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| The resonance of parametric vibration with forced vibration of the axially moving shape memory alloy laminated beam |
| HAO Ying1,2，LI Zhe1,2，HU Yuda1,2 |
1.School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, China;
2.Hebei Key Laboratory of Mechanical Reliability for Heavy Equipment and Large Structures, Yanshan University, Qinhuangdao 066004, China |
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Abstract In this paper, the resonance of parametric vibration with forced vibration of the axially variable-velocity moving SMA (Shape Memory Alloy) laminated beam under harmonic excitation is investigated. Based on the Falk polynomial constitutive model of SMA, the nonlinear vibration equation of the axially moving SMA laminated beam is derived by combining Timoshenko beam theory. The time and space variables of the equation are discretized by using Galerkin integral method, then the amplitude-frequency response equation of resonance by the combined parametric and forced excitations is derived by multiscale method and coordinate transformation method. According to example analysis, the amplitude-frequency response curves and amplitude-parameter curves of different physical parameters are obtained and the effect of axial velocity, temperature and forced excitations on the resonance characteristics are analyzed. The results reveal that the system exhibits typical nonlinear vibration characteristics and complex dynamic behavior.
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Received: 01 November 2021
Published: 28 May 2023
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