黏弹性传输结构横向振动频率摄动分析  

Perturbation Analysis for Transverse Vibration Frequencies of Viscoelastic Transporting Structures

作　　者：骆毅[1] 丁虎[2] 

机构地区：[1]广州航海高等专科学校航务工程系,广州510330 [2]上海大学上海市应用数学和力学研究所,上海200072

出　　处：《力学季刊》2012年第2期298-302,共5页Chinese Quarterly of Mechanics

基　　金：国家杰出青年科学基金(10725209);国家自然科学基金重点项目(10932006);国家自然科学基金项目(10902064);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)

摘　　要：将传输结构模型化为轴向运动黏弹性Euler-Bernoulli梁,通过多尺度摄动方法近似解析地研究了传输结构横向振动频率受黏性的影响。采用物质导数本构关系描述结构的黏性属性。将黏性对横向振动频率的影响视为扰动,即视无量纲黏性系数为小量,运用二阶直接多尺度方法,对两种经典边界下轴向运动梁的控制方程建立了可解性条件,给出了黏性系数与振动频率之间的关系。研究了不同黏性工况下,系统前两阶固有振动频率随传输速度的变化。The transporting structures were modeled as axially moving viscoelastic Euler-Bernoulli beams. The effects of viscoelastic on the frequencies of transverse vibration were investigated via a perturbation analytical method with numerical confirmations. The material time derivative was used in the viscoelastic constitutive relation. The two terms multiple scales method was applied directly to the governing equation without discretization. The relationship between viscoelasticity and vibration frequency was derived via establishing a solvability condition for two kinds of classical boundary conditions. Numerical examples show the effects of the viscoelastic coefficient on the changing first two frequencies with the axial speed.

关 键 词：传输梁 振动 黏弹性 固有频率 多尺度方法 

分 类 号：O32[理学—一般力学与力学基础]