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《固体力学学报(英文版)》 2006-04
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NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS

Yang Xiaodong Department of Engineering Mechanics, Shenyang Institute of Aeronautical Engineering, Shenyang 110034, China Chen Li-Qun Department of Mechanics, Shanghai University, Shanghai 200436, China  
The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equa- tion governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near- and exact-resonant, steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foun- dation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.
【Fund】: Project supported by the National Natural Science Foundation of China (No. 10472060);; Natural Science Founda-tion of Shanghai Municipality (No. 04ZR14058);; Doctor Start-up Foundation of Shenyang Institute of Aeronautical Engineering (No. 05YB04).
【CateGory Index】: TB533
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