Response of composite beam under low-velocity impact of multiple masses

Abstract

A theoretical method is presented to analyse the low-velocity impact dynamics of a system which consists of a laminated beam and multiple impactor masses. The contact forces between the beam and the impactors are treated as the internal forces of the system. The beam displacement field is defined using a higher-order shear deformation theory and the interaction behween the beam and the impactor masses is described with the modified Hertzian contact law. The potential and kinetic energies of the system (the energies associated with the beam and the impactors) are formulated in terms of the displacement field of the beam and the modified contact law. These are substituted into the Lagrangian equation to derive the governing equations of the system, which are nonlinear second-order differential equations. Simple polynomials are assigned to the shape functions of the beam in order to satisfy arbitrary boundary conditions. The present method is general in that it allows the impactors to be of different masses striking the beam with different initial velocities at arbitrary locations on the top surface of the beam. There is no limitation on the number of impactors that can be considered.