黏弹性变速度轴向运动梁的稳定性分析  

ANALYSIS OF STABILITY IN PARAMETRIC RESONANCE OF AN AXIALLY ACCELERATING VISCOELASTIC BEAM

作　　者：丁虏[1] 丁虎[1] 陈立群[1,2] 

机构地区：[1]上海市应用数学和力学研究所, 上海200072 [2]上海大学力学系,上海200072

出　　处：《机械强度》2008年第6期884-887,共4页Journal of Mechanical Strength

基　　金：国家自然科学基金(10472060、10772092);上海大学研究生创新基金项目资助(A16-0101-07-011);上海市教育委员会科研项目(07ZZ07);上海市重点学科建设项目(Y0103)资助项目~~

摘　　要：研究速度变化的轴向运动黏弹性梁参数振动的稳定性。在控制方程的推导中,对黏弹性本构关系采用物质导数,而不是通常采用的只对时间取偏导数的本构关系。对控制方程运用直接多尺度法分析,并把结果与对应于只对时间取偏导数的本构关系的控制方程相比较。给出的数值结果说明两种黏弹性本构关系对失稳区域的影响。Stabihty in transverse parametric vibration of axially accelerating viscoelastic beams is investigated. The governing equation is derived from the viscoelastic constitution relation used material derivative, not simple the partial time derivative. The method of multiple scales is applied directly to the governing without discretization to determine the instabihty boundary due to parametric reso- nance. Results are compared to previous work in which the partial time derivative was used in the viscoelastic constitutive relation. Numerical simulations show the effects of the two viscoelastic constitutive ,elations on the instability boundaries.

关 键 词：轴向运动梁 黏弹性 物质导数 多尺度法 参数共振 稳定性 

分 类 号：O327[理学—一般力学与力学基础]