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.
Highlights
Composite laminates have many advantages, such as high specific strength, high specific stiffness, and good fatigue resistance
When the excitation frequency is the same, the influence of the excitation amplitude on the steady-state solutions with small vibration amplitude of the two-order modes is significant. e solution with small amplitude of the first-order mode increases with the increase in the excitation amplitude
The subharmonic resonance of a rectangular laminated plate under harmonic excitation is studied. e vibration equations of the system are established using von Karman’s nonlinear geometric relation and Hamilton’s principle. e amplitude-frequency equations and the average equations in rectangular coordinates are obtained by using the multiscale method. e amplitude-frequency equations and average equations are numerically simulated in order to obtain the influence of system parameters on the nonlinear characteristics of vibration. e following conclusions can be obtained: (1) e results show that there are many similar characteristics in the nonlinear response of the uncoupled two-order modes, which are excited separately when subharmonic resonance occurs
Summary
Composite laminates have many advantages, such as high specific strength, high specific stiffness, and good fatigue resistance. Eslami and Kandil [14] studied the forced vibration of rectangular laminated composite plates subjected to harmonic excitation.
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