Eur. Phys. J. Spec. Top. (2022) 231: 2199-2209
https://doi.org/10.1140/epjs/s11734-021-00375-8

Regular Article

Dynamic snap-through phenomena and nonlinear vibrations of bistable asymmetric cross-ply composite-laminated square plates with two potential wells under center base excitation

Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, Faculty of Materials and Manufacturing, Beijing University of Technology, 100124, Beijing, People’s Republic of China

Received: 27 July 2021
Accepted: 7 December 2021
Published online: 29 December 2021

Abstract

The dynamic snap-through phenomena and nonlinear vibrations with two potential wells are investigated for a bistable asymmetric cross-ply composite-laminated square plates. The center of the plate is fixed supported. The four edges of the plate are free. A base excitation is given at the center of the plates. The Hamilton’s principle is employed to establish the partial differential governing equations of motions for the bistable plates. Three equilibrium configurations corresponding to two stable configurations and one unstable configuration can be determined by solving the nonlinear static equations. The static bifurcation diagrams are obtained, of which the type is super-critical pitchfork bifurcation. Absolute value of critical temperature difference of bifurcation increases with the increase of the quantity of layers. Two energy potential wells are determined based on two stable configurations. The potential energy curves are determined. The potential curve consists of two potential wells and one potential barrier. Threshold that is the difference between the maximum value and the minimum value of the potential energy curve adds with the adding of the quantity of layers. The influence of the base excitation amplitude on the dynamic snap-through phenomena and nonlinear vibrations is studied. The dynamic snap-through occurs accompanying with the periodic vibration, the quasi-periodic vibration and the chaotic vibration in the dynamic environments.