On the Dynamic Response of a Fluid-Supported Elastic Plate Subjected to a Low Velocity Projectile Impact

Abstract

In this paper, the dynamic response of a rectangular elastic plate supported by a fluid on one side and impacted by a low velocity projectile on the other side is analyzed for the first time. A nonlinear Volterra integral equation for impact force F(t)is derived, and a linear numerical method is proposed, which is used to solve the equation and calculate the transverse deflection of and the bending stress in the plate. The presence of the fluid not only lowers the natural frequency of the plate due to the increased inertia, but also damps its transverse vibration due to the energy dissipated in the form of sound waves. As a practical example, the transverse deflection of a square plate supported at the edges and impacted centrally by a low velocity sphere and the impact force are computed numerically. Our results for the natural frequencies of the system consisting of the plate and the fluid, and the transverse deflection-time curve at the center of the plate in vacuo are in excellent agreement with those reported previously.