This thesis is concerned with the modeling of the stator of a piezoelectric traveling wave rotary ultrasonic motor. Existing models for piezoelectric traveling wave rotary ultrasonic motors are either too complicated to be used in motor control or do not reflect the real behavior of the motor and are of limited use in developing a controller for the motor.

Finite Element methods have been used in the past to examine the properties of piezoelectric structures however, the Finite Volume Method has always been ruled out without justification. The main goal of this thesis is to provide a Finite Volume modeling approach for the stator of the piezoelectric traveling wave rotary ultrasonic motor taking into account the basic theoretical principles from piezoelectricity and structural mechanics. This model can in future be extended to develop a complete model of the motor in addition to other piezoelectric structures.

The Finite Volume Method is shown to have the following specific advantages over the Finite Element Method especially for structures with simple geometries:​ 1. the Finite Volume Method respects the PDEs conservation law structure due to the fact that the fluxes are conserved between cells/domains/subregions, 2. the Finite Volume Method involves only surface integrals thus making it easier to implement a rotor-stator contact model as the contact mechanism occurs at the boundary of the stator, and 3. the Finite Volume Method yields a system of ODEs that more intuitively map onto circuit simulation software.

The Finite Volume Method is initially used to model a simple piezoelectric plate. A corresponding circuit of the piezoelectric plate model, based on the Finite Volume Method, is generated. Two additional but more complex models are considered:​ one for a unimorph plate and one for the stator of an ultrasonic motor. The modeling results obtained with the Finite Volume Method are validated by comparing them with the results obtained with Finite Element simulations performed with COMSOL. Two test platforms designed to test and validate the Finite Volume and COMSOL results for the simple piezoelectric plates and piezoelectric traveling wave rotary ultrasonic motors are also presented in this thesis.