Title :
Vibrations of Z-cut resonator-structure by finite element analysis
Author :
Yong, Y.K. ; Lee, P.C.Y. ; Chuang, S.S.
Author_Institution :
Dept. of Civil & Environ. Eng., Rutgers Univ., Piscataway, NJ, USA
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
Keywords :
Q-factor; crystal resonators; finite element analysis; quartz; Mindlin´s first-order plate equations; SiO2; Z-cut resonator-structure; base area; criterion; displacement mode shapes; finite element analysis; finite-element program; frequency spectrum; mounting length; quality factor; resonator design; resonator motional resistances; strain energy ratio; strain-energy ratios; supporting structure; third-overtone; time area; Anisotropic magnetoresistance; Boundary conditions; Capacitive sensors; Finite element methods; Frequency; Integral equations; Stress;
Conference_Titel :
Frequency Control Symposium, 1988., Proceedings of the 42nd Annual
Conference_Location :
Baltimore, MD
DOI :
10.1109/FREQ.1988.27577
