弹性基上锥壳固有振动的精确解  

The Exact Solution for the Free Vibration of Conical Shells on the Elastic Foundation

作　　者：孙博华[1] 黄义[2] 

机构地区：[1]兰州大学 [2]西安冶金建筑学院

出　　处：《兰州大学学报（自然科学版）》1989年第1期23-31,共9页Journal of Lanzhou University(Natural Sciences)

摘　　要：本文从弹性基(Winkler 模式)上锥壳的 DMV 型位移微分方程组出发,通过引入一个位移函数 U(s,θ,t)(在极限情况下,将退化成 B.3.BπacoB 对于圆柱壳引入的位移函数),将基本微分方程组化成为一个可解偏微分方程.这个方程的精确解用级数形式给出.当固有频率ω=(kg/ρh)^(1/2)时,解用广义超几何函数给出;轴对称问题的解用 Bessel 函数给出.Starting from the DMV type differential equations of conical shells onthe elastid foundation(Winkler Model),and introducing a H—S dis-placement function U(s,θ,t)(in limited cases,it will be reduced intothe Vlasov'sdisplacement function for the circular cylindrical shells),the differential eguations have been changed into a soluble partialdipperential equatial about U(s,θ,t),its exact solution has beengiven in series form.When the eigenfrequence ω=■,the exact solutionof the equation can be given in generalized hypergeometric function,andthe Solution of axial Symmetry in Bessel functions.

关 键 词：弹性基 微分方程组 上锥壳 振动 

分 类 号：O32[理学—一般力学与力学基础]