STUDY ON PRIMARY PARAMETRIC RESONANCE AND PRIMARY RESONANCE OF A THIN CIRCULAR PLATE ON NONLINEAR FOUNDATION

In order to study primary parametric resonance and primary resonance of a thin circular plate subjected to harmonic excitation on nonlinear foundation by applying elastic theory, nonlinear dynamical equation of the system is established. Nonlinear oscillation equation is obtained based on Galerkin’s method. It is Duffing-Mathieu equation. By means of the method of multiple scales for nonlinear oscillations the approximation solution of primary parametric resonance and primary resonance of the system is acquired. Numerical analysis of the influence of damping, foundation coefficient, and geometric parameter on the system is carried out. The calculation results of two kinds of foundation are compared.