Toward optimal design of piezoelectric transducers based on multifunctional and smoothly graded hybrid material systems

Wilfredo M. Rubio, Emilio C.N. Silva, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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; however, 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 optimal material gradation for maximizing specified resonance frequencies; (ii) to design piezoelectric 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 ĝ€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 programming, 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.

Original languageEnglish (US)
Pages (from-to)1725-1746
Number of pages22
JournalJournal of Intelligent Material Systems and Structures
Issue number14
StatePublished - 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Materials Science
  • Mechanical Engineering


  • Continuum material distribution
  • Functionally graded materials (FGMS)
  • Hybrid materials
  • Mode assurance criterion (MAC)
  • Mode-tracking
  • Piezoelectric modal constant (PMC).
  • Piezoelectric transducers
  • Topology optimization


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