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General decay of energy to a nonlinear viscoelastic two-dimensional beam

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Applied Mathematics and Mechanics(English Edition) 2018年第11期39卷 1661-1678页

作者： B.LEKDIM A.KHEMMOUDJ Faculty of Mathematics University of Sciences and Technology Houari Boumedienne

A viscoelastic beam in a two-dimensional space is considered with nonlinear tension. A boundary feedback is applied at the right boundary of the beam to suppress the undesirable vibration. The well-posedness of the pr... 详细信息

关键词： two-dimensional space viscoelastic beam nonlinear tension exponential decay Lyapunov functional

DYNAMICAL BEHAVIOR OF NONLINEAR viscoelastic beamS

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Applied Mathematics and Mechanics(English Edition) 2000年第9期21卷 995-1001页

作者：陈立群程昌钧 Shanghai Institute of Applied Mathematics and Mechanics Shanghai P R China Department of Mechanics Shanghai University Shanghai P R China

The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams was established. The material of the beams obeys the Leaderman nonlinear constitutive relation. rn the case of two simply supported ends, the mathematical model is simplified into an integro-differential equation after a 2nd-order truncation by the Galerkin method. Then the equation is further reduced to an ordinary differential equation which is convenient to carry out numerical experiments. Finally, the dynamical behavior of Ist-order and 2nd-order truncation are numerically compared.

关键词： viscoelastic beam differential equation of motion Leaderman relation Galerkin method

Chaotic Motions of Nonlinear viscoelastic beams

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Advances in Manufacturing 2000年第S1期4卷 7-10页

作者： CHEN Li-qun, CHENG Chang-jun, ZHANG Neng-hui Department of Mechanics, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University Shanghai 200072, China Department of Mechanics Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China

The integro-partial-differential equation that governs the dynamical behavior of homogeneous viscoelastic beams with geometric and material nonlinearities is established. The material of the beams obeys the Leaderman nonlinear constitutive relation. In the case of simple supported ends, the Galerkin method is applied to simplify the integro-partial-differential equation to a integro -differential equation. The equation is further simplified to a set of ordinary differential equations by introducing an additional variable. Finally, the numerical method is applied to investigate the dynamical behavior of the beam, and results show that chaos occurs in the motion of the beam.

关键词： viscoelastic beam geometric nonlinearity leaderman constitutive relation Galerkin method chaos

Analytical solution of fractionally damped beam by Adomian decomposition method

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Applied Mathematics and Mechanics(English Edition) 2007年第2期28卷 219-228页

作者：梁祖峰唐晓艳 Power Engineering College University of Shanghai for Science and Technology Department of Physics Shanghai Jiaotong University

The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the AdoInian decomposition method. The solution contains arbitrary initial conditions and zero input. For specific analysis, the initial conditions were assumed homogeneous, and the input force was treated as a special process with a particular beam. Two simple cases, step and impulse function responses, were considered respectively. Subsequently, some figures were plotted to show the displacement of the beam under different sets of parameters including different orders of the fractional derivatives.

关键词： viscoelastic beam fractional derivative Adomian decomposition method,vibration