Abstract

A finite-element program incorporating R.D. Mindlin's first-order plate equations (1955) is developed. Calculations are performed for a miniature, third-overtone extensional, Z-cut resonator. Its frequency spectrum as a function of the mounting length and displacement mode shapes is discussed. The resonator motional resistances for different mounting lengths are measured. Normalized strain-energy ratios in the base area and time area are computed and compared with the normalized motional resistance at various lengths. Good correlations are found: the peaks in strain energy ratio correspond to peaks in motional resistance. Since the motional resistance is inversely proportional to the quality factor, Q, of the resonator, the strain-energy ratio in the base and tines (the supporting structure) could be used as a relative criterion for judging the Q of a certain resonator design. >

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