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Nonlinear transversal vibration of an axially moving viscoelastic string on a viscoelastic guide subjected to mono-frequency excitation. (English) Zbl 1397.74084

Summary: In this paper, the nonlinear transversal vibration of an axially moving viscoelastic string on a viscoelastic guide subjected to a mono-frequency excitation is considered. The model of the viscoelastic guide is a parallel combination of springs and viscous dampers. The governing equation of motion is developed using Hamilton’s principle. Applying the method of multiple scales to the governing partial differential equation, the solvability condition and approximate solutions are derived. Three cases, namely primary, subharmonic and superharmonic resonances are studied and appropriate analytical solutions are obtained. The effect of mean value velocity, force amplitude, guide stiffness and viscosity coefficient of the string on the frequency response and bifurcation points is investigated. Findings are in good agreement with results extracted from numerical modeling.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K05 Strings
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
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