Low Velocity Impact of a Viscoelastic Beam

Abstract

A theoretical solution for the response of a viscoelastic beam to off-center low speed transverse impact is presented. The flexural model adopted for investigation consists of a uniform Bernoulli-Euler beam whose behavior has been generalized to include a linear viscoelastic constitutive relation for each element of the beam. Further, the beam and rigid impactor are assumed to remain in contact during the resulting motion and a consistent set of initial displacement and velocity distributions is adopted for the beam. The solution method utilizes two Laplace transforms, i.e., one with respect to space and the other with respect to time. Comparison of the numerical predictions of the theoretical model with central impact test results on graphite-epoxy composite laminates indicates a good agreement between theory and experiment.