A Closed Form Solution for the Nonlinear Vibration of Rectangular Viscoelas

In this paper, first, the equations of motion for an isotropic viscoelastic rectangular plate based on the first order shear deformation were derived. Then, by using an Airy stress function, these equations were converted to one coupled equation and a compatibility equation. Using the Galerkin method, a nonlinear differential equation with respect to time was obtained. This equation included all kind of nonlinearity terms as nonlinearity in stiffness, damping and inertia. Then, using the method of multiple scales, this equation has been solved and the nonlinear natural frequencies and amplitude of vibration has been obtained. It is shown that the amplitude of vibration has an exponential reduction with respect to time. Also the nonlinear natural frequency has a logarithmically relation with respect to time. Also the effect of damping coefficient, Poisson's ratio and thickness on the dynamical characteristic of system have been investigated.

کلیدواژه ها:

Multiple Scales Method ، Viscoelastic Plate ، Nonlinear vibration ، Kelvin-Voigt model