Study on vibration and stability of an axially translating viscoelastic Timoshenko beam: Non-transforming spectral element analysis

摘要

Highlights•Derive equations of motion for the translating viscoelastic Timoshenko beam.•Present non-transforming spectral element modeling for translating beam problem.•Highlight the superiorities by comparing its results with those of other methods.•Process both wave and time domain analyzes for translating viscoelastic beam.•Study roles of beam velocity, axial loads and viscoelasticity on dynamic response.AbstractEngineering systems, such as rolled steel beams, chain and belt drives and high-speed paper, can be modeled as axially translating beams. This article scrutinizes vibration and stability of an axially translating viscoelastic Timoshenko beam constrained by simple supports and subjected to axial pretension. The viscoelastic form of general rheological model is adopted to constitute the material of the beam. The partial differential equations governing transverse motion of the beam are derived from the extended form of Hamilton's principle. The non-transforming spectral element method (NTSEM) is applied to transform the governing equations into a set of ordinary differential equations. The formulation is similar to conventional FFT-based spectral element model except that Daubechies wavelet basis functions are used for temporal discretization. Influences of translating velocities, axial tensile force, viscoelastic parameter, shear deformation, beam model and boundary condition types are investigated on the underlying dynamic response and stability via the NTSEM and demonstrated via numerical simulations.