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This paper presents a theoretical study of a finite hybrid piezoelectric phononic crystal (PC) beam with shunting circuits. The vibration transmissibility method (TM) is developed for the finite system. The uniform and non-uniform configurations of the resonators, piezoelectric patches and shunting circuits are respectively considered. The properties of the vibration attenuation of the hybrid PC beam undergoing bending vibration are investigated and quantified. It is shown that the proper relaxation of the periodicity of the PC is conducive to forming a broad vibration attenuation region. The hybrid piezoelectric PC combines the purely mechanical PC with the piezoelectric PC and provides more tunable mechanisms for the target band-gap. Taking the structural and circuit parameters into account, the design of experiments (DOE) method and the multi-objective genetic optimization method are employed to improve the vibration attenuation and meet the lightweight demand of the attachments.

The motor has vibration characteristics of order and multi-band in the frequency domain, which is different from the internal combustion engine when it is used as the vehicle’s drive. These characteristics cannot be briefly attenuated by general methods, but make the phononic crystal (PC) an ideal solution to eliminate the vibration transmission of the motor, because the concentrated vibration peak can easily be blocked by the bandgap. In this paper, one dimensional locally resonant phononic crystal (LRPC) which has low-frequency bandgaps are arranged on the automotive subframe to absorbing vibration. The partial coherence analysis is used to analyze the transfer characteristic of vibration on the subframe. Then, 6 main paths are selected from the 18 vibration transmission paths, based on its high ratio of partial coherence coefficient in a certain frequency, and the arranged position, the spring stiffness and the resonator’s mass of the LRPCs are chosen based on this result.