本文采用Haar小波方法结合Floquet 指数法对不同边界条件下转动锥壳的参激振动稳定性进行了分析。基于Love一阶近似壳体理论,给出了周期性载荷作用下转动锥壳的动力学控制微分方程,采用Haar小波离散方法将其转化为具有周期性时变系数的Mathieu-Hill型常微分方程组。考虑到Bolotin法不能应用于陀螺系统的参激失稳特性分析,以及多尺度法受限于小参数情形的事实,本文采用了对参激系统普遍适用的Floquet 指数法对转动锥壳的参激振动稳定性进行分析。通过与其他文献结果的对比,验证了所采用模型及稳定性分析方法的正确性。在此基础上,讨论了固支-固支、简支-简支、固支-简支和简支-固支等几种不同边界条件下转速和半顶角对转动锥壳不稳定区的影响。
Abstract
In this paper, we studied the parametric vibration characteristics of rotating truncated conical shells with different boundary conditions using the Haar wavelet combined with Floquet exponent method methods. The present work is based on the Love first-approximation theory for classical thin shells. The governing equations of motion for the shell are reduced into a system of Mathieu-Hill equations by means of the Haar wavelet method. In consideration of the fact that Bolotin method could not be applied to gyroscopic systems and the multi-scale method limited to small parameters, Floquet exponent method is employed to conduct parametric stability analysis of rotating truncated conical shells. The correctness of present method is validated by comparing the results with those reported in the literature. In addition, numerical results are presented to bring out the influences of rotation speed and semi-vertex angle on the parametric instability regions of rotating conical shells under four different boundary conditions.
关键词
转动锥壳 /
参激失稳 /
边界条件 /
Floquet指数法
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Key words
rotating conical shells /
parametric instability /
boundary conditions /
Floquet exponent method
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