圆形或扇形薄板竖向小振动两个基本问题探讨

Investigating on two basic problems on vertical small vibration of thin circular or sectorial plate

理论上对圆形或扇形薄板小挠度理论下的竖向小振动问题作了进一步的探讨,再次讨论了圆心处的自然边界条件的提法,纠正了相关文献上的一些不恰当说法,得到用分离变量法求解扇形薄板的小振动问题的过程中,求解结果与先求角向部分变量或先求径向部分变量的次序无关.经典的边界条件的提法与变分法没有矛盾.结论表明,到目前为止,传统的薄板理论在解决板的竖向小振动问题上都是正确的.

The vertical vibration of thin circular or sectorial plate under small flexivity theory is further investigated,and the natural boundary condition problem at the center of circle is discussed.The mistakes in several relative literature are analyzed and corrected.In the process of using variable-separated method to seek the solution of vibration on sectorial plate,the results are unrelative to the order of solving the angular and radical direction function,the classical views on boundary condition agree with the outcomes of variational method.It is concluded that the traditional theories of thin plate on solving the vertical small vibration problems are all proper up to present.