黏弹性Pasternak地基梁振动的复模态分析  

Complex modal analysis for vibrations of a beam on a viscoelastic Pasternak foundation

作　　者：彭丽[1,2] 丁虎[1] 陈立群[1,3] 

机构地区：[1]上海大学上海市应用数学和力学研究所,上海200072 [2]上海师范大学建筑工程学院,上海201418 [3]上海大学力学系,上海200444

出　　处：《振动与冲击》2013年第2期143-146,181,共5页Journal of Vibration and Shock

基　　金：国家杰出青年科学基金(10725209);国家自然科学基金项目(10932006;10902064);上海市重点学科建设项目(S30106);上海市青年科技启明星计划(11QA1402300);上海市教育委员会科研创新项目(12YZ028);上海师范大学青年教师项目(Sk200875)

摘　　要：运用复模态分析研究了有限长黏弹性Pasternak地基梁的振动特性,将梁的振动方程写成状态方程,利用复模态的正交性解耦为常微分方程组,得出复频率和复模态及任意初始条件下外激励的响应。通过两个具体算例对比,分析了简支边界条件下的Pasternak地基梁的固有频率和模态函数的特征,并通过文中给出的复模态函数,计算了两种典型外激励作用下的动力响应。The complex modal analysis was applied to investigate vibration of a beam with a finite length on a viscoelastic Pasternak foundation. The vibration equation of the beam was expressed in the form of state equations and decoupled into a set of ordinary differential equations based on the orthogonality of modal functions. The complex frequencies, modal functions, and dynamical responses to external excitations with any initial conditions were derived. Comparing two specific examples, with a simply supported boundary condition, the characteristics of the natural frequencies and modal functions were analyzed, and with the deduced modal functions, the dynamical responses to two typical external excitations were ziven.

关 键 词：黏弹性 地基梁 固有频率 模态函数 复模态分析法 

分 类 号：O32[理学—一般力学与力学基础]