Study on the vibration attenuation property of one finite and hybrid piezoelectric phononic crystal beam

In this paper, a theoretical method is proposed to effectively improve the vibration attenuation characteristics of a finite hybrid piezoelectric phononic crystal (PC) beam utilizing the non-uniform distribution of shunting circuits. Considering the damping of resonators, the vibration transmissibility method (TM) for the finite electromechanical system is derived based on the Timoshenko beam theory. Numerical results are validated by the finite element method (FEM). Subsequently, a comprehensive study is conducted to investigate the influences of the structural and electrical parameters on the vibration attenuation property of the uniform PC. Furthermore, the organized disorder of the shunting circuits is introduced into the system. Combining with various types of non-uniform circuit configurations, the variation of the vibration attenuation is also examined. It is demonstrated that the hybrid PCs offer more tunable mechanisms to design target band-gaps, compared with the purely mechanical and piezoelectric PCs. The low-frequency vibration reduction over a broadband range could be achieved through the selective coupling ways of the mechanical local resonant band-gap (LRG), electromechanical LRG and Bragg band-gap (BG). It is expected to enhance the vibration attenuation and availability of hybrid PCs using the suitable distribution of shunting circuits in practice.