数值仿真轴向运动黏弹性梁非线性参激振动  

Numerical investigation into nonlinear parametric resonance of axially accelerating viscoelastic beams

作　　者：丁虎[1] 

机构地区：[1]上海市应用数学和力学研究所上海大学,上海200072

出　　处：《计算力学学报》2012年第4期545-550,共6页Chinese Journal of Computational Mechanics

基　　金：国家杰出青年科学基金(10725209);国家自然科学基金(10902064);上海市优秀学科带头人计划(09XD1401700);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(12YZ028);上海市重点学科建设(S3106);长江学者和创新团队发展计划基金课题(IRT0844)资助项目

摘　　要：分别通过两种直接数值方法研究速度变化的经典边界条件下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,采用物质导数黏弹性本构关系和只对时间取偏导数的黏弹性本构关系;分别运用有限差分法和微分求积法对两种经典边界下轴向变速运动黏弹性梁的非线性控制方程求数值解,计算得到梁中点非线性参数振动的稳定稳态响应。数值结果表明,两种黏弹性本构关系对应的稳态响应存在明显差别,同时发现两种直接数值方法的仿真结果基本吻合,证明数值仿真具有较高精度。Steady-state responses of transverse parametric vibration of axially accelerating viscoelastic beam with two classical boundary conditions are respectively investigated via two different numerical ways. The governing equation is derived from the viscoelastic constitution relation respectively in terms of material derivative and the partial time derivative. The differential quadrature method is applied direct- ly to the governing equation to determine the steady-state responses of center of the beam due to nonlin- ear parametric resonance. Numerical simulations show the effects of the two viscoelastic constitutive re- lations on the steady-state responses. The finite difference schemes are developed to verify results via the method of differential quadrature. Quantitative comparisons demonstrate that the approximate analysis results are with rather high precision.

关 键 词：轴向运动梁 黏弹性 参数共振 微分求积法 有限差分法 

分 类 号：O32[理学—一般力学与力学基础]