Power Series Solution of Nonlinear Free Vibration Frequency of Isotropic Rectangular Thin Plates in Large Amplitude

Abstract

Nonlinear vibration computational problem of isotropic thin plates in large amplitude was investigated here. We applied the Von Kármán’s theory of thin plates to derive the governing equations of nonlinear free vibration of isotropic thin plates, and solved the governing equations by direct integration method combined with power series expansion method. We obtained the power series solution of the nonlinear vibration frequency of the rectangular thin plates with four edges simply supported. Finally, the paper gave the computational example and compared the two results from the large amplitude theory and the small one, respectively. Results obtained from this paper provide a new analytical computational approach for calculating the frequency of nonlinear free vibration of isotropic thin plates in large amplitude, and provide more accurate theoretical basis for the vibration control and dynamic design of plate structures.