonic balance method. The chaotic responses are obtained by a numerical integration. The chaotic responses are examined by the Poincare projection, the maximum Lyapunov exponent and bifurcation diagrams. The chaos due to the internal resonance is easily generated by a small amplitude of excitation. As the exciting frequency decreased, transition to the chaos from a periodic response needs larger amplitude of excitation. In a lower range of frequency, the chaotic oscillations are mixed with the internal resonance and the dynamic snap buckling. Two modes of vibration contribute to the chaos related to the internal resonance. Number of the modes increases more than three for the chaos involved the dynamic snap buckling.
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永井, 健一 ; 松村, 修二 ; 池澤, 龍 ; 山口, 誉夫 ; 石田, 光之
概要:
application/pdf<br />Journal Article<br />Experimental results are presented for self-excited vibration of an automotive wiper. The self-excited vibration is generated by a stick-slip motion. It is of practical importance to suppress the
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self-excited vibration of the wiper. To find out modal coupling in the vibration of the wiper, simplified wiper is constructed. Movement of simplified wiper is separated into horizontal and vertical directions to simulate a motion of the actual wiper. The simplified wiper and the actual wiper are used for experiments. Static deformation of a wiper blade is measured. The blade is pressed on a glass surface. The wiper blade shows characteristics of soft-hardening spring involving a buckled deformation. Modal coupling in the self-excited vibration is examined by sweeping the wiper on a rotating glass table with constant angular velocity. Increasing a load pressed on the blade, coupling vibration is generated due to self-excitations along glass surface and parametric movements in vertical direction. The vibration amplitude is suppressed extremely when the load is close to the buckling load. Moreover, the maximum Lyapnov exponent of the dynamic response shows least number of the modes contributed to the self-excited vibration.
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山口, 誉夫 ; 永井, 健一
概要:
application/pdf<br />Journal Article<br />This paper presents numerical results on chaotic vibrations of a shallow cylindrical shell-panel under harmonic lateral excitation. The shell with a rectangular boundary is simply supported
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for deflection and the shell is constrained elastically in both in-plane directions. The effects of bi-axial in-plane elastic constraint on the chaotic behaviors of the shell are focused on. Using the Donnell-Mushtari-Vlasov type equation modified with an inertia force, the basic equation is reduced to nonlinear differential equation of a multiple-degree-of-freedom system by the Galerkin procedure. To estimate regions of the chaos, first, nonlinear responses of steady state vibration are calculated by the harmonic balance method. Next, time progresses of the chaotic response are obtained numerically by the Runge-Kutta-Gill method. The chaotic responses due to dynamic snap-through are examined by Fourier spectrum, Poincare projection and Lyapunov exponent. Contribution of multiple modes of vibration to the chaos is examined carefully by the Lyapunov dimension. The main results can be summarized as follows. Loosening the in-plane constraint perpendicularly along the curved edges and tightening the in-plane constraint along the straight edges, chaotic motion is restricted with less number of modes of vibration.
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山口, 誉夫 ; 永井, 健一 ; 鈴木, 央
概要:
application/pdf<br />Journal Article<br />Chaotic responses are investigated for a post-buckled beam under the interaction between internal resonance and dynamic snap-through. The beam with variable cross section is clamped at both ends and
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the beam is axially compressed to a post-buckled configuration. The buckled beam is excited by a periodic acceleration. Applying the Galerkin method to the governing equation of the beam, nonlinear differential equations of a multi-degree-of-freedom system are reduced. Periodic solutions of steady-state responses are calculated by the harmonic balance method. In a typical frequency region, chaotic response bifurcates from the periodic response. Time progress of the chaotic motion is calculated by the numerical integration. The chaotic response is examined in detail by the Fourier spectrum, the Poincare section, the Lyapunov exponent and the Lyapunov dimension, respectively. Under the condition of the one-to-two internal resonance, the chaos is generated by a small amplitude of excitation. Two modes of the vibration induced in the chaos. Increasing the amplitude of excitation, the chaotic response transits to the complicated response coupled with the dynamic snap-through and the internal resonance. Induced modes in the chaos are counted as nearly four.
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谷藤, 克也 ; 花村, 実 ; 永井, 健一
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application/pdf<br />Journal Article<br />Several papers have been published in the last few years about chaotic behaviors occurring in the running vibration of railway vehicles. Those papers showed the possibility of occurrence of chaotic
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vibration by means of a numerical simulation methed. This paper deals with an experimental study, the aim of which is to establish the practical occurrence of such a chaotic vibration, using a scale model of a single wheelset running on a test stand. As a result, the running vibration of the wheelset shows chaotic behavior when the wheel flange collides hard against the side of the rail due to the hunting motion arising with the increase of running speed. This is the first experimental result on the chaotic vibration of running wheelsets. The chaotic features are confirmed with maximal Lyapunov exponents, correlation dimension and other factors.
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谷藤, 克也 ; 永井, 健一
概要:
application/pdf<br />Journal Article<br />In this study, chaotic behavior of a single wheelset rolling on a rail has been examined numerically. The single wheelset model is assumed to be elastically restrained from an imaginary truck
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frame moving in parallel with a straight track. In the simulation, nonlinear forces of the flange-rail contact and the wheel-rail creep are involved. When the elastic restraint is decreased, self-excited lateral oscillation occurs even in the practical speed range ; then the oscillation bifurcates into chaotic behavior. The chaotic features are confirmed by the correlation dimension, bifurcation diagram, power sepctrum and Poincare map.
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谷藤, 克也 ; 永井, 健一 ; 長屋, 幸助
概要:
application/pdf<br />Journal Article<br />The running vibration of a bogie car is considerably affected by its operation speed. This paper describes the results of a calculation analysis on the vertical vibration of a Shinkansen
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electric car at the speed range up to 510 km/h, assuming a drastic speed-up of the Shinkansen. The vibration of each natural modes, except the body-bending mode, tends to increase uniformly with the operation speed. The vibration of the first body-bending mode varies greatly due to the averaging effects of the track roughness through the length between truck centers in the car, and it deteriorates the riding comfort further in the speed ranges near 270 km/h and higher than 450 km/h. As an example, the flexural rigidity of the car body is examined to determine countermeasures suitable for 270 km/h operation.
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| 10.
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谷藤, 克也 ; 永井, 健一
概要:
application/pdf<br />Journal Article<br />The body-bending vibration of a bogie car is analyzed with two calculation models : one the exact model based on the theory of beam and the other the 1-mode approximation model in which only the
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fundamental mode is taken into consideration. First, the frequency responses calculated with the two models are compared to investigate the effects of the higher bending modes on the whole vertical vibration of the car body. These car body acceleration curves are transformed to the acceleration PSD through a formulated track irregularity PSD and compared with field test data to verify the calculation models. Then, the applicability of the conventional 1-mode approximation model to the quantitative examination is estimated in the range up to 100 Hz, where 4 modes of the car body bending are included.
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