Novel hybrid-controlled graded metamaterial beam for bandgap tuning and wave attenuation

Abstract

In this paper, a tunable functionally graded metamaterial beam is designed for flexural wave attenuation by integrating piezomagnetic shunt damping system and inertial amplification mechanism. The proposed piezomagnetic shunt damping system is a complex mechanic–magnetic–electrical coupling system, which aims to transform and consume the vibration energy through local resonance to form a bandgap with tunable and strong wave attenuation ability. Based on Timoshenko beam theory, the wave equation and transmission spectrum of the metamaterial beam are derived by using transfer matrix method. The theoretical results are compared with the numerical simulation results. The results show that the resonance characteristics of piezomagnetic shunt circuit lead to negative group velocity and strong wave attenuation(−30 dB) at frequency defined by inductance and capacitance in shunt circuit. In varying frequency regimes, the coupled bandgap width can be maximized to 1925 Hz by tuning the external capacitance and coil turns. The superposition of double attenuation peaks caused by inertial amplification mechanism and local resonance coupling can be generated in the bandgap, allowing wave attenuation up to −94 dB. Subsequently, the attenuation capability of locally resonant bandgap can be significantly enhanced without changing the frequency by introducing the negative resistance into shunt circuit. Furthermore, the initiation and termination frequencies of bandgap can be flexibly designed by important material and structural parameters. This work is expected to provide valuable research ideas for the application of advanced intelligent materials in the field of vibration and noise reduction.