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| 1.
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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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| 2.
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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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| 3.
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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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| 4.
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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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| 5.
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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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| 6.
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山口, 誉夫 ; 酒匂, 淳一 ; 永井, 健一 ; 丸山, 真一
概要:
application/pdf<br />Journal Article<br />For chaotic vibrations involving dynamic through generated in a post-buckled beam, influences of an axial displacement on dynamic properties in chaos are clarified by numerical analysis.
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Especially, the chaotic vibrations bifurcated from 1/2 subharmonic resonance are focused on. The beam is constrained by an axial elastic support and both ends of the beam are clamped. Applying Galerkin method to the basic equation of the buckled beam in consideration with geometric nonlinearity, nonlinear cubic simultaneous equations in multi-degrees of freedom are reduced. Further, the equations are transformed into nonlinear ordinary differential equations using normal coordinates corresponding to linear natural modes. By integrating the equations numerically, time histories and Poincare sections are calculated. Moreover, Lyapunov dimension can be obtained using the evolution equations. According to the calculated results, initial axial displacements increase the number of governing modes in the chaos including dynamic snap-through.
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| 7.
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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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| 8.
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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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| 9.
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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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| 10.
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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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| 11.
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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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| 12.
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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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| 13.
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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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| 14.
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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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| 15.
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永井, 健一 ; 大山, 貞夫 ; 山口, 誉夫
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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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| 16.
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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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| 17.
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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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| 18.
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樫本, 弘 ; 長屋, 幸助 ; 白石, 明男
概要:
application/pdf<br />Journal Article<br />This paper proposes a method for obtaining stresses in a rod with arbitrary cross section. The rod consists of two infinite straight portions and one two-dimensional curved portion in which
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the cross section varies. A twisting wave propagates from one of the two infinite straight portions to the other via the curved portion. In this analysis, fundamental equations were extended in order to apply them to the non-circular cross section by using the Fourier expansion collocation procedure, and the transfer matrix was derived. At connecting sections, solutions of curved portion and those of straight portions have been connected. Then it is possible to obtain the principal stress and the principal shearing stress at any location.
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| 19.
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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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| 20.
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Kashimoto, Hiroshi ; Nagaya, Kosuke ; Shiraishi, Akio
概要:
application/pdf<br />Journal Article<br />This paper presents a method for solving the dynamic stress concentration problem of inhomogeneous rods having two-dimensional arbitrary curvature, variable cross section and infinite length
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subjected to in-plane bending wave excitation. In this analysis, the exact solution of the equilibrium equations for curved rods has been obtained, and the transfer matrix, based on the exact solutions with consideration of the inertia forces has been derived. At discontinuous sections, solutions of curved and straight rods have been connected by adjusting the boundary conditions. As examples, stress concentration factors in circular, elliptical and parabolic arc rods with variable cross sections have been calculated.
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| 21.
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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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| 22.
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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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| 23.
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樫本, 弘 ; 長屋, 幸助 ; 白石, 明男
概要:
application/pdf<br />Journal Article<br />An analysis is presented for the dynamic stress concentration problem of an infinite inhomogeneous rod having a discontinuity of the curved portion in which the radius of cross sections varies
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continuously. The rod treated in this study consists of two infinitely straight portions and one finite curved portion of arbitrary curvature. The curved portion lies between the two straight portions. The twisting wave propagates from one of the infinite straight portions to the other, passing through the curved portion. The exact solution for the equilibrium equations for a curved rod has been obtained. The transfer matrix has been derived based on the exact solution and upon considering the internal forces and moments. At discontinuous sections, solutions of curved and straight rods have been connected by adjusting the boundary conditions. As examples, stress concentration factors in circular, elliptical and parabolic arc rods have been obtained.
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| 24.
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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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| 25.
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永井, 健一
概要:
application/pdf<br />Journal Article<br />Experimental results are presented for chaotic vibrations of a compressed buckled beam subjected to periodic lateral excitation. A thin duralumin beam coated with a sheet of thin vinyl was used as
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a test specimen. The beam was clamped at both ends to the base frame of an electromagnetic shaker. Initial axial displacement of the beam was controlled utilizing thermal elongation both of the beam and frame. Typical responses of time history and the strange attractor of the chaotic vibration were observed near the frequency range of the fundamental resonant vibration. It is found that the correlation dimension of the strange attractor yields a value of d=3.8 under twice the axial displacement corresponding to buckling load.
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| 26.
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永井, 健一
概要:
application/pdf<br />Journal Article<br />Parametric vibrations of beams carrying a concentrated mass subjected to both static and periodic axial acceleration are analyzed under four sets of boundary conditions. Introducing
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the mode shape function, which is expressed as the product of the power series truncated to the fourth order, and the trigonometric function, we obtain the boundary conditions at both ends combined with a simply supported end or a clamped end by exchanging the coefficients of the power series. Applying the Galerkin method to basic equations, we reduce the coupled Mathieu's equations. The stability boundaries of the principal, secondary and combination parametric resonances are examined using Hsu's method. Calculations are carried out for various values of the location of the concentrated mass in each boundary condition. It is found that the inertia force caused by the concentrated mass under periodic acceleration expands the instability region extensively. In particular, the boundary is extended when the concentrated mass approaches the end with a movable axial displacement.
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| 27.
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小島, 宏行 ; 森平, 明宏 ; 根津, 紀久雄 ; 坂本, 賢治
概要:
application/pdf<br />Journal Article<br />In this report, the nonlinear forced vibration responses of a plate subjected to alternating electromagnetic attractive force are investigated theoretically and experimentally in
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consideration of the superharmonic and the subharmonic vibrations as well as the harmonic one. In the analysis, first, the electromagnetic attractive force is formulated by applying the least squares method to the experimental results. By the use of this formulation, the matrix equation of motion of the plate is obtained by applying the finite element method. Then, the nonlinear simultaneous equations, which decide the superharmonic and the subharmonic vibrations as well as the harmonic one, are derived by the harmonic balance method and the reduced impedence method. The numerical results carried out by the Newton-Raphson method agree well with the experimental results, and the validity of the present analysis is confirmed.
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| 28.
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永井, 健一 ; 八巻, 昇
概要:
application/pdf<br />Journal Article<br />Theoretical analyses are presented for the title problem under four sets of boundary conditions. By the use of the Galerkin procedure, the Donnell equations modified with the transverse inertia
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force are reduced to the coupled Hill's equations. Stability regions are examined by utilizing Hsu's method. Calculations are carried out for typical shells and the instability boundary of the principal, secondary and combination parametric resonances are determined. It is found that unperturbed axisymmetric bending motion has a significant effect on the stability boundary for shells of moderate length while the effect of longitudinal resonance is generally negligible for thin shells.
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| 29.
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永井, 健一 ; 大月, 和也
概要:
application/pdf<br />Journal Article<br />Theoretical analyses are presented for nonlinear bending vibrations of beam having variable cross sections subjected to periodic lateral forces, considering the effects of initial static deflection
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and axial displacement. By use of the Galerkin procedure, assuming the form function which is composed of the finite power series and the trigonometrical function, basic equations are reduced to coupled nonlinear ordinary differential equations. The steady state harmonic solution is obtained with harmonic balance method. Numerical calcuations are carried out for the six degrees of freedom, nonlinear responses of principal, super-harmonic and subharmonic vibration are determined for various shapes of the beam, with initial deflection and axial displacement. Especially, the characteristic features of the principal responses with the asymmetric mode of vibration are clarified.
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