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Nonlinear Dynamic Response to a Moving Force of Timoshenko Beams Resting on Pasternak Foundations

Y. YANG, H. DING, L.-Q. CHEN

Abstract


The present paper investigates the convergence of the Galerkin method for the dynamic response of Timoshenko beams resting on nonlinear foundations with six parameters subjected to a moving concentrated load. The dynamic response of the beam is obtained via the fourth-order Runge-Kutta method. The effects of different truncation terms on the dynamical responses of the nonlinear vibration are discussed. For the first time, the convergence of the Galerkin truncation for investigating the vibration of Timoshenko beams resting on nonlinear foundations is investigated. The numerical investigation shows that the dynamical response of finite Timoshenko beams supported by nonlinear viscoelastic foundations needs about 150 terms’ truncation. Furthermore, the dependence of the convergence of the Galerkin method on the system parameters is numerically studied.

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