NONLINEAR COMBINATION RESONANCES OF ORTHOTROPIC LAMINATED PLATE UNDER TWO-TERM HARMONIC EXCITATION

The stability and nonlinear combination resonance of a rectangular orthotropic laminated thin plate excited by two-term harmonic forces are studied under the boundary condition simply supported on four sides. Based on the vibration differential equation of orthotropic laminated plates, the nondimensional Duffing nonlinear forced vibration equation is deduced by using Galerkin method. The amplitude frequency response equation of system steady motion under combination resonance is obtained by the method of Multiple Scales. Based on Lyapunov stable theory, the critical conditions of steady-state solutions’ stability are attain. By some examples, several typical composite laminated plates are analyzed. The resonance curves, amplitude-frequency curves and phase trajectories in moving phase plane are derived under different conditions. The influences of different parameters on nonlinear resonance properties of the system are analyzed.