Analysis of nonaxisymmetric vibration mode piezoelectric annular plate and its application to an ultrasonic motor

Abstract

The development of an ultrasonic motor using nonaxisymmetric vibration modes of a piezoelectric annular plate is described. A piezoelectric annular plate is analyzed to find its mode patterns, elliptic motions of displacement for the motor, and the distributions of the induced charge on the plate surface, and to calculate electromechanical coupling factors. On the basis of the analyzed results, motors using the annular plate have been built and their characteristics measured. The construction and characteristics of these motors are discussed.

1.52-GHz micromechanical extensional wine-glass mode ring resonators

“…For the case where no voltages are applied (i.e., no dcbias V P ; purely mechanical resonance), the nominal resonance frequency f o for an EWGR is given by [21] …”

“…In (14), U r (r, θ) and U θ (r, θ) are the radial and tangential displacements of the ring, given by [21] …”

Nonlinear Modeling for Distortion Analysis in Silicon Bulk-Mode Ring Resonators

“…where the elements of M are given by [13,16]: The resonance frequencies of the ring resonator with a given geometry can be obtained by the numerical solution of |M| = 0, as shown in Figure 1. Moreover, the analytical results and mode shapes can be verified and simulated using finite element method (FEM) software, such as ANSYS, as shown in Figure 2.…”

“…Moreover, it is assumed that the ring resonator is made of single crystal silicon. Therefore, the equation governing the in-plane vibration of an annular ring, ignoring body force and internal heat source, can be given by [15,16]:…”

“…h nm and k nm are mode consonants of the bulk-mode of (n,m), where n corresponds to the circumferential order and m corresponds to the radial harmonic [16]. The relationship between k nm and h nm is given by: k nm /h nm = √2/(1 − υ), and the elastic wave constants of (B n /A n , C n /A n , B n /A n ) can be found by solving the following equation:…”