Research on the dynamics of multi-storey buildings
The design of multi-storey buildings is a natural trend in the development of a modern metropolis. Obtaining exact solutions when studying their own and forced oscillations within the framework of a continuous homogeneous medium model (continuum mechanics) with an infinite number of degrees of freed...
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| Format: | Article |
| Language: | English |
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Дальневосточного отделения Российской академии наук, Южно-Сахалинск, Федеральное государственное бюджетное учреждение науки Институт морской геологии и геофизики
2023-09-01
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| Series: | Геосистемы переходных зон |
| Subjects: | |
| Online Access: | http://journal.imgg.ru/web/full/f-e2023-3-6.pdf |
| _version_ | 1797598576752197632 |
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| author | Peter G. Velikanov Yury P. Artyukhin |
| author_facet | Peter G. Velikanov Yury P. Artyukhin |
| author_sort | Peter G. Velikanov |
| collection | DOAJ |
| description | The design of multi-storey buildings is a natural trend in the development of a modern metropolis.
Obtaining exact solutions when studying their own and forced oscillations within the framework of a continuous
homogeneous medium model (continuum mechanics) with an infinite number of degrees of freedom is often
difficult to implement. Therefore, in the article (as part of the modernization of the finite element method), the
model of a multi-storey building is discretized and endowed with a finite number of degrees of freedom placed in
the middle of the finite elements at the nodes (the mass of finite elements is also placed there), which elastically
interact with the finite elements of the model that do not have mass. It is believed that the elements of a multistorey building work only for bending, which is fully justified by comparing the frequencies of its bending and
longitudinal oscillations. The resolving system of differential equations of oscillations of a multi-storey building, in
which expressions for energies (potential, kinetic and Rayleigh) are written in quadratures, is obtained using
Lagrange equations of the second kind. In the article, the problems of free oscillations of 3- and 100-storey
buildings are solved using Green’s functions, stiffness, mass, compliance matrices, etc. The approximate results
obtained in the article, when compared with the little-known approximate results obtained by other methods, as
well as exact results (direct and indirect methods of boundary elements), showed a good correspondence. |
| first_indexed | 2024-03-11T03:24:06Z |
| format | Article |
| id | doaj.art-1beb15b3c0e84eca9ade8c70cac5074d |
| institution | Directory Open Access Journal |
| issn | 2541-8912 2713-2161 |
| language | English |
| last_indexed | 2024-03-11T03:24:06Z |
| publishDate | 2023-09-01 |
| publisher | Дальневосточного отделения Российской академии наук, Южно-Сахалинск, Федеральное государственное бюджетное учреждение науки Институт морской геологии и геофизики |
| record_format | Article |
| series | Геосистемы переходных зон |
| spelling | doaj.art-1beb15b3c0e84eca9ade8c70cac5074d2023-11-18T02:53:14ZengДальневосточного отделения Российской академии наук, Южно-Сахалинск, Федеральное государственное бюджетное учреждение науки Институт морской геологии и геофизикиГеосистемы переходных зон2541-89122713-21612023-09-017304315https://doi.org/10.30730/gtrz.2023.7.3.304-315Research on the dynamics of multi-storey buildingsPeter G. Velikanov0https://orcid.org/0000-0002-3566-6203Yury P. Artyukhin1https://orcid.org/0000-0002-6243-9145Kazan National Research Technical University named after A.N. Tupolev – KAI, Kazan, RussiaKazan (Volga Region) Federal University, Kazan, Russia The design of multi-storey buildings is a natural trend in the development of a modern metropolis. Obtaining exact solutions when studying their own and forced oscillations within the framework of a continuous homogeneous medium model (continuum mechanics) with an infinite number of degrees of freedom is often difficult to implement. Therefore, in the article (as part of the modernization of the finite element method), the model of a multi-storey building is discretized and endowed with a finite number of degrees of freedom placed in the middle of the finite elements at the nodes (the mass of finite elements is also placed there), which elastically interact with the finite elements of the model that do not have mass. It is believed that the elements of a multistorey building work only for bending, which is fully justified by comparing the frequencies of its bending and longitudinal oscillations. The resolving system of differential equations of oscillations of a multi-storey building, in which expressions for energies (potential, kinetic and Rayleigh) are written in quadratures, is obtained using Lagrange equations of the second kind. In the article, the problems of free oscillations of 3- and 100-storey buildings are solved using Green’s functions, stiffness, mass, compliance matrices, etc. The approximate results obtained in the article, when compared with the little-known approximate results obtained by other methods, as well as exact results (direct and indirect methods of boundary elements), showed a good correspondence.http://journal.imgg.ru/web/full/f-e2023-3-6.pdfoscillation of multi-storey buildingsoscillation frequenciesgreen’s functionstiffness matrixmass matrix compliance matrix |
| spellingShingle | Peter G. Velikanov Yury P. Artyukhin Research on the dynamics of multi-storey buildings Геосистемы переходных зон oscillation of multi-storey buildings oscillation frequencies green’s function stiffness matrix mass matrix compliance matrix |
| title | Research on the dynamics of multi-storey buildings |
| title_full | Research on the dynamics of multi-storey buildings |
| title_fullStr | Research on the dynamics of multi-storey buildings |
| title_full_unstemmed | Research on the dynamics of multi-storey buildings |
| title_short | Research on the dynamics of multi-storey buildings |
| title_sort | research on the dynamics of multi storey buildings |
| topic | oscillation of multi-storey buildings oscillation frequencies green’s function stiffness matrix mass matrix compliance matrix |
| url | http://journal.imgg.ru/web/full/f-e2023-3-6.pdf |
| work_keys_str_mv | AT petergvelikanov researchonthedynamicsofmultistoreybuildings AT yurypartyukhin researchonthedynamicsofmultistoreybuildings |