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永井, 健一 ; 大山, 貞夫 ; 山口, 誉夫
概要:
application/pdf<br />Journal Article<br />Analytical results are presented on chaotic vibrations of arches with axial elastic constraints. The arch with variable-cross-section is subjected to a periodic lateral force. The mode shape
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function proposed by the senior author-satisfies four sets of boundary conditions combined with a simply supported end and a clamped end. Basic equation is reduced to an ordinary differential equation of multiple-degrees-of-freedom system by the Galerkin procedure. Steady-state responses of the arches are calculated by the harmonic balance method. When the arch is contained simply supported condition, chaotic responses are excited easily in a specific frequency region. The chaotic responses are examined by the Runge-kutta-gill method. Following conclusion was obtained. In the chaos of the arch with the rigid axial constraint, many natural modes of vibration of both symmetric and asymmetric modes are excited simultaneously. The Lyapunov dimension increases as the rigid axial constraint of the arch becomes more tight. Furthermore, the chaotic attractors in the Poincare section show fractal geometries.
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永井, 健一 ; 春日, 邦夫 ; 鎌田, 昌樹 ; 山口, 誉夫 ; 谷藤, 克也
概要:
application/pdf<br />Journal Article<br />Experimental results are presented on chaotic oscillations of a reinforced beam subjected to lateral excitations. The beam is partially reinforced with boxed-type stringers. The beam is clamped at
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both ends on a base frame. One end of the beam is arranged to move to an axial displacement by attachment to 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. A response is expected from a system with a lower degree of freedom. The chaotic responses are analyzed by the Fourier spectrum, the Poincare section and the maximum Lyapunov exponent. It is found that the chaos of the beam is generated with the fundamental mode of vibration. Chaotic response includes the resonance modes both of a higher lateral vibration and of an axial vibration. The Poincare projections of the chaos show clearly the stretching-and-folding mechanism of the chaos attractor. The instability boundary of the chaos is obtained in the plane of exciting frequency and amplitudes of excitation.
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永井, 健一 ; 山口, 誉夫
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application/pdf<br />Journal Article<br />This paper presents the numerical simulation for the chaotic vibrations of a post-buckled beam with a variable cross section. The beam is clamped at both ends and is compressed in an axial
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direction. When the beam is deformed to a post-buckled configuration, chaotic vibration will be excited easily under periodic lateral acceleration. Applying Galerkin method, the basic equation of the beam is reduced to the ordinary differential equation of multiple-degrees-of-freedom systems. To get the steady-state response of the beam, the harmonic balance method is used. In a typical region of frequency, the chaotic response is excited. The chaotic time progress is calculated by the numerical integration. The chaotic response is examined carefully by the Poincare projection, the Lyapunov exponent and the Lyapunov dimension. The results of tapered beams are compared with that of the straight beam. The chaotic response with the asymmetric mode of vibration appears remarkably. The response shows the complicated projection to the chaotic attracter, moreover, the Lyapunov dimension takes higher value. The chaos of the beam with variable cross section shows the more complicated behavior to that of straight beam.
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永井, 健一 ; 山口, 誉夫
概要:
application/pdf<br />Journal Article<br />This paper presents experimental results on chaotic vibrations of a post-buckled beam carrying a concentrated mass. The concentrated mass is attached at the point apart from the center of
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the beam. The beam is clamped at both ends to a base frame. The beam is deformed into a post-buckled configuration by an initial axial displacement. The displacement is controlled by the thermal elongation of the beam to the base frame. The chaotic vibrations of the post-buckled beam appear within a restricted range of exciting frequency. The chaotic responses are generated in the sub-harmonic resonance regions of both 1/2 and 1/3 orders. The maximum Lyapunov exponent is 1.4. The chaos attractor of the dynamic response is focused clearly onto the Poincare section. The correlation dimension saturates to d=3.6 within the embedded dimension up to 10 or more. Other chaotic responses appear at the regions of a superharmonic resonance of the second order and the ultra-subharmonic resonance of fourth to fifth order corresponding to the lowest mode of vibration.
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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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永井, 健一 ; 山口, 誉夫 ; 谷藤, 克也 ; 楊, 平
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application/pdf<br />Journal Article<br />This paper presents the experimental results on chaotic vibrations of a cantilevered beam deformed by a stretched cable. The beam is deformed to a postbuckled configuration by a cable that is
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extended from the top to bottom of the beam. We call the deformed beam a 'tendon beam'. As a lateral load is applied to the beam statically, the beam changes to another equilibrium position accompanied with a snap through deformation. When the beam is subjected to periodic excitation, a large-ampltiude response is generated by resonance. Chaotic motion appears near the fundamental resonance region as well as the region in the higher mode of vibration. Both chaotic motions are confirmed as the chaos due to maximum Lyapunov exponent with a positive number. By recording the Poincare section of the chaos behavior, fractal attractors are clearly focused in the fundamental resonance region. The more complicated attractor is obtained in the resonance region of the second mode of vibration. The correlation dimension of the chaos in the second mode is higher than that of the fundamental mode. It is generated by the two-to-thirtees internal resonance between the fundamental mode and second mode.
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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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| 8.
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永井, 健一 ; 小山, 富夫 ; 渡辺, 一実 ; 谷藤, 克也 ; 籠谷, 正則
概要:
application/pdf<br />Journal Article<br />Analytical results are presented for nonlinear vibrations of a timing belt with a rotor pulled by a magnetic force. With application of the Galerkin method to the basic equation, the ordinary
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differential equation in a multi-degree-of-freedom system is reduced. The steady-state responses are calculated using the harmonic balance method. The numerical results show the following conclusions. The resonance frequency in each mode of vibration decreases with the increment of the mass in the rotor. The amplitude of nonlinear response decreases with the increment of the cross section in the belt. The magnetic force acting on the belt changes the characteristics of nonlinear spring from the hardening type to the softening-hardening type. The magnetic force on the belt easily shifts the frequency away from the resonance frequency and facilitates supression of the resonance amplitude.
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| 9.
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永井, 健一 ; 大佐々, 吉宏 ; 長屋, 幸助 ; 武田, 定彦 ; 谷藤, 克也
概要:
application/pdf<br />Journal Article<br />An analytical method is presented for the bending vibration of a circular dise carrying concentrated masses, introducing a new mode of shape function to the Galerkin method. Deflection of
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the plate is expressed by a product of the mode shape function along radial direction and the circumferential periodic function. The mode shape function is assumed to be the sum of the product of the trigonometrical function and the finite power series. The coefficients of the power series are found to be satisfied by the boundary condition of the plate. Applying the Galerkin method, the number of sets of differential equation with second-order time functions are reduced. It is found that this method gives good accuracy to the natural frequencies within the small number of terms for unknown time functions
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長屋, 幸助 ; 平田, 康夫 ; 鶴見, 豊明 ; 武田, 定彦 ; 永井, 健一 ; 谷藤, 克也
概要:
application/pdf<br />Journal Article<br />Stresses in elliptical-cross-section coil springs become small as compared to other springs used in practical machines at a certain aspect ratio. This article presents a simplified stress
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expression for designing the elliptical-cross section coil springs. The stresses obtained by the present design formula are compared with those obtained by numerical methods. It is ascertained that the present formula is applicable to design the elliptical-cross section-coil springs.
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