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《Chinese Quarterly of Mechanics》 2008-03
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Steady-state Response of Non-linear Forced Vibration of Axially Moving Viscoelastic Beams

DING Hu~1 CHEN Li-qun~(1,2) GE Xin-sheng~3 1.Shanghai Institute of Applied Mathematics and Mechanics,Shanghai 200072,China 2.Department of Mechanics Shanghai University,Shanghai 200444,China 3.Department of Mechanical Engineering,Beijing Institute of Machinery,Beijing 100085,China  
Forced vibration was investigated for axially moving viscoelastic beams.The governing equation was derived from the viscoelastic constitution relation by using material derivative.The method of multi- ple scales was applied to the mathematical model to calculate the steady state response.The equation of response curves was derived from the solvability condition of eliminating secular terms.The stability of steady state responses was analyzed by use of Lyapunov linearized stability theory.The finite difference schemes were developed to solve the equation of axially moving viscoelastic beams with fixed supports for steady-state response.Numerical examples are presented to highlight the effects of non-linear coeffi- cient,the excitation amplitude,and viscosity coefficient.
【Fund】: 国家杰出青年科学基金(10725209);; 国家自然科学基金(10772092);; 上海市教育委员会科研项目(07ZZ07);; 上海市重点学科建设点项目(Y0103);; 上海大学研究生创新基金(A.16-0101-07-011);; 北京市自然科学基金(1072008)
【CateGory Index】: O322
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