Dynamic response of composite laminated beams under asynchronous/repeated low-velocity impacts of multiple masses

This paper presents a theoretical method for low-velocity impact analysis of composite laminated beams with arbitrary lay-ups and various boundary conditions subjected to asynchronous/repeated impacts of multiple masses. The analysis is based on the higher-order shear deformation beam theory and the modified Hertzian contact law is used for modeling the interaction between the laminated beam and the impactors. Non-linear second-order partial differential equations of the motion are derived using the Lagrangian equations of the second kind. According to the Ritz method, simple polynomials are assigned to the shape functions of the displacement field of the laminated beam in order to satisfy arbitrary boundary conditions. The validity of the formulation is confirmed by comparing the present solutions with results available in the literature. Numerical examples showed that the time of impact play an important role on contact forces, beam displacements, absorbed energies by the beam and normal and shear stresses by positive and negative superposition of induced waves.