Coupled bandgap properties and wave attenuation in the piezoelectric metamaterial beam on periodic elastic foundation

Abstract

In recent years, the innovative design of metamaterials and the study of bandgap characteristics have become the focus of research. The flexible setting of small added mass in locally resonant metamaterials can effectively regulate bandgap characteristics and wave transmission. In this paper, a novel tunable piezoelectric metamaterial beam on periodic elastic foundation is proposed for realizing the wider bandgap region and the stronger attenuation capability. Based on Timoshenko beam theory, wave equation of the metamaterial beam considering the piezoelectric and the inertial amplification effects is obtained from the transfer matrix method, and the calculational results are compared to that of numerical simulation. The results show that periodic elastic foundation can improve the overall stiffness of the structure, and the bending wave attenuation frequency domain will broaden with the increase of the elastic foundation stiffness. The metamaterial beam exhibits the strong wave attenuation in the bandgap induced by external negative capacitance shunt circuit, and the wave transmission loss is improved about 20 dB than the short circuit case. The coupling effects between the local resonance and the inertial amplification mechanism can cause the coupled bandgaps, which expand the original bandgap range by at least 25%. In addition, the coupled bandgaps boundary can be extended to lower frequencies by adjusting the angle of rigid rod and the additional mass separately, resulting in broadband wave attenuation. This work will provide valuable ideas for the design of advanced smart materials and structures in the field of vibration and noise reduction.