Nonlinear free vibration of rectangular plate by a modified multiple scale method ISAV2020

In the present research, the nonlinear free vibration of a rectangular simply supported plate is investigated analytically using a modified Multiple Scales method for the first time. The Von Karman nonlinear strain–displacement relationships are used. The extended Hamilton principle and classical plate theory are used to derive these partial differential equations of motions. By applying Galerkin method, the nonlinear partial differential equations are trans-formed into time dependent nonlinear ordinary differential equations which are solved ana-lytically by a modified Multiple Scales method. The technique is a new form of the classical multiple scales method. The results of this paper are compared with both the published data and numerical method, and good agreements are found.

Keywords:

Nonlinear vibration , multiple scales method , Modified multiple scales method , Rectangular plate