厚度效应对梁冲击响应的影响

INFLUENCE OF THICKNESS EFFECTS ON IMPACT RESPONSES OF BEAM

用一种半解析法——间接模态叠加法,研究了质点与弹性力学梁的冲击问题,这种方法避免了具有未知奇异载荷项的平衡微分方程求解问题。由于可以用解析方法得到简支弹性力学梁的模态函数,并且能够以显式形式给出其频率方程,因此以质点与简支弹性力学梁的冲击问题为例,来考察厚度效应对瞬态响应的影响,并将所得结果与用Timoshenko梁理论所得结果进行了比较,说明了厚度效应在梁冲击问题中的重要影响。讨论了纵波和剪切波对撞击力等动力响应的影响。

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.