部分水下弹性支承等截面梁柱的自由振动分析  

THE FREE VIBRATION ANALYSIS OF A BAEM PARTLY IMMERSED IN A FLUID ON COUPLED ELASTIC FOUNDATION

作　　者：杨骁[1] 徐小辉[2] 

机构地区：[1]上海大学土木工程系,上海200072 [2]上海市应用数学和力学研究所,上海200072

出　　处：《工程力学》2009年第7期60-65,共6页Engineering Mechanics

基　　金：上海市自然科学基金项目(06ZR14037)

摘　　要：研究浸入流体中自由端具有集中质量块的等截面弹性支承悬臂梁的横向自由振动。考虑由集中质量块引起的轴向力作用,建立了支承处弹性水平位移约束和转动约束耦合情形下悬臂梁横向自由振动数学模型。由于集中质量块的惯性力和惯性距,此模型的边界条件与固有频率相关。推导了梁自由振动的频率方程和振动模态的广义正交性条件。数值研究了水深、集中质量块质量、转动惯量、质心距以及弹簧耦合刚度等参数对悬臂梁固有频率和正则模态的影响。The transversal free vibration of an elastically supported cantilever beam carrying a tip mass m a fluid is investigated. Taking the compression axial force due to the tip mass into account, the mathematical model of a cantilever beam, in which constrains of the elastic horizontal displacement and elastic rotation are coupled, is presented. Due to the inertial force and inertial moment of the tip mass, the boundary conditions of the mathematical model are frequency dependent. The frequency equation and the generalized orthogonal condition for the vibration modes are derived analytically. The influences of the draft ratio, tip mass, moment of inertia, location of the tip mass and coupled spring-stiffness on the natural frequencies and vibration modes are discussed numerically.

关 键 词：自由振动 弹性支承 固有频率正则模态集中质量块 

分 类 号：O321[理学—一般力学与力学基础] O39[理学—力学]