含分流电路Galfenol声子晶体的带隙与减振性能

利用Galfenol的逆磁致伸缩效应并通过分流元件调整其声子晶体带隙，以实现有效减振具有重要现实意义。基于磁致伸缩本构方程、Armstrong模型、法拉第定律、传递矩阵法和Bloch定理，推导了含分流电路的Galfenol有效弹性模量表达式，并建立其声子晶体振动模型。模型计算结果与实验结果对比表明，该模型能提供有效弹性模量随频率和分流电容变化的合理数据趋势，并能预测Galfenol参数随应力变化的非线性特性。分析了该声子晶体在开路下，其布喇格带隙(BBG)衰减常数峰值和截止频率随应力的变化规律，确定了器件减振的最佳工作点；分析了该声子晶体在不同分流电容和应力下的BBG、共振带隙(RBG)及其共振公共带隙(RCBG)特性，结果表明，较小分流电容、较大磁机耦合因子和较大电感可显著提高器件减振性能。

Band Gaps and Vibration Reduction of Galfenol Phononic Crystal with Shunt Circuit

It is of great practical significance to make use of the inverse magnetostrictive effect of Galfenol and adjust the band gaps of its phononic crystal(PC) through the shunt element to achieve effective vibration reduction. Based on the magnetostrictive constitutive equations, Armstrong model, Faraday law, transfer matrix method and Bloch theorem, the effective elastic modulus expression of Galfenol with shunt circuit is derived and the vibration model of the PC is established. The comparisons between the calculated and measured results show that the proposed model can provide a reasonable data trend of the effective elastic modulus with the change of frequency and shunt capacitance, and can predict the nonlinear behaviors of Galfenol parameters with the change of the stress. The variation of the peak value of the Bragg band gap(BBG) attenuation constant and the cutoff frequency of the PC under open circuit with stress is analyzed, and the optimal operating point for vibration reduction is determined. The characteristics of BBG, resonance band gap(RBG) and resonance common band gap(RCBG) of the PC under different shunt capacitance and stress are analyzed. The results show that smaller shunt capacitance, larger magnetomechanical coupled factor and larger inductance can significantly improve the vibration reduction performances of the PC.