Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS

Тел.: +7 (495) 625-9241


Oscillation spectrum computation of SC-cut quartz crystal


A.N. Lepetaev – Ph.D. (Eng.), JSC «Omsk research institute of instrument engineering». E-mail:
A.O. Lozhnikov – Head of Sector, JSC «Omsk research institute of instrument engineering». E-mail:

Till now the problem of mathematical model construction for modeling resonator systems operation on the basis of piezo¬electrics remains topical. Recently there were the computer programs, allowing to carry out computations by means of a method of final elements. In the article the application of oscillation eigenmodes model for calculation of eigen-frequency spectrum of the lenticular crystal resonator of the TD-cut is considered. Calculation was made with the use of the program developed by A.N. Lepetaev. As a result of calculation quite good repeatability of A, B and C-modes frequencies calculation results has turned out, however on resistance some results have the big distinction. It is most possibly connected with influence of piezoelectric cells edges on swing. The given influence in the program is not taken into account. In the sequel it is necessary to develop the program with the presence edges influence and piezoelements points of fastening.

  1. Christoffel E.B. Ueber die Fortpflanzung von Stössen durch elastische feste Körper // Annali di Matematica Pura ed Ap­plicata. Ser. 2. 1877. P. 193–243.
  2. Mindlin R.D. An Introduction to the Mathematical Theory of Vibrations of Elastic Plates / Ed. by J. Yang. 2006.
  3. Ballato A. Doubly Rotated Thickness Mode Plate Vibrators. 1977.
  4. Salt D. Hy-Q handbook of Quartz Crystal Devices. 1987.
  5. Tiersten H.F., Stevens D.S. An analysis of contoured SC-cut quartz crystal resonators // Proceedings of the 36th Annual Symposium on Frequency Control. U.S. Army Electronics Research and Development Command. Fort Monmouth. New Jersey. 1982. P. 37–45.
  6. Dulmet B., Bourquin R., Spassov L., Velcheva R. Finite element analysis of activity dips in NLC-cut quartz temperature sensors // Proceedings of the 16th European Frequency and Time Forum. 2002. P. 33.
  7. Yang J. Analysis of Piezoelectric Devices. 2006.
  8. Wang J., Yong Y.-K., Imai T. Finite element analysis of the piezoelectric vibrations of quartz plate resonators with higher-order plate theory // International Journal of Solids and Structure. 1999. V. 36(15). P. 2303–2319.
  9. Postnikov I.I. Matematicheskoe modelirovanie xarakteristik i parametrov VCh kvarczevy'x rezonatorov s p'ezoe'lementami peremennoj tolshhiny' // Akusticheskij zhurnal. 1996. № 42. S. 91–102.
  10. Lepetaev A.N. Matematicheskaya model' sobstvenny'x mod kolebanij linzovy'x p'ezoe'lementov kvarczevy'x rezonatorov // Matematika, ee prilozheniya i matematicheskoe obrazovanie (MPMO’11): Materialy' IV Mezhdunar. konf. Ch. 1. Ulan-Ude': VSGTU. 2011. S. 180–184.
  11. Xomenko I.V., Lepetaev A.N., Kosy'x A.V. Model' sobstvenny'x kolebanij sdviga po tolshhine dlya p'ezokvarczevy'x plastin rezonatorov odno- i dvuxpovorotny'x srezov // Omskij nauchny'j vestnik. 2012. № 3(113).
  12. Lepetaev A.N. Programma dlya rascheta parametrov angarmonicheskix kolebanij kvarczevogo rezonatora / Svidetel'stvo o gosudarstvennoj registraczii programmy' dlya E'VM № 2013610342. Zaregistrirovano v Reestre programm dlya E'VM 9 yanvarya 2013 g.
  13. Kittel' Ch., Najt U. i dr. Mexanika: per. s angl. M.: Nauka. 1975.

June 24, 2020
May 29, 2020

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio