含复杂结构应力的平板振动解析方法研究

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振动与冲击 ›› 2017, Vol. 36 ›› Issue (20) : 12-17.

论文

含复杂结构应力的平板振动解析方法研究

杨念1，陈炉云1，易宏 , 刘勇2

作者信息 +

Analytical Method Study of the Complex Stressed Plate Vibration

Nian Yang 1 Luyun Chen 1 Hong Yi 1 Yong Liu 2

Author information +

文章历史 +

摘要

工程结构物中常常含有分布形式复杂的非均匀结构应力，该应力会影响结构的振动特性。有限元法虽然可以求解，但不利于从本质上分析结构应力与振动的内在物理联系、不方便研究结构应力对振动的影响规律，而且还有施加特定非均布应力操作复杂、计算量较大等限制。在解析方法研究方面，以往的方法主要用来求解含整体均匀分布应力的结构，不适用于实际工程结构中的非均布应力的情况。本文提出一种求解含非均布应力结构振动的解析方法，以平板结构为对象，用特殊级数形式表示非均布的结构应力，将应力影响加到原平板振动方程，并实现结构模态的部分解耦，然后对解耦后的方程进行求解得到解析解。本文推导的解析方法适用于任意应力状态下的平板振动求解，并且相对于有限元法有计算量小、物理解释明晰等优点，方便定性地研究结构应力与振动之间的物理联系，进行考虑结构应力的振动精确预报与控制。

Abstract

There often exists non-uniform distributed stress in practical engineering structure, and this kind of stress would infect the structural vibration. Although Finite Element Method (FEM) can solve this problem, it cannot help us understand the physical link and influence law between structural stress and vibration. At the same time FEM has some shortages like the process of applying non-uniform stress is complicated and calculation cost is huge. In analytical method study, the former methods can’t be applied to deal with the practical stress because they mainly focused on the uniform distributed stress. In this paper, we come up with a novel analytical method, and represent the non-uniform stress into a special series form to obtain the partial de-coupling. Then solve this de-coupling vibration equation and get the analytical solution. The method can be applied to solve the vibration of plate structure with arbitrary stress state and has the advantages to FEM in calculation cost and physical explanation. It can help us to understand the connection between the structural stress and vibration and assist predicting and controlling the vibration.

导出引用

杨念1，陈炉云1，易宏,刘勇2. 含复杂结构应力的平板振动解析方法研究[J]. 振动与冲击, 2017, 36(20): 12-17

Nian Yang 1 Luyun Chen 1 Hong Yi 1 Yong Liu 2. Analytical Method Study of the Complex Stressed Plate Vibration[J]. Journal of Vibration and Shock, 2017, 36(20): 12-17

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