Analysis of Flutter and Nonlinear Dynamics of a Composite Laminated Plate

Abstract

This paper presents the analysis of flutter and nonlinear dynamics of an orthotropic composite laminated rectangular plate subjected to aerodynamic pressures and transverse excitation. The first-order linear piston theory is employed to model the air pressures. Based on Reddy’s third-order shear deformation plate theory and von Karman-type equation for the geometric nonlinearity, the nonlinear governing equations of motion are derived for the composite laminated rectangular plate by applying the Hamilton’s principle. The Galerkin method is utilized to discretize the partial differential governing equations to a set of nonlinear ordinary differential equations. The critical Mach number for occurrence of the flutter of the composite laminated plate is investigated by solving the eigenvalues problem. The relationship between the limit cycle oscillation and the critical Mach number is analyzed based on the nonlinear equations. The numerical simulation is conducted to study the influences of the transverse excitation on the nonlinear dynamics of the composited laminated plate. The numerical results, which include bifurcation diagram, phase plots and waveforms, demonstrate that there exist the bifurcation and chaotic motions of the composited laminated plate subjected to the aerodynamic pressures and the transverse excitation.