Reduced-Order Nonlinear Modal Equations of Plates Based on the Finite Element Method

Abstract

This paper presents a procedure to derive reduced-order nonlinear modal equations of plates using mode vectors obtained by the finite element method. Nonlinear finite element formulation is derived by the principle of virtual work taking into account geometrical nonlinearity. Modal analysis is applied to the nonlinear finite element equation by using mode vectors obtained by finite element analysis. Reduced-order modal equations are derived by using modal coordinates of several dominant modes and neglecting in-plane inertia. Nonlinear modal equations of rectangular plates are derived, and numerical results for the fundamental out-of-plane mode and an internal resonance show good agreement with those presented in other papers.