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| 1.
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小野里, 直樹 ; 丸山, 真一 ; 永井, 健一 ; 山口, 誉夫 ; 黒澤, 正樹
概要:
application/pdf<br />Journal Article<br />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
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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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| 2.
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永井, 健一 ; 丸山, 真一 ; 長谷川, 光貴 ; 山口, 誉夫
概要:
application/pdf<br />Journal Article<br />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
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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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| 3.
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山口, 誉夫 ; 永井, 健一 ; 丸山, 真一 ; 斉藤, 友明
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application/pdf<br />Journal Article<br />This paper describes vibration analysis using finite element method for two viscoelastic blocks connected by a nonlinear concentrated spring. One of the blocks is supported by another linear
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concentrated spring. The restoring force of the nonlinear concentrated spring has cubic nonlinearity and linear hysteresis damping. Finite element for the nonlinear spring is expressed and is connected to the viscoelastic blocks modeled by linear solid finite elements in consideration with complex modulus of elasticity. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. Influences of share of dissipated energy on nonlinear frequency responses for the viscoelastic blocks are clarifi
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| 4.
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永井, 健一 ; 岡田, 賢二 ; 丸山, 真一 ; 山口, 誉夫
概要:
application/pdf<br />Journal Article<br />This paper presents experimental results on chaotic vibrations of a thin circular plate with a circular center hole. The plate is clamped around the outer edge by rigid rings. Asymmetric
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defletion of the plate is induced by initial imperfection and in-plane compressive stress due to thermal elongation of the plate. Two natural modes of vibration with one nodal diameter are generated in each natural frequency. These nodal diameters are perpendicular to each other. Under periodic excitation, a dominant chaotic response generated due to the type of one-to-two internal resonance in a specific frequency range. The chaotic response is inspected by the Fourier spectrum, the Poincare projection and the maximum Lyapunov exponent. The principal component analysis is adapted on the chaotic response to confirm modal contributions. The multiple time responses of the plate are measured at four positions simultaneously for long-time interval. The modes of vibration without nodal diameter and the two modes with one nodal diameter contribute to the chaotic response, predominantly. Furthermore, changing the calculation of principal component with shorttime interval, the chaotic response of the plate shows the motion of irregular traveling waves.
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| 5.
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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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| 6.
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永井, 健一 ; 丸山, 真一 ; 武藤, 康太 ; 山口, 誉夫
概要:
application/pdf<br />Journal Article<br />Analytical results are presented on nonlinear vibrations of a cantilevered beam constrained by a stretched string at the tip end. The beam is subjected to periodic lateral acceleration. Governing
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equations of motion and boundary condition, which have nonlinear geometrical coupling with an axial force, are derived by the Hamilton's principle. The mode shape function proposed by the senior author is introduced to reduce the governing equations to the nonlinear differential equation by the modified Galerkin method. The mode shape function is expressed with the product of the trigonometrical function and the finite power series truncated with the fourth order. The coefficients of the power series are determined by solving the homogeneous equation for the boundary condition at the buckling state of the beam. The trigonometrical function can express the form of higher mode of vibration. Nonlinear periodic responses are calculated by the harmonic balance method. Nonlinear non-periodic responses are obtained by the numerical integration. Comparing the nonlinear responses by the analyses with the approaches of single-degree-of-freedom and of multiple-degree-of-freedom, higher mode of vibration play important roles both in the periodic response and in the chaotic response. It is shown that the analysis based on the approach of the mode shape function makes fairly good prediction to the nonlinear phenomena of the cantilevered beam constrained by the stretched string.
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| 7.
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柳澤, 大 ; 永井, 健一 ; 丸山, 真一
概要:
application/pdf<br />Journal Article<br />Experimental results and analytical results are presented on the effects of axial compressive load on chaotic vibrations of a clamped-supported beam subjected to periodic lateral
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acceleration. The beam is elastically compressed by an axial spring at the simply supported end. In the experiment, nonlinear and chaotic responses are detected under various compressions. In the analysis, the governing equation is reduced to nonlinear differential equations of a multiple-degree-of-freedom system by the Galerkin procedure. The nonlinear periodic responses are calculated by the harmonic balance method. The chaotic responses are numerically integrated by the Runge-Kutta-Gill method. The chaotic responses of the beam under axial compression are examined with the Fourier spectra, the Poincare projections, the maximum Lyapunov exponents and the principal components by the Karhunen-Loeve transformation. Both results of the experiment and the analysis coincide fairly well in detail. The frequency region of the chaos spread with the increment of the axial compressive force. The chaotic responses are generated within the axial compression range of the same ratio to the each buckling load. Distinct fractal pattern can be observed in the attractors of Poincare projections. The number of modes generated in the chaos is counted as three by the maximum Lyapunov exponent and the Lyapunov dimension
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| 8.
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丸山, 真一 ; 永井, 健一 ; 山口, 誉夫 ; 加藤, 考行
概要:
application/pdf<br />Journal Article<br />Numerical results are presented on chaotic vibrations of a cantilevered beam u
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nder vibroimpact. The analytical model consists of a cantilevered beam, subjected to periodic excitation, and a bar that restrains the amplitude of the beam. Equation of the motion of the beam is discretised by the finite element method and impacts of the beam are computed by using the coefficient of restitution rule. Time responses of the beam are calculated with direct integration by the Newmark-β method. Then the responses are inspected with the frequency response curves, the Fourier spectra, the Lyapunov exponents and the principal component analysis. The numerical results are compared with the experimental results that are previously presented by the authors, which verify our numerical results. Effects of the location of the bar and of the clearance between the bar and the beam on the chaotic responses are examined by the numerical results. As the location of the bar becomes farther from the clamped end and the clearance becomes smaller, the frequency region of the impact vibration is enlarged. The chaotic responses of the beam generally have contribution ratio of higher vibration modes less than 5%. However, when the location of the impact is close to a node of a higher mode or super-harmonic resonance of a higher mode is excited, contribution of the higher mode increases up to 10% to 30%.
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| 9.
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丸山, 真一 ; 加藤, 考行 ; 永井, 健一 ; 山口, 誉夫
概要:
application/pdf<br />Journal Article<br />Experimental results are presented on chaotic vibrations of a cantilevered beam under vibroimpact. A rigid bar that is located close to the free end of the beam limits the amplitude of the beam under
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lateral periodic acceleration, and then asymmetric vibroimpacts are induced. In the frequency region of the impact vibration near the fundamental resonance of the lowest mode, two regions of chaotic responses are observed. There is one impact in an excitation cycle in the higher frequency region of the chaos, while occurrence of impacts in the lower frequency region is less frequent than the former one. The maximum Lyapunov exponent of the chaotic response in the higher frequency region takes higher value than that of the chaos in the lower frequency. Mode contributions to the chaos are inspected by the principal component analysis. The lowest mode of vibration prevails in the vibroimpacting response. In the regions of the chaos, contribution of the second mode of vibration to the chaotic responses increases up to 5%. As the exciting frequency is increased, the contribution of the second vibration mode to the chaos becomes larger owing to the increase in the amplitude of impact vibration. Furthermore, contribution of the second vibration mode drastically increases as the super-harmonic resonance of the second mode is generated. The maximum Lyapunov exponent increases as the contribution of the second mode increases, which implies the close relation between the complexity of the chaotic responses and the participation of the higher modes of vibration.
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| 10.
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山口, 誉夫 ; 中原, 直人 ; 永井, 健一 ; 丸山, 真一 ; 藤井, 雄作
概要:
application/pdf<br />Journal Article<br />This paper describes vibration analysis using finite element method for elastic blocks connected by a nonlinear concentrated spring. The restoring force of the spring is assumed to be
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expressed by power series of the relative displacement between ends of the spring. Finite element for the nonlinear spring is expressed and is connected to the elastic blocks modeled by linear solid finite elements. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. Influences of Young's modulus on nonlinear frequency responses for the elastic block are clarified.
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| 11.
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丸山, 真一 ; 永井, 健一 ; 服部, 伯慕 ; 山口, 誉夫
概要:
application/pdf<br />Journal Article<br />Analytical results are presented on chaotic vibrations of a shallow arch with initial configuration of catenary. The shallow arch is simply supported at both ends and is subjected to periodic
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lateral force. Equations of motion are reduced to ordinary differential equations of multiple-degree-of-freedom system by the Galerkin procedure. To clarify effects of sag-to-span ratio on chaotic motions, first, steady-state responses are calculated by the harmonic balance method. The chaotic responses are obtained by numerical integration and are examined by Poincare projection, the maximum Lyapunov exponent and bifurcation diagrams. For the arch with comparatively small sag-to-span ratio, chaotic vibrations are generated mainly in the regions of subharmonic resonance of 1/3 order and of ultra-subharmonic resonance of 3/2 order, accompanied by the lowest-symmetric-mode of vibration. As the sag-to-span ratio increases, chaotic responses are generated from the subharmonic resonances both of 1/2 and 1/3 orders. Furthermore, chaotic motion appears within a wider range of exciting frequency and the number of modes that contribute to the chaos increases. Period doubling bifurcation was mainly observed in the bifurcation from periodic responses to chaotic ones. Hopf bifurcation was also found for the arch that satisfies the condition of internal resonance.
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| 12.
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山口, 誉夫 ; 中原, 直人 ; 永井, 健一
概要:
application/pdf<br />Journal Article<br />This paper describes vibration analysis using finite element method for an elastic block supported by a nonlinear concentrated spring. This block is connected to another block by a
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linear concentrated spring. The restoring force of the nonlinear spring has cubic nonlinearity. In this system, resonance responses mainly involve nonlinearity due to two vibration modes. Finite element for the nonlinear spring is expressed. Then the nonlinear spring element and linear spring element are combined to the elastic blocks modeled by linear solid finite elements. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled differential equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. Influences of Young's modulus on frequency responses are clarifed.
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| 13.
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山口, 誉夫 ; 永井, 健一 ; 丸山, 真一 ; 油田, 知宏
概要:
application/pdf<br />Journal Article<br />This paper describes vibration analysis using finite element method for an elastic block supported by a nonlinear concentrated spring. The restoring force of the spring has cubic
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nonlinearity. Finite element for the nonlinear spring is expressed and is connected to the elastic block modeled by linear solid finite elements. Further, the discretized equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. This transformation yields computation efficiency. Influences of Young's modulus on nonlinear frequency responses for the elastic block are clarified.
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| 14.
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山口, 誉夫 ; 永井, 健一 ; 丸山, 真一
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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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| 15.
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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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| 16.
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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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| 17.
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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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| 18.
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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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| 19.
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MATSUE, Junji ; NAKAZATO, Takashi ; SHIRAI, Hiroyuki
概要:
application/pdf<br />Journal Article<br />A dynamic analysis of a free piston Vuilleumier cycle heat pump was performed by a time-stepping integration method. The nonlinear relationship between displacement and force for pistons was taken
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into account for the motion of reciprocating components, in addition to the pressure change of working gas, nonlinear viscous dissipative force due to an oscillating flow and discontinuous damping force caused by solid friction. The displacement of pistons and pressure changes in the Vuilleumier cycle heat pump were integrated by an ideal isothermal thermodynamic relationship. It was assumed that the flow friction was proportional to the kinematic pressure of working gas, and that the solid friction at the seals was due to the functions of the working gas pressure and the tension of seal springs. In order to investigate the dependence of the characteristics of a machine on various dynamical parameters, some calculations were performed for a proposed case study machine and discussed. The roles of working gas pressure, the displacer piston rod and dissipative force due to flow and solid friction were clarified, and the proposed method was found to be very effective in predicting dynamic behavior of free piston Vuilleumier cycle heat pumps and in designing the machine components.
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| 20.
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NAGAI, Ken-ichi ; KASUGA, Kunio ; KAMADA, Masaki ; YAMAGUCHI, Takao ; TANIFUJI, Katsuya
概要:
application/pdf<br />Journal Article<br />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
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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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| 21.
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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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| 22.
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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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| 23.
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長屋, 幸助 ; 周東, 俊介
概要:
application/pdf<br />Journal Article<br />Three dimensional analytical results for the levitation force of a vibrating high-Tc superconducting levitation system were presented. When the levitated superconductor vibrates, the
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levitation force shows nonlinear relationships with the air gap, amplitude and vibration frequency, so that the convensional models which do not consider dynamic effects cannot be applied. In the model proposed by(Uesaka et al.), dynamic effects are considered, but the critical current is constant. We propose an improved Kim-model which is applicable to vibration problems of conductors. Numerical results for the levitation force were obtained and compared with previously published experimental data. A modeling method for the superconducting levitation system was presented, and the nonlinear spring constants obtained in an analysis which included the effects of air gap, amplitude and frequencies were given. Numerical calculations were carried out for nonlinear vibrations of the system based on the modeling results.
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| 24.
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永井, 健一 ; 山口, 誉夫
概要:
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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| 25.
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長屋, 幸助
概要:
application/pdf<br />Journal Article<br />This paper discusses an actuator consisting of a permanent magnet with an electromagnet and a high Tc superconducting disc. An analytical solution for calculating levitation forces
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for the system was obtained. The obtained levitation force coincided with the previously published result. The equation of motion of the levitated body subjected to base disturbances under control was presented. Numerical calculations were carried out for some typical cases. Nonlinear vibrations of the system were first discussed, then the method of vibration isolation control using the direct disturbance cancellation combining the velocity feedback control was discussed. It was clarified that the present control method is valid for controlling the nonlinear system like the magnetically levitated superconducting body.
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| 26.
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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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| 27.
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松栄, 準治 ; 白井, 紘行 ; 大竹, 雅久 ; 黒沢, 美暁
概要:
application/pdf<br />Journal Article<br />A dynamic analysis of free-piston Vuilleumier-cycle heat pumps has been carried out by a time-stepping integration technique. This technique allows application of a nonlinear relationship between
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displacements and working gas pressure variations in the equations of motion for reciprocating components. Although ideal isothermal thermodynamics was assumed for the Vuilleumier cycle, the present analysis provided more accurate information on its characteristics than the linearized dynamics. Some calculations for a case study were performed, including dissipative forces with a nonlinear relationship in the equations. It was found that the present method was very effective in predicting the dynamic behavior of free-piston Vuilleumier-cycle heat pumps and in designing the components of machines.
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| 28.
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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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| 29.
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永井, 健一 ; 山口, 誉夫 ; 谷藤, 克也 ; 楊, 平
概要:
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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| 30.
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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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| 31.
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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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| 32.
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永井, 健一 ; 渥美, 全弘 ; 杉山, 晋一 ; 長屋, 幸助 ; 谷藤, 克也 ; 武田, 定彦
概要:
application/pdf<br />Journal Article<br />This paper presents analytical results of non-linear vibrations of a traveling beam levitated by magnetic forces. The problem is modeled as the Euler-Bernoulli beam with a variable cross section
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supported by non-linear springs. The beam and the springs move on an undulated line. Introducing a new mode shape function which is expressed as the product of the trigonometric function and the power series truncated to the fourth order and utilizing the galerkin procedure, basic equations are reduced to the coupled non-linear equations. The steady state solutions of the beam was obtained using the harmonic balance method. It is found that the non-linear responses show the type of soft-spring, the unsymmetric support of the spring or the unsymetric cross section to the mid-point of the beam show large amplitude vibrations of a rotating motion and that of a translating motion in relatively large frequency range.
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| 33.
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永井, 健一 ; 長屋, 幸助 ; 武田, 定彦 ; 中村, 欣明
概要:
application/pdf<br />Journal Article<br />Analytical results are presented for nonlinear vibrations of a stretched string connected with a laterally movable end mass at one end. Applying the modified Galerkin method to the basic
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equations, a set of ordinary differential equations with cubic nonlinearity is obtained. The steady-state response is determined by the harmonic balance method. Numerical calculations are carried out for the various values for the end mass to the string and the geometry of the string. It is found that if the mass of the end mass increases to greater than that of the string, the resonant response in the first mode of vibration can be treated as a linear vibration up to a sufficiently large amplitude. However, the resonant curves in the higher mode of vibration show responses with a strong nonlinearity within a small amplitude. The increment of the cross section area of the string also gives a strong nonlinearity to the response in every mode of vibration.
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| 34.
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小島, 宏行
概要:
application/pdf<br />Journal Article<br />When an alternating electromagnetic force is applied to the mechanical vibration system, nonlinear forced vibrations such as superharmonic and subharmonic vibrations are generated owing to the
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nonlinearity of the electromagnetic force. In this report, the analytical method by the finite element method and the harmonic balance method is presented to investigate the nonlinear vibrations of a beam subjected to the alternating electromagnetic force. In the analysis, the equations of motion of the beam are obtained by the finite element method, and the nonlinear matrix equations which decide the force vibration amplitudes are derived in consideration of the second order superharmonic and the one-second order subharmonic by applying the harmonic balance method. Then, the nonlinear matrix equations are reduced, and three simultaneous equations are derived. Furthermore, the numerical results by use of the Newton-Rapson method agree well with the previous numerical results, and the present analytical method is confirmed.
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