Influence of thickness effects on impact responses of beam

In Euler-Benoulli beam theory, Timoshenko beam theory andordinary high order beam theories considering cross-section warping, thenormal strain in the thickness direction is neglected, which can induce someerrors in the analysis of transient responses which involved highfrequencies. In elasticity the beam can be assumed to be in a state of planestress, i.e., there is no any assumption on longitudinal and transversedisplacements, so the beam is a two-dimensional beam. In present study theimpact problem of a particle on a two-dimensional beam is analyzed byindirect mode superposition method which is a semi-analytical method, bythis method the problem of solving the equilibrium equation with singularright term ( point impact force) is avoided. The impact of a particleagainst a simply-supported two-dimensional beam whose modes can be obtainedanalytically and the frequency equation is explicit, is taken as an exampleto investigate the thickness effects on the transient responses, and thecomparisons of results of the two-dimensional beam with that of Timoshenkobeam, demonstrate that the thickness effects play an important role in theanalysis of beam impact problem. The effects of dilatational (longitudinal)and distortional (shear) waves on dynamic responses such as impact loads arediscussed.