切向均布随从力作用下的矩形薄板稳定性分析

Stability analysis on rectangular plate under uniformly distributed tangential follower force

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 paral- lel 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 ifs beyond the value, instability of the plate will always be flutter.