Stability in parametric resonance of axially moving viscoelastic beams with time-dependent speed

Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200030, China
Journal of Sound and Vibration (Impact Factor: 1.81). 06/2005; 284(3-5):879-891. DOI: 10.1016/j.jsv.2004.07.024


Stability in transverse parametric vibration of axially accelerating viscoelastic beams is investigated. The governing equation is derived from Newton's second law, the Kelvin constitution relation, and the geometrical relation. When the axial speed is a constant mean speed with small harmonic variations, the governing equation can be regarded as a continuous gyroscopic system under small periodically parametric excitations and a damping term. The method of multiple scales is applied directly to the governing equation without discretization. The stability conditions are obtained for combination and principal parametric resonance. Numerical examples are presented for beams with simple supports and fixed supports, respectively, to demonstrate the effect of viscoelasticity on the stability boundaries in both cases.

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    • "recoverable nature of SMA and the adhesive property of Ti 2 AlC, the damping behavior of the GCMeC is largely frequencydependent viscoelastic. Even the viscoelastic materials have wide application in solving damping problems of many engineering systems [1] [2] [3] [4], such as aircraft, space structures, automobiles, buildings, bridges and so on, their damping models in most available commercial finite element software do not explicitly represent the environmentally effected behaviors of actual materials (such as excitation frequency, ambient temperature, dynamic loads, etc.). One of the effective viscoelastic damping models in engineering applications was developed by Golla and Hughes [5] and McTavish and Hughes [6], known as the Golla–Hughes–McTavish (GHM) method. "
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    Journal of Sound and Vibration 08/2013; 332(23):6177-6191. DOI:10.1016/j.jsv.2013.06.016 · 1.81 Impact Factor
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    • "Then they obtained the effects of moving speed and viscoelasticity on the variation of the lowest two eigenvalues. The Method of Multiple Scales (a perturbation method) was used by Chen and Yang [20]. They conducted a stability analysis for parametric resonances of axially moving viscoelastic beams. "
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    Advances in Mechanical Engineering 04/2013; 2013. DOI:10.1155/2013/169598 · 0.58 Impact Factor
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