Analytical solution and experimental data of plate deflection on elastic bed under the ball impact

The aim of the present work is to determine the transverse deflection of a plate on the granular material under the impact of a ball. Through the analytical solution, the granular bed is equivalent to the elastic bed. The granular materials behave elastically by with a damping reaction under the impact loading. There are suggestions by literatures for introducing these elastic and damping effects which are used in the present work. The impact force is an intensive short duration force which is considered as a function of time and impact position. The equations of motion are derived by Hamilton's principle and the stress and strain relations are written by the first order shear theory and the vibration response of the plate is derived. Moreover, an experimental apparatus is designed to measure the plate deflection. Experimental parameters include the plate type and thickness, ball speed, impact position and granular thickness. The experimental data are used to validate the theoretical evaluations. The comparison of the evaluated and measured data shows that the theoretical model is acceptably gives the plate deflection.