Linear Analysis Method for the Dynamic Response of a Winkler Foundation-Supported Elastic Plate Subjected to Low Velocity Projectile Impact

This work considers the dynamic response of an elastic plate with arbitrary boundary shape supported by a linear viscoelastic Winkler foundation, and impacted by a low velocity projectile. A nonlinear Volterra integral equation on impact force F (t) is deduced, and an effective numerical method is used to solve the equation and calculate the transverse deflection of the plate. The presence of the foundation in our problem has the effect of damping the transverse vibration of the plate owing to the absorbed energy. As a practical example, the transverse deflection of a square plate with simply supported edges impacted centrally by a sphere and the impact force are computed numerically.