Numerical And Perturbation Analysis Of Dynamic Post-Buckling Of Rectangular Laminated Plates

A new phenomenon for laminated composite plates undergoing dynamic post-buckling is presented. The buckled composite plate subjected to in-plane dynamic load not only gains more non-linearity by the quadratic term, which arises from static buckling, but also changes its dynamic behavior from pure parametric vibration to combined parametric and forcing traverse vibrations. The nonlinear behavior of a simply supported laminated composite plate undergoing dynamic post-buckling is investigated. The range of bifurcation parameter (forcing frequency) for chaotic motion is obtained, and the characteristics of the dynamic behavior of the laminated composite plate in post-buckling are unveiled. Hamilton\u27s Principle, Galerkin\u27s Method, and Lagrange\u27s Equation are utilized to obtain the equations of motion with higher-order shear deformation. The differential equation has quadratic and cubic non-linearities as well as parametric and harmonic excitation terms. The method of multiple scales is used to determine the equations that describe the second order modulation of the amplitude and phase. Floquet theory is used to analyze the stability of periodic responses