Nonlinear vibrations and dynamic snap-through behaviors of four-corner simply supported bistable asymmetric laminated composite square shell

The nonlinear vibrations and dynamic snap-through behaviors are studied for a four-corner simply supported bistable asymmetric laminated composite square shell under the foundation excitation by using the theoretical, Abaqus finite element (FE) and experiment approaches. The first-order shear deformation shell theory and Hamilton principle are adopted to derive the partial differential governing equations of motion. A novel type of nonlinear strain-displacement relations is given by Sander’s strain. Galerkin approach is utilized to discretize the partial differential equations of motion into a three-degree-of-freedom system. The natural frequencies and vibration modes of the bistable shell are calculated by using Chebyshev polynomial method. The nonlinear vibrations and dynamic snap-through are investigated by using the maximum Lyapunov exponent, bifurcation diagrams, time histories, phase portraits, 3D phase portraits and Poincare maps. The theoretical results of the vibrations are well compared with those of the FE and experiment. The effects of the excitation and structural parameters on the dynamic snap-through and nonlinear vibrations are fully discussed. The influences of the initial radius of the curvature on the critical load of the dynamic snap-through behaviors and rule of the chaotic vibrations are analyzed for the bistable asymmetric laminated composite shell.