ABOUT ANALYTICAL UNCERTAINTY THE COMPONENT OF THE TENSOR OF POWER ELECTROMECHANICAL FORCE FACTORS FOR FILM POLYMERIC PIEZO MATERIAL
Abstract
Currently, piezoelectric materials based on films, for example, polyvinylidene fluorides, have found
wide application in various industries. The interest in these materials is justified, first of all, by the advantageous,
in comparison with materials based on piezoceramic compositions, values of the density of the
film material, as well as the values of the effective piezoelectric coefficients, which makes it possible to implement new principles of loading in products in order to convert mechanical energy into electrical
energy. In addition, the lower rigidity of film polymer materials, compared to the rigidity of sensitive elements
of electroacoustic transducers based on piezoceramic compositions, makes it possible to create
designs of large-area transducers or antenna apertures assembled from these transducers, repeating the
contours of carrier housings. The article describes the prospects for the introduction of film polymer
piezomaterials into hydroacoustic and electric generating equipment products. Obviously, the introduction
of new materials into hydroacoustic and piezoelectric generator technology requires a rethinking of methods
for calculating the characteristics of products based on film piezoactive materials. One of the main
characteristics of electroacoustic transducers, used both in hydroacoustic technology and in products for
generating electrical energy through the use of sea or ocean surface waves, is the energy coefficient of
electromechanical coupling. The specified coefficient is a tensor physical quantity, and, accordingly, for
anisotropic materials, which are piezoactive films, for example, from polyvinylidene fluorides, a mathematical
apparatus is needed that would allow determining the components of the tensor of the energy coefficient
of electromechanical coupling during the design of hydroacoustic and piezoelectric generator
products. An attempt to develop such a mathematical apparatus was made by the authors of the article,
but in the course of the work performed, the analytical uncertainty of the components of the tensor of the
energy coefficient of electromechanical coupling was established. The article presents a scientific substantiation
of the identified analytical uncertainty of the components of the tensor of the energy coefficient of
electromechanical coupling from equations that establish the dependence of these components on coefficients
characterizing the mechanical and piezoelectric properties of film materials, taking into account
their anisotropy.
References
obosnovanie primeneniya novykh polivinilidenftoridnykh endoprotezov s karbinovym pokrytiem dlya
gernioplastiki [Experimental substantiation of the use of new polyvinylidene fluoride endoprostheses
with carbine coating for hernioplasty], Vestnik novykh meditsinskikh tekhnologiy [Bulletin of new
medical technologies], 2007, Vol. XIV, No. 1, pp. 99-101.
2. Subochev P., Prudnikov M., Vorobyev V., Postnikova A., Sergeev E., Perekatova V., Orlova A.,
Kotomina V., Turchin I. Wideband linear detector arrays for optoacoustic imaging based on
polyvinylidene difluoride films, Journal of Biomedical Optics, 2018, Vol. 23 (9), 091408. DOI:
10.1117/1.JBO.23.9.091408.
3. Ignatik A.A. Otsenka napryazhenno-deformirovannogo sostoyaniya i prochnosti trekhsloynogo
obraztsa truby iz polipropilena s treshchinopodobnym defektom [Assessment of the stress-strain state
and strength of a three-layer polypropylene pipe sample with a crack-like defect], Oborudovanie i
tekhnologii dlya neftegazovogo kompleksa [Equipment and technologies for the oil and gas complex],
2023, No. 2 (134), pp. 68-75.
4. Anokhina T., Borisov I., Yushkin A., Vaganov G., Didenko A., Volkov A. Phase separation within a thin
layer of polymer solution as prompt technique to predict membrane morphology and transport properties,
Polymers, 2020, Vol. 12, 2785. DOI: 10.3390/polym12122785.
5. Kim K.-B., Lee J. A lead-free piezoelectric fiber generator with a high energy conversion constant
material, Energies, 2022, Vol. 15, No. 6787. Available at: https://doi.org/10.3390/en15186787.
6. Berlincourt D.A., Curran D.R., Jaffe H. Piezoelectric and piezomagnetic materials and their function
in transducers, Physical Acoustics. Principles and Methods. Elsevier, 1964, pp. 169-270.
7. Kharat D.K., Mitra S., Akhtar S., Kumar V. Polymeric piezoelectric transducers for hydrophone applications,
Defence Science Journal, 2007, Vol. 57, No. 1, pp. 7-22.
8. Shatokhin A.V., Polkanov K.I., Seleznev I.A., Zhukov V.B. Napravleniya razvitiya antenn
otechestvennykh gidroakusticheskikh sredstv [Directions for the development of antennas for domestic
sonar systems], Natsional'naya oborona [National Defense], 2020, No. 5 (170), pp. 104-109.
9. Prokimov A.A., Dzhurinskiy K.B., Smirnova Yu.A. Perspektivnye izolyatsionnye materialy dlya
radiochastotnykh kabeley i soediniteley [Promising insulating materials for radio frequency cables and
connectors], Komponenty i tekhnologii [Components and Technologies], 2017, No. 2 (187), pp. 107-
115.
10. Abdullin I.Sh., Fatkhutdinov R.Kh., Mironova O.Yu., Shalyminova D.P., Sayfutdinova I.F.
Issledovanie polimernykh materialov na osnove poliamida dlya izgotovleniya membrannoy
zashchitnoy odezhdy [Study of polyamide-based polymer materials for the manufacture of membrane
protective clothing], Vestnik Kazanskogo tekhnologicheskogo un-ta [Bulletin of the Kazan Technological
University], 2012, Vol. 15, No. 14, pp. 143-145.
11. Kawai H. The piezoelectricity of polyvinilidenefluoride, Japanese Journal of Applied Physics, 1969,
Vol. 8, pp. 975-976.
12. Chen S.E., Yang R.Y., Wu G.K., Wu C.C. A piezoelectric wave-energy converter equipped with a
geared-linkage-based frequency up-conversion mechanism, Sensors, 2021, No. 21, pp. 204.
13. Smaryshev M.D., Dobrovol'skiy Yu.Yu. Gidroakusticheskie antenny: spravochnik po raschetu
napravlennykh svoystv gidroakusticheskikh antenn [Hydroacoustic antennas: a guide to calculating the
directional properties of hydroacoustic antennas]. Leningrad: Sudostroenie, 1984, 304 p.
14. Moffett M.B., Ricketts D., Butler J.L. The effect of electrode stiffness on the piezoelectric and elastic
constants of a piezoelectric bar, Acoustical Society of America, 1988, No. 83 (2), pp. 805-811.
15. Dement'ev I.I., Shabanov V.A., Shabanova N.S. Podkhod k matematicheskomu modelirovaniyu
plenochnykh anizotropnykh konstruktsiy elektroakusticheskikh preobrazovateley [An approach to
mathematical modeling of film anisotropic structures of electroacoustic transducers], Nauchnotekhnicheskiy
sbornika «Gidroakustika / Hydroacoustics» [Scientific and technical collection
“Hydroacoustics”], 2022, Issue 51 (3), pp. 42-49.
16. Dement'ev I.I., Shabanov V.A., Shabanova N.S. Metodika rascheta chuvstvitel'nosti plenochnogo
p'ezoelektricheskogo preobrazovatelya gidroakusticheskoy antenny [Methodology for calculating the
sensitivity of a film piezoelectric transducer of a hydroacoustic antenna], Tr. Vseros. konf. «Prikladnye
tekhnologii gidroakustiki i gidrofiziki» [Proceedings of the All-Russian Conference “Applied Technologies
of Hydroacoustics and Hydrophysics”]. St. Petersburg, 2023, pp. 194-199.
17. Sarkisyan A.A., Sarkisyan S.O. Sobstvennye kolebaniya mikropolyarnykh uprugikh gibkikh plastin i
pologikh obolochek [Natural vibrations of micropolar elastic flexible plates and flat shells],
Akusticheskiy zhurnal [Acoustic Journal], 2022, Vol. 68, No. 2, pp. 139-151.
18. Sharfarets B.P., Dmitriev S.P., Kurochkin V.E., Sergeev V.A. O metode akustoelektricheskogo
preobrazovaniya na osnove elektrokineticheskikh yavleniy [On the method of acoustoelectric transformation
based on electrokinetic phenomena], Akusticheskiy zhurnal [Acoustic Journal], 2022,
Vol. 68, No. 5, pp. 571-578.
19. Isaev A.E., Khatamtaev B.I. Akusticheskiy tsentr izmeritel'nogo gidrofona [Acoustic center of the
measuring hydrophone], Akusticheskiy zhurnal [Acoustic Journal], 2023, Vol. 69, No. 1, pp. 63-72.
20. Poplavko Yu.M., Yakimenko Yu.I. Fizicheskie mekhanizmy p'ezoelektrichestva [Physical mechanisms
of piezoelectricity]. Kiev: Avers, 1997, 153 p.
21. Rud' N.A. P'ezoelektricheskie i segnetoelektricheskie svoystva kristallicheskikh dielektrikov: metod.
ukazaniya [Piezoelectric and ferroelectric properties of crystalline dielectrics: method. Instructions].
Yaroslavl': Izd-vo Yarosl. gos. un-ta, 2003, 44 p.
22. Semenova O.R. Kristallofizika: ucheb. posobie [Crystal physics: textbook]. Perm': Izd-vo Perm. gos.
nats. issled. un-ta, 2019, 179 p.
23. Aabid A., Raheman Md.A., Ibrahim Y.E., Anjum A., Hrairi M., Parveez B., Parveen N., Zayan J.M.
A systematic review of piezoelectric materials and energy harvesters for industrial applications, Sensors,
2021, Vol. 21, No. 12. Available at: https://doi.org/10.3390/s21124145.
24. Zhilin P.A. Ratsional'naya mekhanika sploshnykh sred: ucheb. posobie [Rational mechanics of continuous
media: textbook], ed. by E.A. Ivanovoy. St. Petersburg:: Izd-vo Politekhn. un-ta, 2012, 584 p.
25. Marchenkov N.V. Rentgenodifraktsionnye issledovaniya p'ezoelektricheskikh kristallov pri vozdeystvii
vneshnikh elektricheskikh poley: dis. … kand. fiz.-mat. nauk [X-ray diffraction studies of piezoelectric
crystals under the influence of external electric fields: cand. of phys. and math. sc. dis.]: 01.04.18.
Moscow, 2014, 122 p.
