VIBRATIONS OF CONTOURED AND PARTIALLY PLATED, CONTOURED, RECTANGULAR, AT-CUT QUARTZ PLATES

Thickness shear and flexural vibrations and their anharmonic thickness twist overtones in both contoured and partially plated, contoured, rectangular, AT cut quartz plates are considered. The plated portion of the plate is of uniform thickness while in the unplated, contoured portion, the thickness varies as an exponential function of the length coordinate of the plate. Analytical solutions are obtained for the case of four free edges. A study is made of the effects on the resonant frequencies and mode shapes of the changes of plate parameters, such as the contouring of the plate, the length of the plating, and the ratio of the length of the plating to the length of contoured portion of the plate. © 1969, Acoustical Society of America. All rights reserved.