考虑阻尼力的Hellinger-Reissner变分原理及其应用  

H-R variational principle with damping force and its application

作　　者：卿光辉[1] 冯振宇[1] 邱家俊[2] 

机构地区：[1]中国民用航空学院机械工程学院,天津300300 [2]天津大学机械工程学院力学系,天津300072

出　　处：《振动工程学报》2007年第1期29-34,共6页Journal of Vibration Engineering

基　　金：中国民航学院科研基金(No.05YK07M);国家自然科学基金资助(10072038)

摘　　要：建立了圆柱坐标系下包含粘滞阻尼力的修正后的Hellinger-Reissner变分原理,推导了对应的状态向量方程。考虑阻尼力后,结构的特征方程应有复数根,因而通常用于求解多项式方程实数根的二分法不再适用。为了解决这个问题,本文结合精细积分法和米勒法,为叠层壳的阻尼自由振动提出了新的数值方法,同时,通过数值实例分析了简支边界条件下开口叠层壳的复频响应问题。目前修正后的Hellinger-Reissner变分原理将有利于复杂边界条件下阻尼叠层壳动力学问题的半解析法的推导。In cylindrical coordinate system, a modified mixed variational principle with viscous damping force is established and the corresponding state-vector equation is derived. The consideration of damping force leads to a fact that there exist complex roots to the characteristic equation for the structures. Therefore, the usual dichotomy that is employed for the solution of the real roots to polynomial equation is not suitable for present question. In order to settle the question, via a combination of precise integration method and Muller method, a new numerical solution to the problem of the damping free vibration of laminated shells is proposed, at the same time, the complex-frequency responses of open laminated shells with simply supported conditions is analyzed through numerical examples. The variational formulation will be of benefit to the derivation of the semi-analytical solution for the dynamic problems of damping laminated shell with complex boundaries in this paper.

关 键 词：叠层壳 阻尼 自由振动 Hellinger—Reissner变分原理 状态向量方程 

分 类 号：O316[理学—一般力学与力学基础] O326[理学—力学]