弹性球体在冲击载荷下的应力波传播

给出了弹性球体在冲击载荷下应力波传播的解析解。该解法是利用特征函数展开法,将动力学的一般解分解为满足非齐次边界条件的准静态解和仅满足齐次边界条件的自由振动解,其中准静态解满足欧拉方程,而自由振动解满足贝塞尔(Bessel)方程。利用分离变量法,贝塞尔(Bessel)方程的解是一个由球贝塞尔函数构成的级数形式解,然后将此解和准静态解叠加,可得弹性动力学问题的解。与特征线法,积分变换法,广义射线法相比具有物理意义更加明确,数学解法更加简明的优点,同时这一解法可以推广到任意载荷下,各向同性弹性动力学中的一般球对称问题。

Stress Wave Propagation in Elastic Solid Sphere Subjected to Impact Load

A new analytic solution for stresses within an elastic solid sphere subjected to spherically symmetric impact loads is presented.The solution is based on the eigen-function expansion, which reduces the general dynamic solution to a quasi-static elastic solution and an elastic solution to free vibration problem.The static solution is subjected to Eulerian equation,and the vibration solution is given in the form of a series involving Bessel functions.The present analysis can be useful in investigating general elastodynamic problems.