Free vibration analysis and mode management of bistable composite laminates using deep learning

In this paper, for the first time, the deep learning technique of the artificial neural network method is used to determine the free vibration parameters of the rectangular bistable composite plates. For this purpose, first, the static and free vibration behaviours of a cross-ply bistable composite plate are studied using analytical, finite element and experimental methods. By comparing them, it is turned out that there is a considerable difference among obtained natural frequencies so that the analytical method is only able to determine the fourth natural frequency and cannot estimate the first three natural frequencies. To solve this problem, the deep neural network is employed to model the modal parameters of the bistable laminate as an explicit mathematical relationship that can be generalized to the other bistable composite plates. This mathematical relation makes it possible to obtain the natural frequencies in each of the stable configurations based on the geometric dimensions of the plate. In the following that, the inverse problem method is considered and the mode management capability is investigated. A fast swarm intelligence algorithm called firefly algorithm is used to optimize the optimization function of the mode management problem. Mode management using the evolutionary algorithm provides the appropriate physical dimensions of the plate according to the scenarios for natural frequencies arrangement. The results are validated by comparing them with those obtained by the finite element method and experiment test, which results show that this method estimates the modal parameters with high accuracy. The method used in this paper can also be applied to determine the modal parameters of other morphing structures.