Three-dimensional analytical solution of free vibrations of a simply supported composite plate in contact with a fluid

Background: The quantification of fluid-structure interactions is critical for the design and optimization of marine structures. As composite materials gain more traction in naval construction, there is a dire need of modeling tools to detail the dynamic response of composites in contact with fluids. Current structural theories and finite-element simulations offer promising pathways, but their strong hypotheses on through-the-thickness deformations and high computational cost challenge their practical feasibility. Methods: We propose an analytical three-dimensional solution to the free vibration of a bidirectional composite, separating a fluid column from vacuum. We leverage Pagano's method to describe the three-dimensional displacement field in each ply of the composite plate and the fluid potential in the form of a Fourier series. Results: An analytical solution to the coupled fluid-structure problem is derived by imposing the continuity of displacement and stress at the ply interfaces, as well as boundary conditions on dry and wetted plies. We specialize the solution to sandwich structures of naval interest, offering insight on how the interactions with water can dramatically affect mode shapes and through-the-thickness profiles of displacement and stress. Discussion: The proposed approach provides the foundations for the design of thick composite plates for use in marine structures.