Winkler地基上变厚度圆(环)板的非对称自由振动

THE ASYMMETRIC FREE VIBRATION OF THE CIRCULAR (ANNULAR) PLATES WITH VARIABLE THICKNESS ON WINKLER FOUNDATION

本文提出了Winkler地基上变厚度圆(环)板非对称自由振动的传递矩阵法.应用贝塞尔函数理论,求得等厚度圆板和环板单元非对称自由振动传递矩阵的正确公式.然后将Winkler地基上的变厚度圆(环)板划分成一系列的等厚度的圆板和环板单元,应用传递矩阵原理得到变厚度圆(环)板的整体传递矩阵公式.最后给出了一些数值结果,表明板厚和地基模量变化对固有频率的影响.

In this paper, the transfer matrix method for the asymmetric free vibration of the circular (annular) plates with variable thickness on Winkler foundation is presented. Applying the theory of Bessel function, the exact transfer matrix formulae of the asymmetric free vibration of the circular and annular plate elements with uniform thickness can be obtained. Then, the variable thickness circular (annular) plates on Winkler foundation are decomposed into a series of uniform circular and annular plate elements and the global transfer matrix formulae of the variable thickness circular and annular plates are obtained by use of transfer matrix method. Some numerical results are given, which demonstrate the effects of plate thickness and foundation modulus on the natural frequencies.