Simulation of the dynamic response of GLARE plates subjected to low velocity impact using a linearized spring-mass model

In this article, the low velocity impact response of circular clamped GLARE fiber-metal laminates is treated analytically using a linearized spring-mass model. Differential equations of motion which represent the physical impact phenomenon are formulated and the corresponding initial value problems are set. Then, exact symbolic solutions of these problems are derived and expressions to calculate the impact load, position, velocity and kinetic energy time histories are given. Also, analytical equations to predict the coefficient of restitution and the energy restitution coefficient of the impact event are presented. The analytical formulas are applied in order to simulate published experiments concerning normal central low velocity impact of GLARE 4 and GLARE 5 circular laminates. The analytical and experimental impact load time histories of the two GLARE plates are found in good agreement. Apart from circular clamped GLARE plates, the equations of this article can also be employed in order to approximate the response of other GLARE or hybrid composite structures, when subjected to similar low velocity impact damage phenomena.