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...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.展开更多
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 ca...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.展开更多
The nonlinear dynamic behaviors of nonlinear viscoelastic shallow arches sub- jected to external excitation are investigated. Based on the d＇Alembert principle and the Euler-Bernoulli assumption, the governing equati...The nonlinear dynamic behaviors of nonlinear viscoelastic shallow arches sub- jected to external excitation are investigated. Based on the d＇Alembert principle and the Euler-Bernoulli assumption, the governing equation of a shallow arch is obtained, where the Leaderman constitutive relation is applied. The Galerkin method and numerical in- tegration are used to study the nonlinear dynamic properties of the viscoelastic shallow arches. Moreover, the effects of the rise, the material parameter and excitation on the nonlinear dynamic behaviors of the shallow arch viscoelastic shallow arches may appear to have a are investigated. The results show that chaotic motion for certain conditions.展开更多
基金the National Natural Science Foundation of China(19727027) and the Science Foundation of Shanghai MunicipalCommission of Sci
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China (Nos. 10502020, 10772065)
文摘The nonlinear dynamic behaviors of nonlinear viscoelastic shallow arches sub- jected to external excitation are investigated. Based on the d＇Alembert principle and the Euler-Bernoulli assumption, the governing equation of a shallow arch is obtained, where the Leaderman constitutive relation is applied. The Galerkin method and numerical in- tegration are used to study the nonlinear dynamic properties of the viscoelastic shallow arches. Moreover, the effects of the rise, the material parameter and excitation on the nonlinear dynamic behaviors of the shallow arch viscoelastic shallow arches may appear to have a are investigated. The results show that chaotic motion for certain conditions.
