This paper presents the design of a novel resonator for use in a piezoelectric linear ultrasonic motor. The work is motivated by a motor previously developed by the authors that showed to be capable of achieving a force of 50 mN and a velocity of 14 mm/s, which they found unsatisfactory. To that end, among an existing variety of working principles for Piezoelectric Ultrasonic Motors [1], the principle of giving the material points of the stator in contact with the rotor a “∞” trajectory and thus propelling the rotor was utilized [2][3] .

Our concept is based on Euler-Bernoulli beam theory which shows that the natural frequency ratio of the first and second bending modes for a beam, fixed at both ends, is approximately 3 and we show how a gradient-based optimization algorithm is employed to assist in the design of the structure. Achieving simultaneously the targeted natural frequency ratio of 3 corresponding to the chosen Lissajous pattern, combined with the electromechanical coupling factor as figure of the merit are the optimization criterion for the optimal aspect ratio of our simple resonator.

Follow experimental investigations conducted on the non optimized prototype that illustrate the validity of the concept.