Model of a spatial dome cover. Deformations and oscillation frequency
The object of research. A new scheme of a statically determinate spatial truss is considered. The design has a hexagonal dome resting on two belts. The belts are supported by vertical racks. Two corner supports have spherical and cylindrical hinges. The outer support contra consists of 6n horizontal...
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| container_title | Stroitel'stvo unikal'nyh zdanij i sooruhenij |
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| creator | Kirsanov, Mikhail Nikolaevich |
| description | The object of research. A new scheme of a statically determinate spatial truss is considered. The design has a hexagonal dome resting on two belts. The belts are supported by vertical racks. Two corner supports have spherical and cylindrical hinges. The outer support contra consists of 6n horizontal rods, the inner one consists of 6(n-1) rods. The contours are connected by skews. Formulas are derived for the deflection of the vertex and the angular hinge depending on n. The upper and lower analytical estimates of the first frequency of natural oscillations of the structure are found. Method. Calculation of the forces in the rods is carried out by cutting out the nodes from the solution of the system of equilibrium equations for all nodes in the projection on the coordinate axes. To derive formulas for the dependence of breakdowns, forces, and the frequency of free oscillations, an inductive generalization of the sequence of solutions for structures with a different number of panels is used. The structural stiffness matrix and deflection are calculated using the Maxwell - Mohr formula in analytical form. To find estimates of the lowest frequency of vibrations of nodes endowed with masses, the Dunkerley and Rayleigh methods are used. Results. The vertical load distributed over the nodes and the concentrated load applied to the top are considered. Formulas for the forces in the characteristic bars of the structure are derived. A picture of the distribution of forces throughout the structure is presented. The resulting formulas for the deflection and frequency estimates have a compact form. The upper estimate of the first oscillation frequency of nodes under the assumption of vertical displacements of points has fairly high accuracy. The analytical solution is compared with the lowest oscillation frequency obtained numerically. All analytical transformations are performed in the Maple symbolic mathematics system. Some asymptotics of solutions is found. |
| doi_str_mv | 10.4123/CUBS.99.4 |
| format | Article |
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Deformations and oscillation frequency</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Kirsanov, Mikhail Nikolaevich</creator><creatorcontrib>Kirsanov, Mikhail Nikolaevich</creatorcontrib><description>The object of research. A new scheme of a statically determinate spatial truss is considered. The design has a hexagonal dome resting on two belts. The belts are supported by vertical racks. Two corner supports have spherical and cylindrical hinges. The outer support contra consists of 6n horizontal rods, the inner one consists of 6(n-1) rods. The contours are connected by skews. Formulas are derived for the deflection of the vertex and the angular hinge depending on n. The upper and lower analytical estimates of the first frequency of natural oscillations of the structure are found. Method. Calculation of the forces in the rods is carried out by cutting out the nodes from the solution of the system of equilibrium equations for all nodes in the projection on the coordinate axes. To derive formulas for the dependence of breakdowns, forces, and the frequency of free oscillations, an inductive generalization of the sequence of solutions for structures with a different number of panels is used. The structural stiffness matrix and deflection are calculated using the Maxwell - Mohr formula in analytical form. To find estimates of the lowest frequency of vibrations of nodes endowed with masses, the Dunkerley and Rayleigh methods are used. Results. The vertical load distributed over the nodes and the concentrated load applied to the top are considered. Formulas for the forces in the characteristic bars of the structure are derived. A picture of the distribution of forces throughout the structure is presented. The resulting formulas for the deflection and frequency estimates have a compact form. The upper estimate of the first oscillation frequency of nodes under the assumption of vertical displacements of points has fairly high accuracy. The analytical solution is compared with the lowest oscillation frequency obtained numerically. All analytical transformations are performed in the Maple symbolic mathematics system. Some asymptotics of solutions is found.</description><identifier>EISSN: 2304-6295</identifier><identifier>DOI: 10.4123/CUBS.99.4</identifier><language>eng</language><publisher>St. Petersburg: Production, Research and Design Institution "Venchur", Technological Cluster of Saint-Petersburg State Polytechnical University</publisher><subject>Belts ; Concentrated loads ; Deflection ; Domes ; Equilibrium equations ; Estimates ; Exact solutions ; Formulas (mathematics) ; Free vibration ; Nodes ; Racks ; Rods ; Stiffness matrix ; Vertical loads</subject><ispartof>Stroitel'stvo unikal'nyh zdanij i sooruhenij, 2022-01 (1), p.1-13</ispartof><rights>2022. This work is published under https://creativecommons.org/licenses/by-nc/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,778,782,27907,27908</link.rule.ids></links><search><creatorcontrib>Kirsanov, Mikhail Nikolaevich</creatorcontrib><title>Model of a spatial dome cover. Deformations and oscillation frequency</title><title>Stroitel'stvo unikal'nyh zdanij i sooruhenij</title><description>The object of research. A new scheme of a statically determinate spatial truss is considered. The design has a hexagonal dome resting on two belts. The belts are supported by vertical racks. Two corner supports have spherical and cylindrical hinges. The outer support contra consists of 6n horizontal rods, the inner one consists of 6(n-1) rods. The contours are connected by skews. Formulas are derived for the deflection of the vertex and the angular hinge depending on n. The upper and lower analytical estimates of the first frequency of natural oscillations of the structure are found. Method. Calculation of the forces in the rods is carried out by cutting out the nodes from the solution of the system of equilibrium equations for all nodes in the projection on the coordinate axes. To derive formulas for the dependence of breakdowns, forces, and the frequency of free oscillations, an inductive generalization of the sequence of solutions for structures with a different number of panels is used. The structural stiffness matrix and deflection are calculated using the Maxwell - Mohr formula in analytical form. To find estimates of the lowest frequency of vibrations of nodes endowed with masses, the Dunkerley and Rayleigh methods are used. Results. The vertical load distributed over the nodes and the concentrated load applied to the top are considered. Formulas for the forces in the characteristic bars of the structure are derived. A picture of the distribution of forces throughout the structure is presented. The resulting formulas for the deflection and frequency estimates have a compact form. The upper estimate of the first oscillation frequency of nodes under the assumption of vertical displacements of points has fairly high accuracy. The analytical solution is compared with the lowest oscillation frequency obtained numerically. All analytical transformations are performed in the Maple symbolic mathematics system. Some asymptotics of solutions is found.</description><subject>Belts</subject><subject>Concentrated loads</subject><subject>Deflection</subject><subject>Domes</subject><subject>Equilibrium equations</subject><subject>Estimates</subject><subject>Exact solutions</subject><subject>Formulas (mathematics)</subject><subject>Free vibration</subject><subject>Nodes</subject><subject>Racks</subject><subject>Rods</subject><subject>Stiffness matrix</subject><subject>Vertical loads</subject><issn>2304-6295</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqNis0KgkAYAJcgSMpDb_BBZ23_tPaaFV06VWdZdAVl9bNdDXr7JHqATgMzQ8ia0VgyLrbZ43CLlYrljARcUBmlXCULEnrfUEqZ4IlgMiCnK5bGAlagwfd6qLWFElsDBb6Mi-FoKnTt5LHzoLsS0Be1tV8BlTPP0XTFe0XmlbbehD8uyeZ8umeXqHc4HX7IGxxdN6WcpwlnSu7kXvx3fQBOTT6l</recordid><startdate>20220101</startdate><enddate>20220101</enddate><creator>Kirsanov, Mikhail Nikolaevich</creator><general>Production, Research and Design Institution "Venchur", Technological Cluster of Saint-Petersburg State Polytechnical University</general><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BYOGL</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>HCIFZ</scope><scope>KR7</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20220101</creationdate><title>Model of a spatial dome cover. Deformations and oscillation frequency</title><author>Kirsanov, Mikhail Nikolaevich</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_26521947483</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Belts</topic><topic>Concentrated loads</topic><topic>Deflection</topic><topic>Domes</topic><topic>Equilibrium equations</topic><topic>Estimates</topic><topic>Exact solutions</topic><topic>Formulas (mathematics)</topic><topic>Free vibration</topic><topic>Nodes</topic><topic>Racks</topic><topic>Rods</topic><topic>Stiffness matrix</topic><topic>Vertical loads</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kirsanov, Mikhail Nikolaevich</creatorcontrib><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>East Europe, Central Europe Database</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>SciTech Premium Collection</collection><collection>Civil Engineering Abstracts</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><jtitle>Stroitel'stvo unikal'nyh zdanij i sooruhenij</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kirsanov, Mikhail Nikolaevich</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Model of a spatial dome cover. Deformations and oscillation frequency</atitle><jtitle>Stroitel'stvo unikal'nyh zdanij i sooruhenij</jtitle><date>2022-01-01</date><risdate>2022</risdate><issue>1</issue><spage>1</spage><epage>13</epage><pages>1-13</pages><eissn>2304-6295</eissn><abstract>The object of research. A new scheme of a statically determinate spatial truss is considered. The design has a hexagonal dome resting on two belts. The belts are supported by vertical racks. Two corner supports have spherical and cylindrical hinges. The outer support contra consists of 6n horizontal rods, the inner one consists of 6(n-1) rods. The contours are connected by skews. Formulas are derived for the deflection of the vertex and the angular hinge depending on n. The upper and lower analytical estimates of the first frequency of natural oscillations of the structure are found. Method. Calculation of the forces in the rods is carried out by cutting out the nodes from the solution of the system of equilibrium equations for all nodes in the projection on the coordinate axes. To derive formulas for the dependence of breakdowns, forces, and the frequency of free oscillations, an inductive generalization of the sequence of solutions for structures with a different number of panels is used. The structural stiffness matrix and deflection are calculated using the Maxwell - Mohr formula in analytical form. To find estimates of the lowest frequency of vibrations of nodes endowed with masses, the Dunkerley and Rayleigh methods are used. Results. The vertical load distributed over the nodes and the concentrated load applied to the top are considered. Formulas for the forces in the characteristic bars of the structure are derived. A picture of the distribution of forces throughout the structure is presented. The resulting formulas for the deflection and frequency estimates have a compact form. The upper estimate of the first oscillation frequency of nodes under the assumption of vertical displacements of points has fairly high accuracy. The analytical solution is compared with the lowest oscillation frequency obtained numerically. All analytical transformations are performed in the Maple symbolic mathematics system. Some asymptotics of solutions is found.</abstract><cop>St. Petersburg</cop><pub>Production, Research and Design Institution "Venchur", Technological Cluster of Saint-Petersburg State Polytechnical University</pub><doi>10.4123/CUBS.99.4</doi><oa>free_for_read</oa></addata></record> |
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| identifier | EISSN: 2304-6295 |
| ispartof | Stroitel'stvo unikal'nyh zdanij i sooruhenij, 2022-01 (1), p.1-13 |
| issn | 2304-6295 |
| language | eng |
| recordid | cdi_proquest_journals_2652194748 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Belts Concentrated loads Deflection Domes Equilibrium equations Estimates Exact solutions Formulas (mathematics) Free vibration Nodes Racks Rods Stiffness matrix Vertical loads |
| title | Model of a spatial dome cover. Deformations and oscillation frequency |
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