Low Order Model for the Dynamics of Bi-Stable Composite Plates

This article presents the derivation and validation of a low order model for the non-linear dynamics of cross-ply bi-stable composite plates focusing on the response of one stable state. The Rayleigh–Ritz method is used to solve the associated linear problem to obtain valuable theoretical insight into how to formulate an approximate non-linear dynamic model. This allows us to follow a Galerkin approach projecting the solution of the non-linear problem onto the mode shapes of the linear problem. The order of the non-linear model is reduced using theoretical results from the linear solution yielding a low order model. The dynamic response of a bi-stable plate specimen is studied to simplify the model further by only keeping the non-linear terms leading to observed oscillations. Simulations for the dynamic response using the derived model are presented showing excellent agreement with the experimentally observed behaviour. Additionally, deflection shapes are measured and compared with the calculated mode shapes, showing good agreement.