In-plane Acceleration Research Articles

Acceleration sensitivity of surface acoustic wave resonators

The acceleration sensitivity of acoustic surface wave resonators (and delay lines) on quartz substrates supported uniformly at the base has been calculated. For normal acceleration the calculated sensitivity is almost two orders of magnitude lower than the lowest published measurements. For in-plane acceleration the calculated sensitivity is comparable to the best published measurements. This causes us to believe that uniform base support has not been realized in practice and, in fact, may be impossible to achieve. For normal acceleration and nonuniform base support the calculations indicate that increasing the thickness of the substrate decreases the acceleration sensitivity. Experimental verification of this is presented. However, for in-plane acceleration the calculations indicate that increasing the thickness of the substrate increases the acceleration sensitivity.

Moderately Large Amplitude Plate Vibration Modes

The influence of moderately large amplitudes on the frequency of vibration for the fundamental mode and some higher modes of the simply supported rectangular plate is established. Plate equations that are valid for the moderately large motions are programmed for solution on the analog computer. The effect of eliminating in-plane motions and accelerations on the system response is quantitatively established. It is shown that frequency ratio versus amplitude ratio is aspect ratio dependent and the study shows how simplifying assumptions made in some previous studies affect this dependence.

Effects of acceleration on the resonance frequencies of crystal plates

The changes in the thickness-shear resonance frequencies of circular crystal plates subjected to steady in-plane acceleration of arbitrary direction are studied. A closed-form solution for a circular plate under acceleration with three or more points of mounting is obtained. From this solution, initial stress and strain fields are computed at each and every point of the plate as a function of plate orientation, direction of acceleration, and positions of supports. These fields are then taken into account in the coupled equations of the incremental thickness-shear and flexural vibrations through the second- and third-order elastic stiffness coefficients of the crystal. Due to the space dependence or nonuniformity of the initial fields and the smallness of the frequency changes, (Δf/fo in order of 10−9) a perturbation method is used to calculate the changes in the thickness-shear resonances. The frequency changes as function of the acceleration direction for several configurations of the supports for AT cut of quartz are computed. These are then compared with experimental values of A. W. Werner [Interim Reps. 10−11, Bell Telephone Labs. (1959)] and W. L. Smith [Interim Reps. 12−13, Bell Telephone Labs. (1960)].

Vibrations of rectangular cantilever plates subjected to in-plane acceleration loads

The vast literature dealing with the free vibrations of plates contains virtually no references for plates which are loaded by acceleration fields or gravity forces in their plane. The present paper studies the case of the rectangular cantilever plate. In-plane forces caused by an arbitrarily oriented acceleration field must first be determined by solving a plane problem of the theory of elasticity. The transverse free vibration eigenvalue problem is then analyzed by the Ritz method using mode shapes which are the sum of products of the eigenfunctions for vibrating beams. The in-plane forces are included in this analysis. The resulting matrix eigenvalue problem is solved by standard techniques on the digital computer to obtain numerical results for the vibration frequencies and mode shapes of loaded plates. Results are presented which show the effects of varying the intensity of loading, the angle of acceleration, and the aspect ratio of the plate.