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Forced Vibrations of a Thin-Walled Rod of a Symmetric Profile
https://orcid.org/http://orcid.org/0000-0001-9516-7644
https://orcid.org/http://orcid.org/0000-0002-1304-0138
The paper provides an analytical solution to the problem of natural and forced vibrations of a thin-walled elastic rod with a symmetric profile. The mathematical model also considers the forces of viscous resistance, which, in accordance with the frequency-independent Voigt hypothesis, are introduced in the process of solving the problem. The solution is constructed for an arbitrary dynamic load and two types of boundary conditions: hinged support in constrained torsion and free warping of the end sections of the rod; rigid fastening with constrained torsion and the absence of warping. A feature of the problem is the presence of a complete system of inertial terms, which determines the specifics of the application of the method of finite integral transformations, which serves as an effective way to solve problems in mechanics. The spectrum of circular frequencies of vibrations of the rod, expressions for linear displacements and angles of twisting are obtained.
Forced Vibrations of a Thin-Walled Rod of a Symmetric Profile
https://orcid.org/http://orcid.org/0000-0001-9516-7644
https://orcid.org/http://orcid.org/0000-0002-1304-0138
The paper provides an analytical solution to the problem of natural and forced vibrations of a thin-walled elastic rod with a symmetric profile. The mathematical model also considers the forces of viscous resistance, which, in accordance with the frequency-independent Voigt hypothesis, are introduced in the process of solving the problem. The solution is constructed for an arbitrary dynamic load and two types of boundary conditions: hinged support in constrained torsion and free warping of the end sections of the rod; rigid fastening with constrained torsion and the absence of warping. A feature of the problem is the presence of a complete system of inertial terms, which determines the specifics of the application of the method of finite integral transformations, which serves as an effective way to solve problems in mechanics. The spectrum of circular frequencies of vibrations of the rod, expressions for linear displacements and angles of twisting are obtained.
Forced Vibrations of a Thin-Walled Rod of a Symmetric Profile
https://orcid.org/http://orcid.org/0000-0001-9516-7644
https://orcid.org/http://orcid.org/0000-0002-1304-0138
The paper provides an analytical solution to the problem of natural and forced vibrations of a thin-walled elastic rod with a symmetric profile. The mathematical model also considers the forces of viscous resistance, which, in accordance with the frequency-independent Voigt hypothesis, are introduced in the process of solving the problem. The solution is constructed for an arbitrary dynamic load and two types of boundary conditions: hinged support in constrained torsion and free warping of the end sections of the rod; rigid fastening with constrained torsion and the absence of warping. A feature of the problem is the presence of a complete system of inertial terms, which determines the specifics of the application of the method of finite integral transformations, which serves as an effective way to solve problems in mechanics. The spectrum of circular frequencies of vibrations of the rod, expressions for linear displacements and angles of twisting are obtained.
Forced Vibrations of a Thin-Walled Rod of a Symmetric Profile
Lecture Notes in Civil Engineering
Akimov, Pavel (Herausgeber:in) / Vatin, Nikolai (Herausgeber:in) / Elekina, Elena N. (Autor:in) / Vronskaja, Elena S. (Autor:in)
International Conference on Russian-Polish-Slovak Seminar Theoretical Foundation of Civil Engineering ; 2021 ; Moscow, Russia
XXX Russian-Polish-Slovak Seminar Theoretical Foundation of Civil Engineering (RSP 2021) ; Kapitel: 41 ; 350-356
15.09.2021
7 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Thin-walled bar , Symmetric profile , Boundary value problem , Dynamic load , Natural vibrations , Natural vibration frequency , Forced vibrations , Integral transformations Engineering , Building Construction and Design , Geotechnical Engineering & Applied Earth Sciences , Transportation Technology and Traffic Engineering , Structural Materials
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