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A platform for research: civil engineering, architecture and urbanism
Nonlinear Vibrations of an Orthotropic Viscoelastic Rectangular Plate Under Periodic Loads
https://orcid.org/http://orcid.org/0000-0002-8907-7869
https://orcid.org/http://orcid.org/0000-0001-8114-1187
https://orcid.org/http://orcid.org/0000-0001-5526-8723
https://orcid.org/http://orcid.org/0000-0002-5018-3533
https://orcid.org/http://orcid.org/0000-0003-0356-1383
https://orcid.org/http://orcid.org/0000-0002-1196-8004
Modern methods and technologies for the manufacture of structures make it possible to obtain structures of various shapes and sizes. This, in turn, determines the possibility of using structures of variable thickness in modern technology and engineering. During operation, they are often subjected to various loads. Among the loads, periodic loads are of particular interest. On the basis of the Kirchhoff-Love theory, nonlinear parametric vibrations of an orthotropic viscoelastic rectangular plate of variable thickness are investigated without considering the elastic wave propagation. The mathematical model of the problem is described by a system of nonlinear integrodifferential equations, where the weakly singular Koltunov-Rzhanitsyn kernel is used as the relaxation kernel. The resolving equations of the problem are obtained by the Bubnov-Galerkin method and by a numerical method based on the use of quadrature formulas. The behavior of an orthotropic viscoelastic rectangular plate under the action of an external periodic load is investigated. The graphs obtained with the developed computer program show the effect on the amplitude-frequency response of the plate on various physical, mechanical, and geometrical parameters.
Nonlinear Vibrations of an Orthotropic Viscoelastic Rectangular Plate Under Periodic Loads
https://orcid.org/http://orcid.org/0000-0002-8907-7869
https://orcid.org/http://orcid.org/0000-0001-8114-1187
https://orcid.org/http://orcid.org/0000-0001-5526-8723
https://orcid.org/http://orcid.org/0000-0002-5018-3533
https://orcid.org/http://orcid.org/0000-0003-0356-1383
https://orcid.org/http://orcid.org/0000-0002-1196-8004
Modern methods and technologies for the manufacture of structures make it possible to obtain structures of various shapes and sizes. This, in turn, determines the possibility of using structures of variable thickness in modern technology and engineering. During operation, they are often subjected to various loads. Among the loads, periodic loads are of particular interest. On the basis of the Kirchhoff-Love theory, nonlinear parametric vibrations of an orthotropic viscoelastic rectangular plate of variable thickness are investigated without considering the elastic wave propagation. The mathematical model of the problem is described by a system of nonlinear integrodifferential equations, where the weakly singular Koltunov-Rzhanitsyn kernel is used as the relaxation kernel. The resolving equations of the problem are obtained by the Bubnov-Galerkin method and by a numerical method based on the use of quadrature formulas. The behavior of an orthotropic viscoelastic rectangular plate under the action of an external periodic load is investigated. The graphs obtained with the developed computer program show the effect on the amplitude-frequency response of the plate on various physical, mechanical, and geometrical parameters.
Nonlinear Vibrations of an Orthotropic Viscoelastic Rectangular Plate Under Periodic Loads
https://orcid.org/http://orcid.org/0000-0002-8907-7869
https://orcid.org/http://orcid.org/0000-0001-8114-1187
https://orcid.org/http://orcid.org/0000-0001-5526-8723
https://orcid.org/http://orcid.org/0000-0002-5018-3533
https://orcid.org/http://orcid.org/0000-0003-0356-1383
https://orcid.org/http://orcid.org/0000-0002-1196-8004
Modern methods and technologies for the manufacture of structures make it possible to obtain structures of various shapes and sizes. This, in turn, determines the possibility of using structures of variable thickness in modern technology and engineering. During operation, they are often subjected to various loads. Among the loads, periodic loads are of particular interest. On the basis of the Kirchhoff-Love theory, nonlinear parametric vibrations of an orthotropic viscoelastic rectangular plate of variable thickness are investigated without considering the elastic wave propagation. The mathematical model of the problem is described by a system of nonlinear integrodifferential equations, where the weakly singular Koltunov-Rzhanitsyn kernel is used as the relaxation kernel. The resolving equations of the problem are obtained by the Bubnov-Galerkin method and by a numerical method based on the use of quadrature formulas. The behavior of an orthotropic viscoelastic rectangular plate under the action of an external periodic load is investigated. The graphs obtained with the developed computer program show the effect on the amplitude-frequency response of the plate on various physical, mechanical, and geometrical parameters.
Nonlinear Vibrations of an Orthotropic Viscoelastic Rectangular Plate Under Periodic Loads
Lecture Notes in Civil Engineering
Vatin, Nikolai (editor) / Roshchina, Svetlana (editor) / Serdjuks, Dmitrijs (editor) / Mirsaidov, Mirziyod (author) / Abdikarimov, Rustamkhan (author) / Khodzhaev, Dadakhan (author) / Normuminov, Bakhodir (author) / Roshchina, Svetlana (author) / Vatin, Nikolai (author)
2022-01-30
9 pages
Article/Chapter (Book)
Electronic Resource
English
Nonlinear Vibrations of Orthotropic Viscoelastic Plates with a Concentrated Mass
| Springer Verlag | 2021
Dynamic Behavior of Orthotropic Rectangular Plates under Moving Loads
| Online Contents | 2003