轴向运动形状记忆合金层合梁的参强联合共振

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (10) : 1-7.

论文

郝颖1,2，李哲1,2，胡宇达1,2

作者信息 +

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

Author information +

文章历史 +

摘要

本文研究了轴向变速运动形状记忆合金（shape memory alloy,SMA）层合梁在简谐激励下的参强联合共振问题。基于SMA的Falk多项式本构模型，结合Timoshenko梁理论推导了轴向运动SMA层合梁的非线性振动方程。利用伽辽金积分法对其进行时间变量和空间变量的离散，用多尺度法以及坐标变换的方法推导系统参强联合共振的幅频响应方程。通过算例分析，得到不同物理参数变化时的幅频响应曲线图和振幅-参数曲线图，分析了轴向速度、温度及强迫激励对系统参强联合共振特性的影响。结果表明系统呈现典型的非线性振动特征和复杂的动力学行为。

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.

导出引用

郝颖1,2，李哲1,2，胡宇达1,2. 轴向运动形状记忆合金层合梁的参强联合共振[J]. 振动与冲击, 2023, 42(10): 1-7

HAO Ying1,2，LI Zhe1,2，HU Yuda1,2. The resonance of parametric vibration with forced vibration of the axially moving shape memory alloy laminated beam[J]. Journal of Vibration and Shock, 2023, 42(10): 1-7

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