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Effect of rotary inertia on stability of axially accelerating viscoelastic Rayleigh beams

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Abstract

The dynamic stability of axially moving viscoelastic Rayleigh beams is presented. The governing equation and simple support boundary condition are derived with the extended Hamilton’s principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscosity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method (DQM) is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.

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Authors and Affiliations

  1. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai, 201418, China

    Bo Wang

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  1. Bo Wang
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Correspondence to Bo Wang.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11202136, 11372195, 11502147, and 11602146)

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Wang, B. Effect of rotary inertia on stability of axially accelerating viscoelastic Rayleigh beams. Appl. Math. Mech.-Engl. Ed. 39, 717–732 (2018). https://doi.org/10.1007/s10483-018-2322-6

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  • DOI: https://doi.org/10.1007/s10483-018-2322-6

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Chinese Library Classification

2010 Mathematics Subject Classification

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