Effects of biasing fields on piezoelectric resonators

A systematic analysis of the problem of frequency shifts in piezoelectric resonators due to various effects is performed and reported in this dissertation based on the theory for small fields superposed on finite biasing fields in an electroelastic body. This research includes the study of nonlinear effect of large accelerations on resonators that are mounted on moving objects and are under finite biasing fields. A second-order perturbation procedure is developed to estimate the frequency shifts. The effect of biasing fields on degenerate resonant frequencies is studied by a perturbation procedure. It is found that the degenerate frequency may split into different frequencies due to biasing fields. Stress induced frequency shifts in resonators made from langasite (La3Ga 5SiO14 or LGS), a new piezoelectric crystal promising for future resonator applications, are calculated and zero stress sensitivity orientations of the crystal are determined. The results have important applications in high accuracy resonator design. The frequency shifts due to intrinsic film stresses in asymmetric electrodes deposited on resonators are calculated. The result shows that frequency shifts are partially due to the mode center (nodal plane) shift in resonators with unequal thickness electrodes. The effects of a small curvature of the middle surface of a thickness-shear mode crystal resonator on its vibration frequencies, modes, and acceleration sensitivity are studied. The results have important applications in design of plano-convex resonators. Third-order nonlinear elastic constants are essential in calculating the frequency shifts of resonators. The PMN-PT electrostrictive ceramics, a new materials used for electromechanical transducers with the composition of (1−x)[Pb(Mg1/3Nb2/3)O3]-(x)[PbTiO 3], are examined experimentally by studying the propagation of small amplitude ultrasonic waves in specimens under biasing stresses and their third-order elastic constants are determined. In addition, a set of two-dimensional nonlinear equations for electroelastic plates in large amplitude thickness-shear vibrations are developed and are employed in the calculation of frequency-electric current amplitude behavior near nonlinear resonance of piezoelectric resonators. General expressions for the second-order frequency shifts and degenerate frequency shifts in an electroelastic body are obtained and the explicit forms of effective material constants at different orders are given. The research results provide valuable information on minimizing the frequency shifts in crystal resonators due to environmental effects such as acceleration, temperature, stress or other biasing fields. They can also be used on various types of sensor and transducer designs, in which case it is desirable to maximize the frequency shifts