Forced Vibration Analysis of a Hydroelastic System with an FGM Plate, Viscous Fluid, and Rigid Wall Using a Discrete Analytical Method

This study examines the forced vibration behavior of a hydroelastic system composed of a functionally graded material (FGM) plate, a barotropic compressible Newtonian viscous fluid, and an adjacent rigid wall. The fluid occupies the gap between the plate and the wall. A time-harmonic force, applied in and along the free surface of the FGM plate, excites vibrations within the system. The plate’s motion is modeled using the exact equations of elastodynamics, while the fluid dynamics are described by the linearized Navier–Stokes equations for compressible viscous flow. The governing equations, which feature variable coefficients, are solved using a discrete analytical approach. Boundary conditions enforce impermeability at the rigid wall and continuity of both forces and velocities at the fluid–plate interface. The investigation focuses on the plane strain state of the plate coupled with the corresponding two-dimensional fluid flow. Numerical analyses are conducted to evaluate normal stresses and velocity distributions along the interface. The primary objective is to assess how the graded material properties of the plate influence the frequency-dependent responses of stresses and velocities at the plate–fluid boundary.