Nonlinear Dynamics Modeling and Subharmonic Resonances Analysis of a Laminated Composite Plate

Abstract

The nonlinear subharmonic resonance of an orthotropic rectangular laminated composite plate is studied. Based on the theory of high-order shear laminates, von Karman's geometric relation for the large deformation of plates, and Hamilton's principle, the nonlinear dynamic equations of a rectangular, orthotropic composite laminated plate subjected to the transverse harmonic excitation are established. According to the displacement boundary conditions, the modal functions that satisfy the boundary conditions of the rectangular plate are selected. The two-degree-of-freedom ordinary differential equations that describe the vibration of the rectangular plate are obtained by the Galerkin method. The multiscale method is used to obtain an approximate solution to the resonance problem. Both the amplitude-frequency equation and the average equations in the Cartesian coordinate form are obtained. The amplitude-frequency curves, bifurcation diagrams, phase diagrams, and time history diagrams of the rectangular plate under different parameters are obtained numerically. The influence of relevant parameters, such as excitation amplitude, tuning parameter, and damping coefficient, on the nonlinear dynamic response of the system is analyzed.

Chaotic Dynamics of Piezoelectric Composite Laminated Beams

“…where A represents the area enclosed by homoclinic orbits and zA is the boundary of A, i.e., From (7), (20), and ( 25), the third term of (50) can be simplified as follows:…”

“…Abe et al [6] studied the nonlinear dynamics characteristics of rectangular planar laminated shells with 1 : 1 internal resonance. Using the Galerkin method and multiscale method, Ma et al [7] investigated nonlinear subharmonic resonance of an orthotropic rectangular laminated composite plate subjected to the transverse harmonic excitation. Based on the general von Karman-type equations and the Reddy third-order shear deformation plate theory, the dynamic model of simply supported laminated piezoelectric composite beam with axial and transverse loading was established by Yao et al [8].…”