Chen, Liqun; Yang, Xiaodong Steady-state response of axially moving viscoelastic beams with pulsating speed: comparison of two nonlinear models. (English) Zbl 1093.74526 Int. J. Solids Struct. 42, No. 1, 37-50 (2005). Summary: Principal parametric resonance in transverse vibration is investigated for viscoelastic beams moving with axial pulsating speed. A nonlinear partial differential equation governing the transverse vibration is derived from the dynamical, constitutive, and geometrical relations. Under certain assumption, the partial differential equation reduces to an integro-partial differential equation for transverse vibration of axially accelerating viscoelastic nonlinear beams. The method of multiple scales is applied to two equations to calculate the steady-state response. Closed-form solutions for the vibration amplitude are derived from the solvability condition by eliminating secular terms. The stability of straight equilibrium and nontrivial steady-state response are analyzed by use of the Lyapunov linearized stability theory. Numerical examples are presented to highlight the effects of speed pulsation, viscoelasticity and nonlinearity. Finally, we compare the results obtained from two equations. Cited in 34 Documents MSC: 74H45 Vibrations in dynamical problems in solid mechanics 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 74D05 Linear constitutive equations for materials with memory 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics Keywords:principal parametric resonance; method of multiple scales; Lyapunov linearized stability theory PDF BibTeX XML Cite \textit{L. Chen} and \textit{X. Yang}, Int. J. Solids Struct. 42, No. 1, 37--50 (2005; Zbl 1093.74526) Full Text: DOI OpenURL