含复杂结构应力的平板振动解析方法研究  

An analytical study of complex stressed plate vibration

作　　者：杨念[1] 陈炉云[1] 易宏[1] 刘勇 

机构地区：[1]上海交通大学船建学院海洋工程重点实验室,上海200240 [2]中船重工第七0二研究所上海分部,上海200011

出　　处：《振动与冲击》2017年第20期12-17,共6页Journal of Vibration and Shock

基　　金：海洋工程国家重点实验室基金资助(1507)

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。提出了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。推导出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。There often exists non-uniform distributed stress in practical engineering structures, and this kind ofstress affects structural vibration. Although finite element method （FEM） can solve this problem, it cannot help us with understanding the physical mechanism between structural stress and vibration. At the same time, FEM has other shortages like the process of applying non-uniform stress is complicated and calculation cost is huge. For analytical methods, the traditional methods cannot be applied to deal with practical stress because they mainly focus on uniform distributed stress. In this paper, we come up with a novel analytical method, and represent the non-uniform stress with a special series form to obtain the partial decoupling. Then we solve this de-coupling vibration equation and get the analytical solution. The method can be applied to solve the vibration of plate structures with arbitrary stress state and has the advantages to FEM in calculation cost and physical explanation. It can help us with understanding the connection between the structural stress and vibration and assists predicting and controlling the vibration.

关 键 词：复杂应力 平板结构 振动 解析法 

分 类 号：TB535[理学—物理]