Journal
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
Volume 27, Issue 6, Pages 1108-1120Publisher
GAUTHIER-VILLARS/EDITIONS ELSEVIER
DOI: 10.1016/j.euromechsol.2007.11.014
Keywords
Axially accelerating beam; Parametric resonance; Instability; The material time derivative; Method of multiple scales; The finite difference
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Funding
- National Natural Science Foundation of China [10672092, 10725209]
- Shanghai Municipal Education Commission Scientific Research Project [07ZZ07]
- Innovation Foundation for Graduates of Shanghai University [A.16-0101-07-011]
- Shanghai Leading Academic Discipline Project [Y0103]
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Stability is investigated for an axially accelerating viscoelastic beam. The material time derivative is used in the viscoelastic constitutive relation, not simply the partial time derivative. The method of multiple scales is applied directly to the governing equation without discretization. When the axial speed is characterized as a simple harmonic variation about the constant mean speed, the instability conditions are presented for axially accelerating viscoelastic beams constrained by simple supports with rotational springs in parametric resonance. The finite difference schemes are developed to solve numerically the equation of axially accelerating viscoelastic beams with fixed supports for the instability regions in the principal parametric resonance. The numerical calculations confirm the analytical results. Numerical examples show the effects of the constraint stiffness, the mean axial speed, and the viscoelasticity. (C) 2008 Published by Elsevier Masson SAS.
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