Influence of thickness effects on impact responses of beam
厚度效应对梁冲击响应的影响

In Euler-Benoulli beam theory,Timoshenko beam theory and ordinary high order beam theories considering cross-section warping,the normal strain in the thickness direction is neglected,which can induce some errors in the analysis of transient responses which involved high frequencies.In elasticity the beam can be assumed to be in a state of plane stress,i.e.,there is no any assumption on longitudinal and transverse displacements,so the beam is a two-dimensional beam.In present study the impact problem of a particle on a two-dimensional beam is analyzed by indirect mode superposition method which is a semi-analytical method,by this method the problem of solving the equilibrium equation with singular right term ( point impact force) is avoided.The impact of a particle against a simply-supported two-dimensional beam whose modes can be obtained analytically and the frequency equation is explicit,is taken as an example to investigate the thickness effects on the transient responses,and the comparisons of results of the two-dimensional beam with that of Timoshenko beam,demonstrate that the thickness effects play an important role in the analysis of beam impact problem.The effects of dilatational (longitudinal) and distortional (shear) waves on dynamic responses such as impact loads are discussed.