A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is ...A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is applied to discretize the state variables, and the Runge- Kutta method is applied to solve the resulting differential-integral equation system. A linear iterative process is designed to compute the integral terms at each time step, which makes the numerical method more efficient and accurate. As examples, nonlinear parametric vibrations of an axially moving viscoelastic string are analyzed.展开更多
Both the inplane and out-of-plane transverse vibrations of aviscoelastic cable subjected to an initial stress distributinguniform on the cross section are studied. The constitution of thecable material is as- sumed to...Both the inplane and out-of-plane transverse vibrations of aviscoelastic cable subjected to an initial stress distributinguniform on the cross section are studied. The constitution of thecable material is as- sumed to be of the hereditary integral type.The partial differential -integral equations of motion are derivedfirst. Then by applying Galerkin's method, the governing equationsare reduced to a set of second-order non- linear differential-integral equations which are solved by finite difference numericalintegration procedures. Finally, the effects of the viscosityparameter and the elastic parameter on the transient amplitudes ofthe first Mode are investigated by numerical simulation.展开更多
The almost sure stability of homogeneous viscoelastic platessubjected to a random wide-band stationary in-plane load isinvestigated. The viscoelastic behavior of the plate is described interms of the Bo- ltzmann super...The almost sure stability of homogeneous viscoelastic platessubjected to a random wide-band stationary in-plane load isinvestigated. The viscoelastic behavior of the plate is described interms of the Bo- ltzmann superposition principle, the relaxationkernels of which are represented by the sums of exponents. On theassumption that the in-plane load is random wide-band stationaryprocess, sufficient conditions for al- Most sure stability ofviscoelastic plates are obtained by the applications of Lyapunov'sdirect method.展开更多
基金supported by the National Outstanding Young Scientists Fund of China (No. 10725209)the National ScienceFoundation of China (No. 10672092)+1 种基金Shanghai Municipal Education Commission Scientific Research Project (No. 07ZZ07)Shanghai Leading Academic Discipline Project (No. Y0103).
文摘A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is applied to discretize the state variables, and the Runge- Kutta method is applied to solve the resulting differential-integral equation system. A linear iterative process is designed to compute the integral terms at each time step, which makes the numerical method more efficient and accurate. As examples, nonlinear parametric vibrations of an axially moving viscoelastic string are analyzed.
基金the National Natural Science Foundation of China (No.59635140)the National Postdoctoral Foundation of China.
文摘Both the inplane and out-of-plane transverse vibrations of aviscoelastic cable subjected to an initial stress distributinguniform on the cross section are studied. The constitution of thecable material is as- sumed to be of the hereditary integral type.The partial differential -integral equations of motion are derivedfirst. Then by applying Galerkin's method, the governing equationsare reduced to a set of second-order non- linear differential-integral equations which are solved by finite difference numericalintegration procedures. Finally, the effects of the viscosityparameter and the elastic parameter on the transient amplitudes ofthe first Mode are investigated by numerical simulation.
基金the National Natural Science Foundation of China (No.59635140)the National Postdoctoral Foundation.
文摘The almost sure stability of homogeneous viscoelastic platessubjected to a random wide-band stationary in-plane load isinvestigated. The viscoelastic behavior of the plate is described interms of the Bo- ltzmann superposition principle, the relaxationkernels of which are represented by the sums of exponents. On theassumption that the in-plane load is random wide-band stationaryprocess, sufficient conditions for al- Most sure stability ofviscoelastic plates are obtained by the applications of Lyapunov'sdirect method.
