不连续Reissner矩形板的自由振动  

Free Vibration Analysis for Reissner's Rectangular Plate with Discontinuities

作　　者：武兰河[1] 王道斌[1] 

机构地区：[1]石家庄铁道学院,石家庄050043

出　　处：《应用力学学报》2001年第2期98-102,共5页Chinese Journal of Applied Mechanics

摘　　要：用分区加权残值法研究Reissner矩形板在几何形状、边界条件等有突变时的自由振动问题。将研究对象按照结构几何形状和边界条件的具体情况划分为若干子域 ,在每个子域内用不同的试函数代入该域内的控制方程到内部残值 ,并代入板的边界条件和各子域的协调条件得到边界残值和连续性残值 ,然后用最小二乘法消除残值 ,得到特征方程。文中讨论了该方法的收敛性和计算精度 ,求解了开孔矩形板的固有频率 ,并与已有结果进行了比较 ,结果表明 :该方法收敛性好 ,精度较高 。In this paper, a numerical method, the weighted residual method is developped fo r the vibration problems of Reissne's plates with different discontinuities incl uding the discontionus geometry and the mixed boundaries. The basic idea of thi s method is, according the structure and boundary conditions, divide the whole variable domain into several subdomains, and apply the weighted residula method for each subdonain with various trial functions. The characteristic equation is derived by eliminating the residuals obtained from governing equations, boundar y conditions and compatibility conditions with the list square method. The conv ergency and accuracy of the method are carefully investigated for the solution of natural frequencies of Reissner's plates. Finally, the method of weighted re siduals is applied to analyzed several vibration problems of Reissner's rectang ular plates with cutouts. The accuracy and aplicability of this method have bee n examined by comparing the present solutions with existing ones obtained by oth er numerical methods.

关 键 词：不连续Reissner矩形板 自由振动 加权残值法 自然频率 最小二乘法 

分 类 号：O343.1[理学—固体力学] TU311.3[理学—力学]