Jild 37 № 3 (2026): Iyul - sentyabr
2026-09-30
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Qovushqoq-elastik muhitdagi to‘ldirilgan elliptik silindrda SH-to‘lqinning difraksiyasi

R.A. Sabirova

Qabul qilingan: 2026-10-13

Nashr etilgan: 2026-09-30

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Annotatsiya

Cheksiz qovushqoq-elastik muhitda Rjanitsin–Koltunov yadrosi bilan to‘ldirilgan elliptik silindrda vaqt bo‘yicha garmonik SH-to‘lqinning difraksiyasi o‘rganiladi; dastlab to‘ldirilmagan bo‘shliq holati tahlil qilinadi. Muzlatish usuli masalani kompleks to‘lqin soniga ega Gelmgolts tenglamasiga keltiradi va u kompleks parametrli Mathieu funksiyalari yordamida aniq yechiladi. Algoritm statik chegara, aylana bo‘shliq uchun yechim va fundamental yechimlar usuli bilan solishtirish orqali tekshirilgan (\(10^{-12}\) aniqlikkacha moslik). So‘nuvchi tushuvchi to‘lqinni koordinata boshida normallashtirish dinamik kuchlanish konsentratsiyasi koeffitsiyentini (DSCF) 27% gacha oshirib ko‘rsatadi; shu sababli birinchi kontakt nuqtasida normallashtirish taklif etiladi. Qovushqoqlik ta’siri ikki tarkibga ajratiladi: yumshatish, bu DSCF spektrini 37–45% ga past chastotalar tomon siljitadi, va so‘nish, bu DSCF ni 15% gacha kamaytiradi. \(k_0a \approx 1\) yaqinida DSCF 14–29% ga kamayadi, uning maksimumi esa atigi 1–5% ga pasayadi. Yadro parametrlaridan \(A\) va \(\alpha\) eng katta ta’sir ko‘rsatadi, \(\beta\) ning ta’siri esa juda kichik (1,5% dan kam). Qovushqoq-elastik to‘ldirgich uchun to‘ldirgich va muhit qovushqoqliklari nisbati kuchlanish holatini belgilaydi: qattiq to‘ldirgichda chegara sirtidagi kuchlanish −15% dan +17% gacha, yumshoq to‘ldirgichda esa tangensial kuchlanish −17% dan +24% gacha o‘zgaradi.

Kalit so‘zlar

Adabiyotlar ro'yxati

  1. Pao YH, Mow CC. Diffraction of Elastic Waves and Dynamic Stress Concentrations. Crane, Russak; 1973.

  2. Guz’ AN, Kubenko VD, Čerevko MA. Difrakciâ uprugih voln [Diffraction of elastic waves]. Naukova Dumka; 1978. (In Russian).

  3. Chen Z, Liu D, Yang Z. Dynamic stress concentration and scattering of SH-wave by interface elliptic cylindrical cavity. Earthq Eng Eng Vib. 2003;2(2):299–306. https://doi.org/10.1007/s11803-003-0013-9.

  4. Tao M, Zhao R, Du K, Cao W, Li Z. Dynamic stress concentration and failure characteristics around elliptical cavity subjected to impact

  5. loading. Int J Solids Struct. 2020;191–192:401–417. https://doi.org/10.1016/j.ijsolstr.2020.01.009.

  6. Qi H, Chu F, Guo J. Dynamic analysis of non-confocal elliptical lined tunnel under the action of SH wave. Math Methods Appl Sci. 2022;45(7):3624–3643. https://doi.org/10.1002/mma.8008.

  7. Yang Z, Zhu Y, Ren H, Yang Y, Zhao J, Chen Y. Dynamic stress analysis of an elliptical cavity during elastic wave propaga- tion in a density-inhomogeneous medium with the modulus varying as a power function. Eur J Mech A Solids. 2022;96:104740.

  8. https://doi.org/10.1016/j.euromechsol.2022.104740.

  9. Wang Z, Zhou C, Zhang X, et al. Magnetoacoustic wave scattering and dynamic stress concentration around the elliptical opening in exponential-gradient piezomagnetic materials. Materials (Basel). 2022;15(13):4564. https://doi.org/10.3390/ma15134564.

  10. Yang Z, Guo D, Bian J, Yang Y. Scattering of SH waves by elliptical cavity and type-III crack in deep anisotropic geology. Soil Dyn Earthq Eng. 2024;182:108695. https://doi.org/10.1016/j.soildyn.2024.108695.

  11. Lu P, Wang Y, Liu R, et al. Mathematical modeling of dynamic stress concentration in piezoelectric materials with elliptical openings under SH waves. Actuators. 2025;14(3):121. https://doi.org/10.3390/act14030121.

  12. Hu H, Szekrényes A, Dai M, Gao CF. Scattering of harmonic P-wave and dynamic stress concentration by a nanosized elliptical hole with surface effect. Math Mech Solids. Published online 2026. https://doi.org/10.1177/10812865261422754.

  13. Pillai TAK, Varadan VV, Varadan VK. Sound scattering by rigid and elastic infinite elliptical cylinders in water. J Acoust Soc Am. 1982;72(3):1032–1037.

  14. Scharstein RW, Davis AMJ. Acoustic scattering by a rigid elliptic cylinder in a slightly viscous medium. J Acoust Soc Am. 2007;121(6):3300–3310.

  15. Hasheminejad SM, Sanaei R. Ultrasonic scattering by a fluid cylinder of elliptic cross section, including viscous effects. IEEE Trans Ultrason Ferroelectr Freq Control. 2008;55(2):391–404.

  16. Koltunov MA. Polzučest’ i relaksaciâ [Creep and relaxation]. Vysšaâ Škola; 1976. (In Russian).

  17. Rabotnov ÛN. Èlementy nasledstvennoj mehaniki tvërdyh tel [Elements of the hereditary mechanics of solids]. Nauka; 1977. (In Russian).

  18. Filatov AN. Asimptotičeskie metody v teorii differencial’nyh i integro-differencial’nyh uravnenij [Asymptotic methods in the theory of differential and integro-differential equations]. Fan; 1974. (In Russian).

  19. Safarov II, Ahmedov MŠ, Umarov AO. Dinamičeskie naprâženiâ i smeˆseniâ vblizi cilindričeskoj podkreplënnoj polosti ot ploskoj garmoničeskoj volny [Dynamic stresses and displacements near a reinforced cylindrical cavity due to a plane harmonic wave]. Prospero. 2014;(3):57–61. (In Russian).

  20. Ruziyev T, Safarov I, Teshayev M, et al. Assessment of the dissipative properties of viscoelastic hollow cylindrical bodies with filler during the propagation of natural waves. J Compos Sci. 2026;10(8):437. https://doi.org/10.3390/jcs10080437.

  21. Axmedov OS. Diffraction of a harmonic wave propagating through an elliptical cylinder in a viscoelastic medium. Theor Appl Sci. 2025;142(2):10–13.

  22. Axmedov OS. Qovushqoq-elastik to‘ldiruvchili elliptik silindrik qobiqqa garmonik to‘lqin tarqalishini Matye funksiyalardagi yechimi [Solution in Mathieu functions for harmonic wave propagation in a viscoelastic filled elliptic cylindrical shell]. BuxDU Ilmiy Axboroti. 2025;(2):7–12. (In Uzbek).

  23. Axmedov OS. Qovushqoq-elastik elliptik silindrga bo‘ylama va ko‘ndalang garmonik to‘lqin difraksiyasi [Diffraction of longitudinal and transverse harmonic waves by a viscoelastic elliptic cylinder]. Ilm Sarchashmalari. 2025;(12):7–13. (In Uzbek).

  24. McLachlan NW. Theory and Application of Mathieu Functions. Clarendon Press; 1947.

  25. National Institute of Standards and Technology. NIST Digital Library of Mathematical Functions. Chapter 28: Mathieu functions and Hill’s equation. Accessed October 6, 2026. https://dlmf.nist.gov/28.

  26. Alhargan FA. Algorithm 804: subroutines for the computation of Mathieu functions of integer orders. ACM Trans Math Softw. 2000;26(3):390–407. https://doi.org/10.1145/358407.358422.

  27. Brimacombe C, Corless RM, Zamir M. Computation and applications of Mathieu functions: a historical perspective. SIAM Rev. 2021;63(4):653–720. https://doi.org/10.1137/20M135786X.

  28. Fairweather G, Karageorghis A. The method of fundamental solutions for elliptic boundary value problems. Adv Comput Math. 1998;9:69–95.

  29. Teshaev MKh, Safarov II, Kuldashov NU, Ishmamatov MR, Ruziev TR. On the distribution of free waves on the surface of a viscoelastic cylindrical cavity. J Vib Eng Technol. 2020;8(4):579–585. https://doi.org/10.1007/s42417-019-00160-x.

Mualliflar haqida

R.A. Sabirova
r.sabirova@tkti.uz
Toshkent Kimyo-Texnologiya Instituti

Litsenziya

Mualliflik huquqi (c) 2026 “Mexanika muammolari” O‘zbekiston jurnali

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Qovushqoq-elastik muhitdagi to‘ldirilgan elliptik silindrda SH-to‘lqinning difraksiyasi. (2026). “Mexanika Muammolari” O‘zbekiston Jurnali, 37(3). https://pmjournal.uz/jour/article/view/23

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