Complex stability boundaries of axially moving beams with interdependent speed and tension

In this article, dynamic stabilities of axially accelerating viscoelastic beams with interdependent speed and tension is investigated. The effect of the interdependent speed and tension is highlighted. However, time dependent speeds and time dependent tensions are independent of each other in previous studies. The dynamic equilibrium approach is used to obtain the governing equation of the axially accelerating viscoelastic beam with internal and principal parametric resonance. Another highlight is that the simply supported boundary conditions are given in precise forms, that are, inhomogeneous forms. The non-homogeneous terms are closely related to Kelvin-Voigt viscoelastic constitutive relation. The method of directly multiple scales with a first-order uniform expansion is employed. By using the technique of the modified solvability conditions, the complex variable modulation equations are deduced in detail. By some numerical examples, the influences of viscosity, internal resonance, axial tension perturbation amplitude, axial speed perturbation amplitude, and old and current models on the stability boundaries are given. In addition, the approximate analytical results are compared with the numerical integration results by applying the differential quadrature method. (C) 2020 Elsevier Inc. All rights reserved.