A semi-analytical method to evaluate the dynamic response of functionally graded plates subjected to underwater shock

•A method for the underwater shock response of FG plates is proposed.•The method is based on the state space approach and numerical Laplace inversion.•In the new method Taylor׳s 1D FSI model is extended to include 3D for FG plate.•Validation of the present method is made by comparing it against published results.•The influences of back conditions and FG parameters are investigated in detail.

Functionally graded (FG) plates are of current interest and are widely used in a variety of applications including deep sea exploration and naval/marine and coastal engineering, despite the fact that there has, to date, been little research undertaken on the subject. In order to remedy the situation, an analytical method to investigate the elastic dynamic responses of FG plates to underwater shock is proposed here, their material properties varying by the same exponential law along the thickness direction. Taylor׳s one dimensional fluid solid interaction (FSI) model is extended to fit a three dimensional model suitable for FG plates. The extended FSI model and Laplace transform are integrated into the state space method, with the transient solution in the time domain being obtained by using the numerical inversion of the Laplace transform. The solutions of the total forces acting throughout the front and back faces in the time domain are derived for the first time. The present method is validated by comparing it with the results of other methods and experiments found in the relevant literature. The influence of the boundary conditions at the backside of the plate and FG parameters on front and back side pressures, cavitations, displacements, stresses and total forces acting throughout the faces are then investigated, with the time progression of the cavitation areas of air-backed plates and water-backed plates being investigated in detail. The method proposed in this paper may prove useful for the future three-dimensional assessment of the response of FG structures when FSI effects are taken into consideration. It is hoped that the results will lead to a full understanding of the mechanism of the interaction between fluid and an FG plate, and that they can be used as benchmark solutions in further research.