Low-velocity impact response for laminated stepped beam

Abstract

A numerical method is presented to evaluate the response of a laminated stepped beam under a transverse low velocity impact. The impactor and the laminated beam are considered as a single system and thus the impact force becomes the internal force of the system. The energies associated with each span of the beam and the impactor mass are derived in the form of a higher order shear deformation theory and Sun's modified contact law. These are substituted in the Lagrangian equation of motion to arrive at the governing equations of the system. The equations are uncoupled by principal coordinate transformations and then solved numerically. The solutions can be obtained for arbitrary boundary conditions. Natural frequency parameters are compared with the available literature results wherever possible and very good agreement is achieved. New case studies are discussed in detail to demonstrate the efficiency of the method.