A Semi-analytical Solution of Wave-Controlled Impact on Composite Laminates

Based on the structural model for wave-controlled impact, a modified Hertzian contact law was used to investigate impact responses of composite laminates. The original nonlinear governing equation was transformed into two linear equations using the method of asymptotic expansion. Closed-form solution can be derived for the first linear homogeneous equation, which is the equation of motion for single degree of freedom system with viscous damping. The second linear non-homogeneous equation was solved numerically. The overall impact responses for wave-controlled impacts can be obtained semi-analytically and agree well with the numerical solutions of nonlinear governing equations. The proposed methodology is useful for providing guidance to numerical simulation of impact on complex composite structures with contact laws fitting from experimental data.