NON-LINEAR FORCED VIBRATION OF AXIALLY MOVING VISCOELASTIC BEAMS  

作　　者：Yang Xiaodong Chen Li-Qun 

机构地区：[1]Department of Engineering Mechanics, Shenyang Institute of Aeronautical Engineering, Shenyang 110034, China [2]Department of Mechanics, Shanghai University, Shanghai 200436, China

出　　处：《Acta Mechanica Solida Sinica》2006年第4期365-373,共9页固体力学学报（英文版）

基　　金：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).

摘　　要：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 equation 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 foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.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 equation 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 foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.

关 键 词：axially moving beam VISCOELASTICITY non-linear forced vibration method of multiple scales 

分 类 号：TU311[建筑科学—结构工程]