变厚度旋转圆柱壳的自由振动研究

Free vibration of rotating cylindrical shells with variable thickness

为了提高旋转圆柱壳结构的使用性能和工作效率,减轻其质量已成为有效方式之一,针对这一需求,旋转圆柱壳结构有设计为厚度沿轴向变化即变厚度的趋势。基于此,利用Chebyshev-Ritz方法,对厚度沿轴向有3种线性变化形式的变厚度旋转圆柱壳的自由振动进行研究。考虑科氏力与离心力的影响,基于Sanders壳理论,将圆柱壳的位移场近似展开为Chebyshev多项式与边界函数乘积的形式,计算变厚度旋转圆柱壳的动能与势能,再根据Ritz方法获得变厚度旋转圆柱壳的频率方程。在此基础上,将所得结果与已有文献中的结果进行比较,验证了建模方法的准确性,并对计算结果进行了收敛性研究。最后比较了不同厚度变化形式下旋转圆柱壳的自由振动,并讨论了转速、厚度变化参数、圆柱壳长径比等参数对变厚度旋转圆柱壳自由振动的影响。

In order to improve the performance and efficiency of the rotating cylindrical shell structure,reducing its mass has be-come one of the effective ways.In response to this demand,the rotating cylindrical shell structure has a tendency to be designed to vary the thickness along the axial direction,i.e.,variable thickness.The vibration traveling wave characteristics are investigated by using the Chebyshev-Ritz method.The displacement field of the cylindrical shell is expanded in the form of the product of the Che-byshev polynomial and the boundary function.The kinetic and potential energies of the rotating cylindrical shell with variable thick-ness are calculated based on the Sanders shell theory considering the effects of Coriolis forces and centrifugal forces.Then,the fre-quency equation of the rotating cylindrical shell with variable thickness is obtained according to the Ritz method.The accuracy of the modeling method is verified by comparing the present results with those in literature,and the convergence of the calculated re-sults is studied.Finally,the free-vibration traveling wave characteristics of the rotating cylindrical shell in different forms of thick-ness variation are compared,and the effects of parameters such as rotational speed,thickness variation parameters and cylindrical shell aspect ratio on the free-vibration traveling wave characteristics of the rotating cylindrical shell with variable thickness are dis-cussed.