考虑弹性地基的正交双曲蜂窝夹层壳体自由振动分析

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摘要本文给出了一种针对具有弹性地基的复杂形状蜂窝夹层壳体自由振动的半解析求解方法。基于一阶剪切理论并结合改进的Gibson公式，得到了正交双曲壳的运动学及动力学关系。通过对剪切因子进行修正并利用哈密顿原理，获得了系统在弹性地基约束下的自由振动控制方程，并利用改进傅里叶法对控制方程进行求解。数值算例表明，此方法具有较高的精度和计算效率；对蜂窝壳体的参数分析表明，系统固有频率随芯层厚度比的变化规律取决于弹性地基刚度，随蜂窝厚度比的增大而降低，随胞元角度及铺层方向的改变而波动变化。

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	倪臻
	李旦望1
	夏烨1
	周凯2
	3
	4
	华宏星2
	3
	4

关键词 ：正交双曲蜂窝夹层壳, 自由振动, 一阶剪切理论, 弹性地基

Abstract：A semi-analytical solution was proposed for the free vibration of doubly-curved honeycomb shell with elastic foundation. The kinematics and kinetics of the shell was obtained based on the first-order shear deformation theory and the modified Gibson’s formula. The governing equations for the free vibration of the shell were derived using the Hamilton’s principle with a modified shear correction factor, and solved by a modified Ritz’s method. Numerical results show the accuracy and efficiency of the proposed method. Parametric studies indicate that the trend of natural frequencies versus the thickness ratio is dependent on the stiffness of the elastic foundation, the natural frequencies decrease as the cell wall thickness increases, and fluctuate with the change of the cell angle and lamination angle of the honeycomb structure.

Key words： orthogonal doubly-curved honeycomb shell free vibration first-order shear deformation theory elastic foundation

收稿日期: 2021-02-01 出版日期: 2022-05-15

引用本文:

倪臻,李旦望1，夏烨1，周凯2,3,4，华宏星2,3,4. 考虑弹性地基的正交双曲蜂窝夹层壳体自由振动分析[J]. 振动与冲击, 2022, 41(9): 1-8.
NI Zhen1, LI Danwang1, XIA Ye1, ZHOU Kai2,3,4, HUA Hongxing2,3,4. Free vibration of orthogonal doubly-curved honeycomb shell considering elastic foundation. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(9): 1-8.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I9/1

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