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.

本文提出了一种理论方法，可以利用分流电路的不均匀分布有效地改善有限混合压电声子晶体（PC）梁的振动衰减特性。考虑到谐振器的阻尼，基于蒂莫申科梁理论推导了有限机电系统的振动传递率（TM）。数值结果通过有限元方法（FEM）进行了验证。随后，进行了全面的研究，以研究结构和电学参数对均匀PC的振动衰减特性的影响。此外，将分流电路的有组织的混乱引入系统中。结合各种类型的非均匀电路配置，还检查了振动衰减的变化。事实证明，与纯机械和压电PC相比，混合PC提供了更多的可调机制来设计目标带隙。可以通过机械局部共振带隙（LRG），机电LRG和布拉格带隙（BG）的选择性耦合方式来实现宽带范围内的低频振动减小。在实践中，期望通过使用合适的分流电路分配来增强混合PC的振动衰减和可用性。可以通过机械局部共振带隙（LRG），机电LRG和布拉格带隙（BG）的选择性耦合方式来实现宽带范围内的低频振动减小。在实践中，期望通过使用合适的分流电路分配来增强混合PC的振动衰减和可用性。可以通过机械局部共振带隙（LRG），机电LRG和布拉格带隙（BG）的选择性耦合方式来实现宽带范围内的低频振动减小。在实践中，期望通过使用合适的分流电路分配来增强混合PC的振动衰减和可用性。