Theory and experiment of nonlinear vibrations and dynamic snap-through phenomena for bi-stable asymmetric laminated composite square panels under foundation excitation

摘要

This paper theoretically and experimentally investigates the dynamic snap-through phenomena and the nonlinear vibrations of the bi-stable asymmetric laminated composite square panel under the foundation excitation. We propose a new method to describe the dynamic snap-through phenomena of the bi-stable asymmetric laminated composite square panel by using the time-varying principle curvatures. The boundary conditions of the bi-stable asymmetric laminated composite square panel are clamped at the center of the panel and free at four edges. The mode shapes are obtained by employing Rayleigh-Ritz method and Lagrangian multipliers method. According to the double curvature type of von-Karman nonlinear strain-displacement relations, the third-order shear deformation theory and Hamilton principle, the nonlinear partial differential governing equations of motion are derived for the bi-stable asymmetric laminated composite square panel. The nonlinear ordinary differential governing equation of motion is obtained by using Galerkin method. Numerical simulations are used to study the nonlinear vibrations and the dynamic snap-through phenomena of the bi-stable asymmetric laminated composite square panel including the effect of the structural damping by using the 4-order Runge-Kutta method. Analyzing the phase portrait and time history of the principle curvature, the dynamic snap-through phenomena of the bi-stable asymmetric laminated composite square panel are observed through changing the amplitude of the foundation excitation. The vibration experiments are also finished to find the dynamic snap-through phenomena and the nonlinear vibrations of the bi-stable asymmetric laminated composite square panel. It is known that the theoretical and the experimental results are the qualitative agreement and the experimental results provide a reference for the application of the bi-stable asymmetric laminated composite square panel in the aeronautic and mechanical engineering fields.