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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2022. Vol 39

Investigation of the Amplitude-Frequency Response of a Dam-Type Viscoelastic Body With Steady-State Forced Harmonic Vibrations

Author(s)
Sultan M. Gaynazarov1, Askhad M. Polatov1, Akhmat M. Ikramov1, Sukhbatulla I. Pulatov1

1National University of Uzbekistan, Tashkent, Republic of Uzbekistan, asad3@yandex.ru

Abstract
The article discusses the amplitude-frequency response of a viscoelastic body of the dam type, under steady-state forced harmonic vibrations. An important factor is the determination of the number of frequencies and resonance peaks that arise in the process of harmonic effect of the water body on the dam. The use of the finite element method (FEM) for the numerical solution of dynamic problems allows, by expanding the solution in terms of eigenmodes and frequencies, to reduce the original problem to a system of separated linear integro-differential equations with respect to the sought parameters of generalized functions. The process of the influence of viscoelastic properties of the dam material on the resonance curves that arise under harmonic loads of different frequencies at different dimensions of the foot of the dam is investigated. The analysis of the curves of the amplitude-frequency responses of a dam-type viscoelastic body, under steady-state forced harmonic oscillations, showed that the occurrence of resonance peaks depends on the viscoelastic properties of the dam body and the dimensions of the foot of the dam. The main resonance peaks occur at frequencies less than the sixth eigenfrequency, as a result of which a further increase in the number of eigenmodes in the expansion does not introduce any significant changes in the amplitude of the distribution of resonance curves of the amplitude-frequency response of the dam.
About the Authors

Sultan M. Gaynazarov, Cand. Sci. (Phys.–Math.), Prof., National University of Uzbekistan, Tashkent, 100174, Republic of Uzbekistan, gaynazarsm@mail.ru

Askhad M. Polatov, Dr. Sci. (Phys.–Math.), Prof., National University of Uzbekistan, 100174, Tashkent, Republic of Uzbekistan, asad3@yandex.ru

Akhmat M. Ikramov, Cand. Sci. (Phys.–Math.), Assoc. Prof., National University of Uzbekistan, Tashkent, 100174, Republic of Uzbekistan, axmat3@yandex.ru

Sukhbatulla I. Pulatov, Cand. Sci. (Phys.–Math.), Assoc. Prof., National University of Uzbekistan, 100174, Tashkent, Republic of Uzbekistan, s.pulatov@nuu.uz

For citation
Gaynazarov S. M., Polatov A.M., Ikramov A.M., Pulatov S.I. Investigation of the Amplitude-Frequency Response of a Dam-Type Viscoelastic Body with Steady-State Forced Harmonic Vibrations. The Bulletin of Irkutsk State University. Series Mathematics, 2022, vol. 39, pp. 51–61. https://doi.org/10.26516/1997-7670.2022.39.51
Keywords
dam, viscoelasticity, harmonic vibrations, amplitude, resonance peaks, FEM
UDC
51.7+519.63
MSC
45J99, 65L10
DOI
https://doi.org/10.26516/1997-7670.2022.39.51
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