Band Gap and Vibration Reduction of Laminated Galfenol Phononic Crystal with Shunt Circuit

It is of great significance to adjust bandgaps (BGs) of laminated Galfenol phononic crystal (PC) by using nonlinearity of Villari effect and shunt elements for effectively reducing vibration. Based on the modified constitutive equations, the effective elastic modulus, and transfer matrix method (TMM), a dynamic nonlinear model with tunable elastic modulus for the PC is established. Comparisons between the calculated and measured results show that the model can describe the changing laws of the Galfenol rod’s effective elastic modulus with frequency and shunt capacitance, and can predict nonlinearity of the rod. The effects of stress and bias field on the attenuation constant peak and cutoff frequency of Bragg BGs (BBGs) are analyzed, and the optimal and suboptimal operating points of BBGs are determined. The effects of shunt capacitance and stress on BBGs, resonant BGs (RBGs), and common BGs (CBGs) are analyzed, and it is found that larger magnetomechanical coupled factor and smaller shunt capacitance can effectively reduce vibration.