Torsional vibrations of a cylindrical shell in a linear viscoelastic medium
In this paper, we consider the natural vibrations of inhomogeneous mechanical systems, i.e., cylindrical bodies located in a deformable viscoelastic medium. The theory and methods for studying the natural vibrations of a cylindrical shell in a viscoelastic medium are constructed. The viscoelastic pr...
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| Veröffentlicht in: | IOP conference series. Materials Science and Engineering 2020-07, Vol.883 (1), p.12190 |
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| creator | Safarov, I Teshaev, M Toshmatov, E Boltaev, Z Homidov, F |
| description | In this paper, we consider the natural vibrations of inhomogeneous mechanical systems, i.e., cylindrical bodies located in a deformable viscoelastic medium. The theory and methods for studying the natural vibrations of a cylindrical shell in a viscoelastic medium are constructed. The viscoelastic properties of the medium are taken into account using the hereditary Boltzmann-Walter theory. For the statement of the problem, the general equation of the theory of viscoelasticity in the potentials of displacements in a cylindrical coordinate system is used. An algorithm has been developed to solve the tasks posed on a computer using the Bessel, Hankel, and Mueller and Gauss methods. The considered problems were reduced to finding complex natural frequencies for the system of equations of motion of a cylindrical shell in an infinite viscoelastic medium using radiation conditions. It is shown that the problem has a discrete complex spectrum. The eigen frequencies of oscillations of a low-contrast heterogeneity are found. Revealed that the imaginary part of the eigen frequencies is comparable with the real one, which can lead to aperiodic movements of the systems considered. |
| doi_str_mv | 10.1088/1757-899X/883/1/012190 |
| format | Article |
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The theory and methods for studying the natural vibrations of a cylindrical shell in a viscoelastic medium are constructed. The viscoelastic properties of the medium are taken into account using the hereditary Boltzmann-Walter theory. For the statement of the problem, the general equation of the theory of viscoelasticity in the potentials of displacements in a cylindrical coordinate system is used. An algorithm has been developed to solve the tasks posed on a computer using the Bessel, Hankel, and Mueller and Gauss methods. The considered problems were reduced to finding complex natural frequencies for the system of equations of motion of a cylindrical shell in an infinite viscoelastic medium using radiation conditions. It is shown that the problem has a discrete complex spectrum. The eigen frequencies of oscillations of a low-contrast heterogeneity are found. 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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Institute of Physics Open Access Journal Titles; IOPscience extra; Free Full-Text Journals in Chemistry |
| subjects | Algorithms Cylindrical bodies Cylindrical coordinates Cylindrical shells Equations of motion Formability Heterogeneity Mechanical systems Resonant frequencies Viscoelasticity |
| title | Torsional vibrations of a cylindrical shell in a linear viscoelastic medium |
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