Optimal Design of Piezoelectric Transducers 1745 at PENNSYLVANIA STATE UNIV on May 16, 2016jim.sagepub.comDownloaded from

ABSTRACT: This work explores the design of piezoelectric transducers based on functional material gradation, here named functionally graded piezoelectric transducer (FGPT). Depending on the applications, FGPTs must achieve several goals, which are essentially related to the transducer resonance frequency, vibration modes, and excitation strength at specific resonance frequencies. Several approaches can be used to achieve these goals; how-ever, this work focuses on finding the optimal material gradation of FGPTs by means of topology optimization. Three objective functions are proposed: (i) to obtain the FGPT opti-mal material gradation for maximizing specified resonance frequencies; (ii) to design piezo-electric resonators, thus, the optimal material gradation is found for achieving desirable eigenvalues and eigenmodes; and (iii) to find the optimal material distribution of FGPTs, which maximizes specified excitation strength. To track the desirable vibration mode, a mode-tracking method utilizing the ‘modal assurance criterion ’ is applied. The continuous change of piezoelectric, dielectric, and elastic properties is achieved by using the graded finite element concept. The optimization algorithm is constructed based on sequential linear pro-gramming, and the concept of continuum approximation of material distribution. To illustrate the method, 2D FGPTs are designed for each objective function. In addition, the FGPT performance is compared with the non-FGPT one. Key Words: piezoelectric transducers, hybrid materials, functionally graded materials (FGMs), topology optimization, mode-tracking, continuum material distribution, mode assurance criterion (MAC), piezoelectric modal constant (PMC)