Advanced nonlinear dynamic modelling of bi-stable composite plates

This paper proposes a novel analytical model to study the nonlinear dynamics of cross-ply bi-stable composite plates. Based on Hamilton's principle, in conjunction with the Rayleigh-Ritz method, an advanced analytical model with only 17 unknown terms is developed to predict the entire nonlinear dynamic response of bi-stable composite plates, which are excited by an electrodynamic shaker. The coupling between the bi-stable plate and the shaker is considered in the development of the analytical model. This work, for the first time, simulates the full dynamics of bi-stable plates using an analytical model, including the prediction of the nonlinear characteristics of single well vibration and cross well vibration. Numerical results on three vibrational patterns of two standard cross-ply composite plates are obtained to study the nonlinear dynamics of bi-stable plates. The prediction accuracy on the dynamic characteristics of different vibrational patterns of bi-stable plates are verified by both finite element analysis (FEA) and experimental results. Large amplitude cross-well vibrations due to the transitions between different stable states of bi-stable plates are also characterized accurately. Applying this 17-term analytical model for the dynamic analysis of bi-stable plates is straightforward, as the mass and stiffness properties are obtained directly from the geometry and material properties. Only the damping coefficients for different plates need to be determined from experiments. Furthermore, this proposed 17-term analytical model has much higher computational efficiency than FEA.