点弹性支承的非保守矩形薄板的稳定性

The Stability of Non Conservative Rectangular Plate with Spring Attachments

对带有点弹性支承且受随从力作用的矩形薄板，采用积分方程理论，把问题的控制微分方程化成相应的积分方程，并根据退化核特性得到了相应的特征方程，分析了点弹性支承的刚度及其位置对非保守矩形薄板的自振频率和稳定性的影响。该方法可以方便地解决控制微分方程中因点弹性支承而出现的奇异项问题。

The differential equation of vibration mode of rectangular plates with spring attachments under the action of uniformly distributed tangential follower force is reduced to the corresponding integral equation using the integral equation theory. The characteristic equation is derived in accordance with the properties of degenerative nucleus. Also, the effects of stiffness factor and locations of spring attachments upon the self vibrating frequency and stability of the non conservative rectangular plate are analysed. This method is convenient to be used in solving the singular term problems occured in the governed differential equation because of spring attachments.