Technical Report: Modeling of Composite Piezoelectric Structures with the Finite Volume Method

TL;DR

This paper introduces a finite volume method for modeling composite piezoelectric structures, offering advantages over traditional finite element approaches, especially in boundary treatment and circuit interpretation.

Contribution

It extends previous work by presenting a new implementation of boundary conditions in composite piezoelectric structures using the finite volume method.

Findings

Effective boundary condition implementation demonstrated

Finite volume approach offers circuit interpretation benefits

Modeling example of a unimorph structure provided

Abstract

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.