锻压技术

切向均布随从力作用下的矩形薄板稳定性分析

英文标题：Stability analysis on rectangular plate under uniformly distributed tangential follower force

作者：杨峰王忠民韩玉强

分类号：O317；TG386

出版年,卷(期):页码：2012,37(4):43-45

摘要：

对于不同边界条件下受切向均布随从力的矩形板，通过改变边长比，板的失稳临界值发生变化。建立受切向均布随从力的矩形板的运动微分方程，利用微分求积法得到复特征方程。通过求解复特征方程，得出矩形板振动复频率与随从力的变化关系，以及边长比对梁失稳形式的影响。计算结果表明：方板在随从力作用下存在二次稳定问题；保持与随从力垂直方向的边长不变，而增大与随从力平行方向的边长，板失稳临界值增大幅度明显；对边简支另一对边固支矩形板，当边长比小于某一数值时，板的失稳形式为发散；而当边长比大于该值时，板的失稳形式为颤振失稳。

By changing ratio of side length, the critical value of follower force of unstability of rectangular plate under uniformly distributed tangential follower force with different boundry conditions were changed. The differential equation of motion of the rectangular plate was established. By using differential quadrature method, numerical results of the complex characteristic equation were calculated. Relations between frequency and follower force, influence of ratio of length on the instability form were induced. The results show that there are a secondary buckling behavior of square plate under follower force; keeping the side length perpendicular to the follower force, improving the side length parallel to the follower force, the critical value of follower force increases evidently. To the rectangular plate with SCSC boundry condition, when the ratio is under a certain value, instability of the plate will always be divergence, when it's beyond the value, instability of the plate will always be flutter.

基金项目：

参考文献：

［1］周祥玉,范祖尧.受压薄板屈曲试验研究[J].上海交通大学学报, 1992, 26(4): 14-19.
［2］Goman D J. Free Vibration Analysis of Rectangular Plates[M]. Elsevier North Holland, Inc. 1982.
［3］仝立勇.任意变厚度矩形薄板的屈曲和振动[J].应用力学学报,1988,(1):120-125.
［4］王忠民, 计伊周. 矩形薄板在随从力作用下的动力稳定性分析[J]. 振动工程学报,1992, 5(1): 78-83.
［5］王忠民, 计伊周. 具有弹性约束的非保守矩形薄板的振动和稳定性[J].应用力学学报, 1996,13(增刊）: 14-18.
［6］王忠民, 赵凤群. 弹性非保守简支矩形薄板的后屈曲性态[J]. 西安理工大学学报，1997, 13 (3): 238-242.
［7］杨峰，王忠民.点支承对受随从力梁稳定性的影响[J].机械工程学报,2010,46(20): 92-96.
［8］沈观林，胡更开.复合材料力学[M].北京：清华大学出版社，2006.

服务与反馈：

【本网站尚未开通全文下载服务】【加入收藏】