Mutual influence of the supports stiffness and the first natural frequency at bending vibrations of a spring-hinged beam
This paper discusses the analytical finding of the required stiffness values of the supports, which would provide the given first natural frequency of bending vibrations for a spring-hinged beam. The solution is obtained through the support coefficient, the value of which, according to the theory of...
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| Veröffentlicht in: | IOP conference series. Materials Science and Engineering 2021-06, Vol.1155 (1), p.12099 |
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| container_title | IOP conference series. Materials Science and Engineering |
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| creator | Mityaev, A E Kudryavtsev, I V Khomutov, M P Brungardt, M V Rabetskaya, O I |
| description | This paper discusses the analytical finding of the required stiffness values of the supports, which would provide the given first natural frequency of bending vibrations for a spring-hinged beam. The solution is obtained through the support coefficient, the value of which, according to the theory of beam vibrations, connects the stiffness of the support of the beam and the value of its first vibration frequency. For this purpose, preliminary approximation of dependence of support coefficient values on a support stiffness is performed using quadratic analytical functions. In this case, the problem of determining the stiffness of the supports becomes inverse and is reduced to finding combinations of the supports stiffness values, at which there is a solution of the quadratic analytical functions for the required support coefficient and, accordingly, the required first beam frequency. Normalization of the obtained support coefficients is proposed for a more convenient estimation of their influence on the first frequency of beam vibration. |
| doi_str_mv | 10.1088/1757-899X/1155/1/012099 |
| format | Article |
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The solution is obtained through the support coefficient, the value of which, according to the theory of beam vibrations, connects the stiffness of the support of the beam and the value of its first vibration frequency. For this purpose, preliminary approximation of dependence of support coefficient values on a support stiffness is performed using quadratic analytical functions. In this case, the problem of determining the stiffness of the supports becomes inverse and is reduced to finding combinations of the supports stiffness values, at which there is a solution of the quadratic analytical functions for the required support coefficient and, accordingly, the required first beam frequency. 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In this case, the problem of determining the stiffness of the supports becomes inverse and is reduced to finding combinations of the supports stiffness values, at which there is a solution of the quadratic analytical functions for the required support coefficient and, accordingly, the required first beam frequency. Normalization of the obtained support coefficients is proposed for a more convenient estimation of their influence on the first frequency of beam vibration.</description><subject>Bending</subject><subject>Coefficients</subject><subject>Mathematical analysis</subject><subject>Resonant frequencies</subject><subject>Stiffness</subject><subject>Vibration</subject><issn>1757-8981</issn><issn>1757-899X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>O3W</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNqFkE9LxDAQxYsouK5-BgOePNRmkqZNj7Ksf2AXDyp4C2mbuF1205qk4n57UysrguBlMsy838vwougc8BVgzhPIWR7zonhJABhLIMFAcFEcRJP95nDfcziOTpxbY5zlaYon0cey973coMboTa9MpVCrkV8p5Pqua613yPlGa6OcQ9LUXyvdWOeRkb63gdRWvQ3kDkmPSmXqxryi96a00jetcYOfRK6zYRyvQlF1UMntaXSk5caps-93Gj3fzJ9md_Hi4fZ-dr2IK4JpEaekJKWsCa8xBkYJY7oqoco1y0kYAmgtFQVdyZTSknLGdZ3yjBIqJeRY0ml0Mfp2tg13Oi_WbW9N-FIQlmKOswzSoMpHVWVb56zSIhy8lXYnAIshZjEEKIYwxRCzADHGHEg6kk3b_Vj_T13-QS0f5791oqs1_QSIsY6U</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Mityaev, A E</creator><creator>Kudryavtsev, I V</creator><creator>Khomutov, M P</creator><creator>Brungardt, M V</creator><creator>Rabetskaya, O I</creator><general>IOP Publishing</general><scope>O3W</scope><scope>TSCCA</scope><scope>AAYXX</scope><scope>CITATION</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>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>KB.</scope><scope>L6V</scope><scope>M7S</scope><scope>PDBOC</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20210601</creationdate><title>Mutual influence of the supports stiffness and the first natural frequency at bending vibrations of a spring-hinged beam</title><author>Mityaev, A E ; Kudryavtsev, I V ; Khomutov, M P ; Brungardt, M V ; Rabetskaya, O I</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2039-42b2bad28d00153255fcb1c7f57228d11ffae31fca433b3858fd486323aa170a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Bending</topic><topic>Coefficients</topic><topic>Mathematical analysis</topic><topic>Resonant frequencies</topic><topic>Stiffness</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mityaev, A E</creatorcontrib><creatorcontrib>Kudryavtsev, I V</creatorcontrib><creatorcontrib>Khomutov, M P</creatorcontrib><creatorcontrib>Brungardt, M V</creatorcontrib><creatorcontrib>Rabetskaya, O I</creatorcontrib><collection>IOP Publishing Free Content</collection><collection>IOPscience (Open Access)</collection><collection>CrossRef</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</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Materials Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Materials Science Collection</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>IOP conference series. Materials Science and Engineering</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mityaev, A E</au><au>Kudryavtsev, I V</au><au>Khomutov, M P</au><au>Brungardt, M V</au><au>Rabetskaya, O I</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Mutual influence of the supports stiffness and the first natural frequency at bending vibrations of a spring-hinged beam</atitle><jtitle>IOP conference series. Materials Science and Engineering</jtitle><addtitle>IOP Conf. Ser.: Mater. Sci. Eng</addtitle><date>2021-06-01</date><risdate>2021</risdate><volume>1155</volume><issue>1</issue><spage>12099</spage><pages>12099-</pages><issn>1757-8981</issn><eissn>1757-899X</eissn><abstract>This paper discusses the analytical finding of the required stiffness values of the supports, which would provide the given first natural frequency of bending vibrations for a spring-hinged beam. The solution is obtained through the support coefficient, the value of which, according to the theory of beam vibrations, connects the stiffness of the support of the beam and the value of its first vibration frequency. For this purpose, preliminary approximation of dependence of support coefficient values on a support stiffness is performed using quadratic analytical functions. In this case, the problem of determining the stiffness of the supports becomes inverse and is reduced to finding combinations of the supports stiffness values, at which there is a solution of the quadratic analytical functions for the required support coefficient and, accordingly, the required first beam frequency. Normalization of the obtained support coefficients is proposed for a more convenient estimation of their influence on the first frequency of beam vibration.</abstract><cop>Bristol</cop><pub>IOP Publishing</pub><doi>10.1088/1757-899X/1155/1/012099</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| source | IOP Publishing Free Content; EZB-FREE-00999 freely available EZB journals; IOPscience extra; Free Full-Text Journals in Chemistry |
| subjects | Bending Coefficients Mathematical analysis Resonant frequencies Stiffness Vibration |
| title | Mutual influence of the supports stiffness and the first natural frequency at bending vibrations of a spring-hinged beam |
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