THE BIFURCATION ANALYSIS ON THE LAMINATED COMPOSITE PLATE WITH 1:1 PARAMETRICALLY RESONANCE

A simply supported rectangular symmetric cross-plylaminated composite plate with parametric excitation is considered. Thegoverning equations of motion for the laminated composite plate arederived by means of von K\'arm\'an equation. The material nonlinearity,geometric nonlinearity and nonlinear damping are included in thegoverning equations of motion. The Galerkin's approach is used toobtain a two-degree-of-freedom nonlinear system under parametricexcitation. The method of multiple scales is utilized to transform thesecond-order non-autonomous differential equations to first-orderaveraged equations. The averaged equations are numerically solved toobtain the bifurcation responses and to analyze the stability for thelaminated composite plate. Under certain conditions the laminatedcomposite plate may occur two non-steady-state bifurcation solutionsand jumping phenomena. The bifurcation and chaotic motion of therectangular symmetric cross-ply laminated composite plate is simulatednumerically. The effect of the Galerkin's truncation to nonlineardynamic analysis is presented. The way of the system going into chaosis also investigated and explained.