含复杂预应力圆薄板振动模态解析方法研究  

Analytical method of vibration modal for circular thin plate with complex pre-stress distribution

作　　者：陈炉云[1,2] 黄惜春[3] CHEN Lu-yun;HUANG Xi-chun(State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;.MOE Key Lab Marine Intelligent Equipment&System,Shanghai Jiao Tong University,Shanghai 200240,China;China Ship Development and Design Center,Wuhan 430064,China)

机构地区：[1]上海交通大学海洋工程国家重点实验室,上海200240 [2]上海交通大学海洋智能装备与系统教育部重点实验室,上海200240 [3]中国舰船研究设计中心,武汉430064

出　　处：《船舶力学》2020年第8期1062-1071,共10页Journal of Ship Mechanics

基　　金：海洋工程国家重点实验室基金资助项目(1507)。

摘　　要：本文研究预应力对圆薄板结构动力响应的影响,解决圆薄板结构中非均匀分布预应力的动力响应问题。根据含预应力的薄板结构应力-应变方程,建立含预应力圆薄板结构的运动控制微分方程。将焊接残余应力定义为复杂预应力,提出一种适用于复杂预应力分布的圆薄板解析求解方法。以具有周边简支边界条件薄圆板结构为例,对比焊接残余应力的不同分布形式对薄圆板结构固有频率及振型的影响。最后,利用有限元法对文中所提方法有效性进行验证。The influence of the pre-stress on circular thin plate is investigated to solve the dynamic response problem with non-uniform pre-stress distribution. According to the structure pre-stress theory, the differential equation of the circular plate with complex pre-stress distribution is derived based on the strain-displacement equation. The welding residual stress is defined as complex pre-stress, and the approach to analyze the dynamic characteristics of thin circular plate with complex pre-stress distribution is proposed. By taking a circular plate with simply-supported boundary conditions as an example, the influences of different types of welding residual stress distribution on the natural frequency and mode shape are compared. Finally,the effectiveness of the proposed model is verified through finite element method(FEM).

关 键 词：复杂预应力 圆薄板 解析解 振型 固有频率 

分 类 号：TB535[理学—物理]