Vibration characteristics of thin rotating cylindrical shells with various boundary conditions
Vibration characteristics of thin rotating cylindrical shells with various boundary conditions
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DOI：
10.1016/j.jsv.2012.04.018
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发表时间：
2012-08
影响因子：
4.7
通讯作者：
Shupeng Sun;S. Chu;D. Cao
中科院分区：
文献类型：
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作者：
Shupeng Sun;S. Chu;D. Cao
本文用傅里叶级数展开法分析了各种边界条件下旋转圆柱薄壳的振动特性。本文从Sanders壳体方程出发，导出了考虑离心力、科氏力以及旋转引起的初始环向张力影响的壳体运动控制方程。位移场表示为傅立叶级数表达式的产品，代表轴向模态位移和三角函数，代表周向模态位移。利用斯托克斯变换导出了傅里叶级数表达式的导数。然后，通过公式推导过程，可以得到具有任何类型的经典边界条件的旋转薄柱的精确频率方程的显式表达式。一旦确定了频率方程，就可以数值计算频率。为了验证本分析，本方法的结果和以前的研究进行比较，并取得了很好的协议。最后，将该方法应用于研究旋转圆柱薄壳在各种边界条件下的振动特性，给出了计算结果。
An analysis is presented for the vibration characteristics of thin rotating cylindrical shells with various boundary conditions by use of Fourier series expansion method. Based on Sanders’ shell equations, the governing equations of motion which take into account the effects of centrifugal and Coriolis forces as well as the initial hoop tension due to rotating are derived. The displacement field is expressed as a product of Fourier series expressions which represents the axial modal displacements and trigonometric functions which represents the circumferential modal displacements. Stokes’ transformation is employed to derive the derivatives of the Fourier series expressions. Then, through the process of formula derivation, an explicit expression of the exact frequency equation can be obtained for a thin rotating cylinder with classical boundary conditions of any type. Once the frequency equation has been determined, the frequencies are calculated numerically. To validate the present analysis, comparisons between the results of the present method and previous studies are performed and very good agreement is achieved. Finally, the method is applied to investigate the vibration characteristics of thin rotating cylindrical shells under various boundaries, and the results are presented.