GDQR求解切向力下复杂弹性支承梁的稳定性  

Stability of elastically supported beams subjected to a partially tangential force based on GDQR

作　　者：李威[1] 曾志松[1] 韩旭[2] 

机构地区：[1]华中科技大学船舶与海洋工程学院,湖北武汉430074 [2]湖南大学机械与运载工程学院,湖南长沙410082

出　　处：《华中科技大学学报（自然科学版）》2012年第11期68-71,共4页Journal of Huazhong University of Science and Technology(Natural Science Edition)

基　　金：国家杰出青年科学基金资助项目(10725208)

摘　　要：针对具有复杂弹性支承条件下的欧拉梁,建立其在切向力作用下的运动微分方程.采用广义微分求积法(GDQR)对微分方程在空间上进行离散,获得由动力方程组及边界条件组成的特征值矩阵方程,通过求解特征值矩阵方程来分析梁的稳定性.由计算结果可以发现:剪切系数对临界载荷的影响与梁两端4个支撑弹簧的刚度组合关系密切,当两端各有一个弹簧刚度取无穷大时,剪切系数对临界载荷大小没有影响;随着剪切系数的变化,一端固支、一端弹性支承梁的失稳形式会发生突变.t The motion differential equations for complex elastically supported Euler beam subjected to tangential force were established. The matrix eigenvalue equations consist of the dynamic equations and boundary conditions were obtained after discretized by generalized differential quadrature rule （GDQR） in space,then the stability of beam could be analysed through solving the eigenvalue matrix equations. From the calculation results, it showed that there was a close relationship between the in- fluence of tangential force to critical load and the combination of 4 supporting spring stiffness at both ends, especially when one spring stiffness value takeing infinite at each end, tangency coefficient made no effects on the value of critical load, meanwhile, with the change of tangency coefficient, the insta- bility style of clamped-elastically suppported beam would change.

关 键 词：广义微分求积法 稳定性 弹性支承梁 切向力 临界载荷 

分 类 号：O327[理学—一般力学与力学基础]