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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.

Aiming at the laborious process in motor structure modeling for acoustic noise calculation, an improved stator structure modeling scheme is proposed, which includes stator structure simplification and equivalent material parameters identification. The stator assembly is modeled as a homogeneous solid with the same size as the stator core, and the influence of model simplification is compensated by orthotropic equivalent material parameters. The equivalent material parameters are acquired through an optimization algorithm by minimizing the error between FEM calculated modal frequencies and the modal tested results. With the stator assembly model, the motor assembly model is built, and the constrained modal characteristics of the motor assembly are verified by comparing the modal frequencies to the resonance bands in the vibration acceleration spectrum. Finally, the motor structure model is used to calculate the electromagnetic noise of an induction motor.