Technical Report: Modeling of Composite Piezoelectric Structures with   the Finite Volume Method
  Piezoelectric devices, such as piezoelectric traveling wave rotary ultrasonic motors, have composite piezoelectric structures. A composite piezoelectric structure consists of a combination of two or more bonded materials, where at least one of them is a piezoelectric transducer. Numerical modeling of piezoelectric structures has been done in the past mainly with the finite element method. Alternatively, a finite volume based approach offers the following advantages: (a) the ordinary differential equations resulting from the discretization process can be interpreted directly as corresponding circuits and (b) phenomena occurring at boundaries can be treated exactly. This report extends the work of IEEE Transactions on UFFC 57(2010)7:1673-1691 by presenting a method for implementing the boundary conditions between the bonded materials in composite piezoelectric structures. The report concludes with one modeling example of a unimorph structure. 
Valentin Bolborici, Francis P. Dawson, and Mary C. Pugh
math.NA cs.NA