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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.