The Experts below are selected from a list of 3273 Experts worldwide ranked by ideXlab platform
Takao Yamaguchi - One of the best experts on this subject based on the ideXlab platform.
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Chaotic vibrations of a post-buckled L-shaped beam with an Axial Constraint
Nonlinear Dynamics, 2012Co-Authors: Naoki Onozato, Ken-ichi Nagai, Shinichi Maruyama, Takao YamaguchiAbstract:Analytical results are presented on chaotic vibrations of a post-buckled L-shaped beam with an Axial Constraint. The L-shaped beam is composed of two beams which are a horizontal beam and a vertical beam. The two beams are firmly connected with a right angle at each end. The beams joint with the right angle is attached to a linear spring. The other ends are firmly clamped for displacement. The L-shaped beam is compressed horizontally via the spring at the beams joint. The L-shaped beam deforms to a post-buckled configuration. Boundary conditions are required with geometrical continuity of displacements and dynamical equilibrium with Axial force, bending moment, and share force, respectively. In the analysis, the mode shape function proposed by the senior author is introduced. The coefficients of the mode shape function are fixed to satisfy boundary conditions of displacements and linearized equilibrium conditions of force and moment. Assuming responses of the beam with the sum of the mode shape function, then applying the modified Galerkin procedure to the governing equations, a set of nonlinear ordinary differential equations is obtained in a multiple-degree-of-freedom system. Nonlinear responses of the beam are calculated under periodic lateral acceleration. Nonlinear frequency response curves are computed with the harmonic balance method in a wide range of excitation frequency. Chaotic vibrations are obtained with the numerical integration in a specific frequency region. The chaotic responses are investigated with the Fourier spectra, the Poincaré projections, the maximum Lyapunov exponents and the Lyapunov dimension. Applying the procedure of the proper orthogonal decomposition to the chaotic responses, contribution of vibration modes to the chaotic responses is confirmed. The following results have been found: The chaotic responses are generated with the ultra-subharmonic resonant response of the two-third order corresponding to the lowest mode of vibration. The Lyapunov dimension shows that three modes of vibration contribute to the chaotic vibrations predominantly. The results of proper orthogonal decomposition confirm that the three modes contribute to the chaos, which are the first, second, and third modes of vibration. Moreover, the results of the proper orthogonal decomposition are evaluated with velocity which is equivalent to kinetic energy. Higher modes of vibration show larger contribution to the chaotic responses, even though the first mode of vibration has the largest contribution ratio.
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Chaotic vibrations of a post-buckled L-shaped beam with an Axial Constraint
Nonlinear Dynamics, 2011Co-Authors: Naoki Onozato, Ken-ichi Nagai, Shinichi Maruyama, Takao YamaguchiAbstract:Analytical results are presented on chaotic vibrations of a post-buckled L-shaped beam with an Axial Constraint. The L-shaped beam is composed of two beams which are a horizontal beam and a vertical beam. The two beams are firmly connected with a right angle at each end. The beams joint with the right angle is attached to a linear spring. The other ends are firmly clamped for displacement. The L-shaped beam is compressed horizontally via the spring at the beams joint. The L-shaped beam deforms to a post-buckled configuration. Boundary conditions are required with geometrical continuity of displacements and dynamical equilibrium with Axial force, bending moment, and share force, respectively. In the analysis, the mode shape function proposed by the senior author is introduced. The coefficients of the mode shape function are fixed to satisfy boundary conditions of displacements and linearized equilibrium conditions of force and moment. Assuming responses of the beam with the sum of the mode shape function, then applying the modified Galerkin procedure to the governing equations, a set of nonlinear ordinary differential equations is obtained in a multiple-degree-of-freedom system. Nonlinear responses of the beam are calculated under periodic lateral acceleration. Nonlinear frequency response curves are computed with the harmonic balance method in a wide range of excitation frequency. Chaotic vibrations are obtained with the numerical integration in a specific frequency region. The chaotic responses are investigated with the Fourier spectra, the Poincare projections, the maximum Lyapunov exponents and the Lyapunov dimension. Applying the procedure of the proper orthogonal decomposition to the chaotic responses, contribution of vibration modes to the chaotic responses is confirmed. The following results have been found: The chaotic responses are generated with the ultra-subharmonic resonant response of the two-third order corresponding to the lowest mode of vibration. The Lyapunov dimension shows that three modes of vibration contribute to the chaotic vibrations predominantly. The results of proper orthogonal decomposition confirm that the three modes contribute to the chaos, which are the first, second, and third modes of vibration. Moreover, the results of the proper orthogonal decomposition are evaluated with velocity which is equivalent to kinetic energy. Higher modes of vibration show larger contribution to the chaotic responses, even though the first mode of vibration has the largest contribution ratio.
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Chaotic Vibrations of Shallow Arches with Variable-cross-section constrained by an Axial Elastic Support.
Transactions of the Japan Society of Mechanical Engineers Series C, 1998Co-Authors: Ken-ichi Nagai, Sadao Ohyama, Takao YamaguchiAbstract: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 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.
J. Lipkin - One of the best experts on this subject based on the ideXlab platform.
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Analysis of Axial deformation response during reverse shear
Journal of the Mechanics and Physics of Solids, 1991Co-Authors: T.c. Lowe, J. LipkinAbstract:The response of a polycrystalline metal undergoing torsional shearing deformation is examined in detail using a strain-rate dependent model of the deformation of polycrystals. Several boundary value problems are solved to determine the roles of anisotropic elasticity and boundary Constraints on the stresses and strains that develop along the torsion axis during forward and reverse shearing deformation. An initially random orientation distribution of 300 grains is assumed, and boundary conditions are chosen to represent a thin-walled tube with fixed, free and intermediate stiffness end Constraints. A constant quasi-static shear strain rate of γ = 0.00775 s−1 is imposed to prestrain the polycrystal to a maximum shear strain γ = 1.6. At this point the sign of the shear strain rale is reversed and deformation is continued until the shear strain is reduced to essentially zero. For calculations in which some degree of Axial Constraint is imposed, the Axial stress increases monotonically in compression during forward shearing. During reverse shearing, the Axial stress response depends sensitively upon the degree of Axial Constraint, the textural anisotropy induced during forward shearing of the polycrystal. and the elastic anisotropy of the constituent grains. The model predictions demonstrate the role of anisotropic elasticity and the importance of minor strain components when modeling elastic plastic transients in textured polycrystals. Finally, the model predictions are compared with the results of experiments on short, thin-walled tubes of 304L stainless steel. Satisfactory agreement between a number of predicted and measured features of the response was obtained.
M.p. Païdoussis - One of the best experts on this subject based on the ideXlab platform.
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NONLINEAR VIBRATIONS OF SIMPLY SUPPORTED, CIRCULAR CYLINDRICAL SHELLS, COUPLED TO QUIESCENT FLUID
Journal of Fluids and Structures, 1998Co-Authors: Marco Amabili, Francesco Pellicano, M.p. PaïdoussisAbstract:The nonlinear free and forced vibrations of a simply supported, circular cylindrical shell in contact with an incompressible and inviscid, quiescent and dense fluid are investigated. Donnell's shallow-shell theory is used, so that moderately large vibrations are analysed. The boundary conditions on radial displacement and the continuity of circumferential displacement are exactly satisfied, while Axial Constraint is satisfied on the average. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. The mode shape is expanded by using three degrees of freedom; in particular, two asymmetric modes (drivenandcompanionmodes), plus an axisymmetric mode are employed. The time dependence of each term of the expansion is general and the axisymmetric mode is obtained from a series involving all axisymmetric linear modes. Different tangential Constraints can be imposed at the shell ends. Effects of both internal and external dense fluid are studied. Internally, the shell is considered completely filled, while externally, an unbounded fluid domain is considered around the shell in the radial direction. The solution is obtained both numerically and by theMethod of Normal Forms. Numerical results are obtained for both free and forced vibrations of empty and water-filled shells.
Ken-ichi Nagai - One of the best experts on this subject based on the ideXlab platform.
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Chaotic vibrations of a post-buckled L-shaped beam with an Axial Constraint
Nonlinear Dynamics, 2012Co-Authors: Naoki Onozato, Ken-ichi Nagai, Shinichi Maruyama, Takao YamaguchiAbstract:Analytical results are presented on chaotic vibrations of a post-buckled L-shaped beam with an Axial Constraint. The L-shaped beam is composed of two beams which are a horizontal beam and a vertical beam. The two beams are firmly connected with a right angle at each end. The beams joint with the right angle is attached to a linear spring. The other ends are firmly clamped for displacement. The L-shaped beam is compressed horizontally via the spring at the beams joint. The L-shaped beam deforms to a post-buckled configuration. Boundary conditions are required with geometrical continuity of displacements and dynamical equilibrium with Axial force, bending moment, and share force, respectively. In the analysis, the mode shape function proposed by the senior author is introduced. The coefficients of the mode shape function are fixed to satisfy boundary conditions of displacements and linearized equilibrium conditions of force and moment. Assuming responses of the beam with the sum of the mode shape function, then applying the modified Galerkin procedure to the governing equations, a set of nonlinear ordinary differential equations is obtained in a multiple-degree-of-freedom system. Nonlinear responses of the beam are calculated under periodic lateral acceleration. Nonlinear frequency response curves are computed with the harmonic balance method in a wide range of excitation frequency. Chaotic vibrations are obtained with the numerical integration in a specific frequency region. The chaotic responses are investigated with the Fourier spectra, the Poincaré projections, the maximum Lyapunov exponents and the Lyapunov dimension. Applying the procedure of the proper orthogonal decomposition to the chaotic responses, contribution of vibration modes to the chaotic responses is confirmed. The following results have been found: The chaotic responses are generated with the ultra-subharmonic resonant response of the two-third order corresponding to the lowest mode of vibration. The Lyapunov dimension shows that three modes of vibration contribute to the chaotic vibrations predominantly. The results of proper orthogonal decomposition confirm that the three modes contribute to the chaos, which are the first, second, and third modes of vibration. Moreover, the results of the proper orthogonal decomposition are evaluated with velocity which is equivalent to kinetic energy. Higher modes of vibration show larger contribution to the chaotic responses, even though the first mode of vibration has the largest contribution ratio.
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Chaotic vibrations of a post-buckled L-shaped beam with an Axial Constraint
Nonlinear Dynamics, 2011Co-Authors: Naoki Onozato, Ken-ichi Nagai, Shinichi Maruyama, Takao YamaguchiAbstract:Analytical results are presented on chaotic vibrations of a post-buckled L-shaped beam with an Axial Constraint. The L-shaped beam is composed of two beams which are a horizontal beam and a vertical beam. The two beams are firmly connected with a right angle at each end. The beams joint with the right angle is attached to a linear spring. The other ends are firmly clamped for displacement. The L-shaped beam is compressed horizontally via the spring at the beams joint. The L-shaped beam deforms to a post-buckled configuration. Boundary conditions are required with geometrical continuity of displacements and dynamical equilibrium with Axial force, bending moment, and share force, respectively. In the analysis, the mode shape function proposed by the senior author is introduced. The coefficients of the mode shape function are fixed to satisfy boundary conditions of displacements and linearized equilibrium conditions of force and moment. Assuming responses of the beam with the sum of the mode shape function, then applying the modified Galerkin procedure to the governing equations, a set of nonlinear ordinary differential equations is obtained in a multiple-degree-of-freedom system. Nonlinear responses of the beam are calculated under periodic lateral acceleration. Nonlinear frequency response curves are computed with the harmonic balance method in a wide range of excitation frequency. Chaotic vibrations are obtained with the numerical integration in a specific frequency region. The chaotic responses are investigated with the Fourier spectra, the Poincare projections, the maximum Lyapunov exponents and the Lyapunov dimension. Applying the procedure of the proper orthogonal decomposition to the chaotic responses, contribution of vibration modes to the chaotic responses is confirmed. The following results have been found: The chaotic responses are generated with the ultra-subharmonic resonant response of the two-third order corresponding to the lowest mode of vibration. The Lyapunov dimension shows that three modes of vibration contribute to the chaotic vibrations predominantly. The results of proper orthogonal decomposition confirm that the three modes contribute to the chaos, which are the first, second, and third modes of vibration. Moreover, the results of the proper orthogonal decomposition are evaluated with velocity which is equivalent to kinetic energy. Higher modes of vibration show larger contribution to the chaotic responses, even though the first mode of vibration has the largest contribution ratio.
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Chaotic Vibrations of Shallow Arches with Variable-cross-section constrained by an Axial Elastic Support.
Transactions of the Japan Society of Mechanical Engineers Series C, 1998Co-Authors: Ken-ichi Nagai, Sadao Ohyama, Takao YamaguchiAbstract: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 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.
T.c. Lowe - One of the best experts on this subject based on the ideXlab platform.
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Analysis of Axial deformation response during reverse shear
Journal of the Mechanics and Physics of Solids, 1991Co-Authors: T.c. Lowe, J. LipkinAbstract:The response of a polycrystalline metal undergoing torsional shearing deformation is examined in detail using a strain-rate dependent model of the deformation of polycrystals. Several boundary value problems are solved to determine the roles of anisotropic elasticity and boundary Constraints on the stresses and strains that develop along the torsion axis during forward and reverse shearing deformation. An initially random orientation distribution of 300 grains is assumed, and boundary conditions are chosen to represent a thin-walled tube with fixed, free and intermediate stiffness end Constraints. A constant quasi-static shear strain rate of γ = 0.00775 s−1 is imposed to prestrain the polycrystal to a maximum shear strain γ = 1.6. At this point the sign of the shear strain rale is reversed and deformation is continued until the shear strain is reduced to essentially zero. For calculations in which some degree of Axial Constraint is imposed, the Axial stress increases monotonically in compression during forward shearing. During reverse shearing, the Axial stress response depends sensitively upon the degree of Axial Constraint, the textural anisotropy induced during forward shearing of the polycrystal. and the elastic anisotropy of the constituent grains. The model predictions demonstrate the role of anisotropic elasticity and the importance of minor strain components when modeling elastic plastic transients in textured polycrystals. Finally, the model predictions are compared with the results of experiments on short, thin-walled tubes of 304L stainless steel. Satisfactory agreement between a number of predicted and measured features of the response was obtained.
