Three-Mode Response of Simply Supported, Rectangular Laminated Plates.

Abstract

This paper describes the three-mode response of simply supported, rectangular laminated plates subjected to harmonic excitation.It is assumed that the linear natural frequencies, ω1, ω2 and ω3 of the symmetric vibration modes have the relationship 2ω2 ≈ ω1+ω3 and that internal resonance occurs.Galerkin's procedure is applied to the governing equation in consideration of the geometric nonlinearity, and the method of multiple scales is used to analyze the steady-state response.The effects of the lamination sequence, the amplitude of the excitation, and the relationship among the linear natural frequencies on the three-mode response are studied.In order to confirm the analytical results, the equation of motion is integrated numerically using the Runge-Kutta method.Numerical simulation shows that the three-mode response is not a periodic motion but a quasi-periodic motion.