Analytical and experimental study of a metamaterial beam with grading piezoelectric transducers for vibration attenuation band widening

This paper analytically and experimentally investigates the potential of a piezoelectric metamaterial beam with a spatial grading pattern for broadband vibration attenuation. Distributed bimorph piezoelectrics with varying lengths form the “graded” manner. A fully coupled analytical model based on the transfer matrix function is developed to exhibit the vibration attenuation capabilities. The band structure of the graded supercell structure and the transmittance response of the finite-length counterpart show that the bandwidth of the vibration attenuation zone can be significantly broadened by the spatial variation of the piezoelectric transducers, while multiple resonant-related passbands/peaks occur. By properly introducing electrical damping (e.g., 200 Ω), the resonant peaks can be significantly attenuated. Subsequently, for the first time, we experimentally confirmed the broadband vibration attenuation performance of the graded piezoelectric metamaterial. The harmonic excitation test demonstrates that the enlarged attenuation region can be achieved: with the spatial variation of 1 mm, the attenuation bandwidth can be increased up to 80 % as compared to conventional metamaterial with identical piezoelectric patches. Furthermore, the white noise excitation test verifies the broadband attenuation capabilities. The results show that the root-mean-square (RMS) acceleration of the graded metamaterial beam is remarkably reduced as compared to that of the conventional one.