ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)
Menu

12
Issue
vol 63 / December, 2020
Article

DOI 10.17586/0021-3454-2020-63-5-444-450

UDC 681.586

Dynamics Analysis of the Membrane Elastic Element with Attached Concentrated Mass

V. L. Tkalich
ITMO University; Professor


M. E. Kalinkina
ITMO University, Saint Petersburg, 197101, Russian Federation; Postgraduate


A. G. Korobeynikov
Saint Petersburg Branch Organization of the Russian Academy of Sciences “Institute of Earth Magnetism, Ionosphere and Radio waves named after N.V. Pushkov RAS”;ITMO University, Saint Petersburg, 197101, Russian Federation ; Deputy Director for Science


O. I. Pirozhnikova
ITMO University; student


Abstract. The dynamics of unsteady oscillations of a rectangular membrane with one and two attached masses is studied. Adequate mathematical models are constructed using methods for solving direct problems in the mechanics of an elastically deformable body, namely, the Volterra equations and the Cramer method. It is noted that the obtained solution of the direct problem has an experimental application to the problems of analy-sis of displacements, deflections, deformations and stresses during unsteady vibrations of membranes with at-tached concentrated mass used in switching elements (membrane reed switches) and micromechanical pres-sure sensors. Based on the developed mathematical models, calculations of membrane elastic elements of a patented series of switching elements and pressure sensors are performed.
Keywords: membrane element, attached masses, concentrated mass, loading force, non-stationary oscillations, deflection value, Volterra equations, Cramer method, direct problem solution

References:

 

  1. Banichuk N.V. Izvestiya AN SSSR. Mekhanika tverdogo tela, 1969, no. 1, pp. 128–135. (in Russ.)
  2. Galin L.A. Prikladnaya matematika i mekhanika, 1949, no. 3(13), pp. 285–296. (in Russ.)
  3. Kachanov L.M. Osnovy teorii plastichnosti (Fundamentals of the Theory of Plasticity), Moscow, 1969, 420 р. (in Russ.)
  4. Nadai A. Theory of Flow and Fracture of Solids, McGraw-Hill, 1950, 1277 р.
  5. Prager W., Hodge Ph.G. Theory of Perfectly Plastic Solids, NY, John Wiley and Sons; London, Chapman and Hall, 1951.
  6. Sokolovskiy V.V. Teoriya plastichnosti (Plasticity Theory), Moscow, 1969, 608 р. (in Russ.)
  7. Hill R. The Mathematical Theory of Plasticity, Oxford, Clarendon press, 1950.
  8. Chernous'ko F.L. Zhurnal vychislitel'noy matematiki i matematicheskoy fiziki, 1965, no. 4(5), pp. 749–754. (in Russ.)
  9. Chernous'ko F.L, Banichuk N.V. Variatsionnyye zadachi mekhaniki i upravleniya (Variational Problems of Mechanics and Control), Moscow, 1973, 238 р. (in Russ.)
  10. Tertychny-Dauri V.Yu. Problems of Information Transmission, 2005, no. 1(41), pp. 45–58.
  11. Grishentsev A.Yu., Korobeynikov A.G. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2012, no. 4(80), pp. 75–79. (in Russ.)
  12. Kalinkina M.E., Korobeynikov A.G., Konovalov N.Yu., Pirozhnikova O.I., Tkalich V.L., Shmakov N.A. Nauchno-tekhnicheskiy vestnik Povolzh'ya, 2019, no. 1, pp. 78–80. (inRuss.)
  13. Patent RU 2287837 (С1), G01R 33/038, Datchik magnitometra (Magnetometer Sensor), V.M. Musalimov, V.L. Tkalich, A.G. Korobeynikov, M.S. Petrishchev, P.A. Sergushin,  Patent application no. 2005111814/28, Priority 20.04.2005, Published 20.11.2006. (in Russ.)
  14. Patent RU 2309419 (C2), G01R 33/24, Ustroystvo dlya izmereniya parametrov magnitnogo polya (Device for Measuring Magnetic Field Parameters), V.M. Musalimov, V.L. Tkalich, A.G. Korobeynikov, M.S. Petrishchev, Patent application no. 2005130568/28, Priority 03.10.2005, Published 27.10.2007. (in Russ.)
  15. Patent RU144305 (U1), H01H 1/66. Magnitoupravlyayemyy kontakt (Magnetically Controlled Contact), V.L. Tkalich, A.G. Korobeynikov, R.Ya. Labkovskaya, O.I. Pirozhnikova, Patent application no. 2014108108/07, Priority 03.03.2014, Published 20.08.2014. (in Russ.)
  16. Patent RU 136920 (U1), H01H 1/66, Magnitoupravlyayemyy kontakt (Magnetically Controlled Contact), V.L. Tkalich, A.G. Korobeynikov, R.Ya. Labkovskaya, O.I. Pirozhnikova, Patent application no. 2013137233/07, Priority 08.08.2013, Published 20.01.2014. (in Russ.)
  17. Patent RU 166022 (U1), H01H 1/66, H01H 37/52, G08B 17/06, Membrannyy termobimetallicheskiy magnitoupravlyayemyy kontakt (Membrane thermobimetallic magnetically controlled contact), V.L. Tkalich, R.Ya. Labkovskaya, O.I. Pirozhnikova, A.S. Kozlov, Patent application no. 2016115033/07, Priority 18.04.2016, Published 10.11.2016. (in Russ.)
  18. Patent RU 176399 (U1), G01R 33/038, Datchik magnitometra (Magnetometer Sensor), V.L. Tkalich, R.Ya. Labkovskaya, O.I. Pirozhnikova, A.S. Kozlov, Patent application no. 2017120116, Priority 07.06.2017, Published 17.01.2018. (in Russ.)
  19. Patent RU 192957 (U1), G01L 9/04, B82Y 40/00, Chuvstvitel'nyy element pretsizionnogo datchika davleniya (Sensor Element for Precision Pressure Detector), V.L. Tkalich, R.Ya. Labkovskaya, O.I. Pirozhnikova, A.S. Kozlov, M.E. Kalinkina, Patent application no. 2017120116, Priority 07.06.2017, Published 17.01.2018.  (in Russ.)
  20. Bogatyrev V.A., Bogatyrev S.V. Journal of Instrument Engineering, 2017, no. 2(60), pp. 171–177. (in Russ.)
  21. Bogatyrev V.A., Bogatyrev S.V. Journal of Instrument Engineering, 2017, no. 11(60), pp. 1033–1039. (in Russ.)
  22. Grishentsev A.Yu., Gur'yanov A.V., Kuznetsova O.V., Shukalov A.V., Korobeynikov A.G. Matematicheskoye obespecheniye v sistemakh avtomatizirovannogo proyektirovaniya (Software in Computer-Aided Design Systems), St. Petersburg, 2017, 88 р. (in Russ.)
  23. Grishentsev A.Yu., Korobeynikov A.G. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2012, no. 3(79), pp. 124–127. (in Russ.)