Free linear vibrations of a viscoelastic spherical shell with filler

Purpose. Thin multilayered shells are widely used in aviation, shipbuilding, and mechanical engineering. Recently, interest in the dynamic analysis of shell structures under various load effects has increased. This study examines the effect of moving normal internal pressure on a viscoelastic cylind...

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Main Authors: Mirsaidov, Mirziyod Mirsaidovich, Safarov, Ismoil Ibrohimovich, Teshaev, Muhsin Khudoyberdiyevich, Eliboyev, Nurali Rajabaliyevich
Format: Article
Language:English
Published: Saratov State University 2025-07-01
Series:Известия высших учебных заведений: Прикладная нелинейная динамика
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Online Access:https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2025/07/and_2025-4_mirsaidov_et-al_485-496.pdf
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author Mirsaidov, Mirziyod Mirsaidovich
Safarov, Ismoil Ibrohimovich
Teshaev, Muhsin Khudoyberdiyevich
Eliboyev, Nurali Rajabaliyevich
author_facet Mirsaidov, Mirziyod Mirsaidovich
Safarov, Ismoil Ibrohimovich
Teshaev, Muhsin Khudoyberdiyevich
Eliboyev, Nurali Rajabaliyevich
author_sort Mirsaidov, Mirziyod Mirsaidovich
collection DOAJ
description Purpose. Thin multilayered shells are widely used in aviation, shipbuilding, and mechanical engineering. Recently, interest in the dynamic analysis of shell structures under various load effects has increased. This study examines the effect of moving normal internal pressure on a viscoelastic cylindrical shell. Methods. The viscoelastic medium filling the spherical shell has a significantly lower instantaneous modulus of elasticity than the shell itself. The solution is presented for the free vibrations of the viscoelastic system "shell–filler."An analytical frequency equation in the form of a transcendental equation is derived and solved numerically using the M¨uller method. Results. It has been found that, at certain values of viscoelastic and density parameters, low-frequency natural vibrations occur. These vibrations represent an aperiodic motion since the imaginary part of the natural frequency is large. For viscoelastic mechanical systems, the dependence of damping coefficients on physical and mechanical parameters has been identified. Conclusion. A theory and methods for calculating the complex natural frequencies of vibrations of an elastic spherical inhomogeneity in an elastic medium have been developed. A classification of such vibrations into radial, torsional, and spheroidal modes has been carried out. The problem is reduced to finding those frequencies at which the system of motion equations has nonzero solutions in the class of infinitely differentiable functions.  
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publishDate 2025-07-01
publisher Saratov State University
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series Известия высших учебных заведений: Прикладная нелинейная динамика
spelling doaj-art-762c8e5eb4cc49ad889456ebb0a301652025-08-20T03:09:45ZengSaratov State UniversityИзвестия высших учебных заведений: Прикладная нелинейная динамика0869-66322542-19052025-07-0133448549610.18500/0869-6632-003162Free linear vibrations of a viscoelastic spherical shell with fillerMirsaidov, Mirziyod Mirsaidovich0Safarov, Ismoil Ibrohimovich1Teshaev, Muhsin Khudoyberdiyevich2Eliboyev, Nurali Rajabaliyevich3Tashkent state technical University Named after Islam Karimov, Uzbekistan, Tashkent, st. Navoi, 32Tashkent state technical University Named after Islam Karimov, Uzbekistan, Tashkent, st. Navoi, 32Institute of Mathematics. V.I.Romanovsky, Uzbekistan, Bukhara, st. M.Ikbol, 11Tashkent chemical - technological Institute, Uzbekistan, Tashkent, Kara-Su-6, 12, apt. 64Purpose. Thin multilayered shells are widely used in aviation, shipbuilding, and mechanical engineering. Recently, interest in the dynamic analysis of shell structures under various load effects has increased. This study examines the effect of moving normal internal pressure on a viscoelastic cylindrical shell. Methods. The viscoelastic medium filling the spherical shell has a significantly lower instantaneous modulus of elasticity than the shell itself. The solution is presented for the free vibrations of the viscoelastic system "shell–filler."An analytical frequency equation in the form of a transcendental equation is derived and solved numerically using the M¨uller method. Results. It has been found that, at certain values of viscoelastic and density parameters, low-frequency natural vibrations occur. These vibrations represent an aperiodic motion since the imaginary part of the natural frequency is large. For viscoelastic mechanical systems, the dependence of damping coefficients on physical and mechanical parameters has been identified. Conclusion. A theory and methods for calculating the complex natural frequencies of vibrations of an elastic spherical inhomogeneity in an elastic medium have been developed. A classification of such vibrations into radial, torsional, and spheroidal modes has been carried out. The problem is reduced to finding those frequencies at which the system of motion equations has nonzero solutions in the class of infinitely differentiable functions.  https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2025/07/and_2025-4_mirsaidov_et-al_485-496.pdfspherical shellfilleroscillationsfrequency equationdamping coefficient
spellingShingle Mirsaidov, Mirziyod Mirsaidovich
Safarov, Ismoil Ibrohimovich
Teshaev, Muhsin Khudoyberdiyevich
Eliboyev, Nurali Rajabaliyevich
Free linear vibrations of a viscoelastic spherical shell with filler
Известия высших учебных заведений: Прикладная нелинейная динамика
spherical shell
filler
oscillations
frequency equation
damping coefficient
title Free linear vibrations of a viscoelastic spherical shell with filler
title_full Free linear vibrations of a viscoelastic spherical shell with filler
title_fullStr Free linear vibrations of a viscoelastic spherical shell with filler
title_full_unstemmed Free linear vibrations of a viscoelastic spherical shell with filler
title_short Free linear vibrations of a viscoelastic spherical shell with filler
title_sort free linear vibrations of a viscoelastic spherical shell with filler
topic spherical shell
filler
oscillations
frequency equation
damping coefficient
url https://andjournal.sgu.ru/sites/andjournal.sgu.ru/files/text-pdf/2025/07/and_2025-4_mirsaidov_et-al_485-496.pdf
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