Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method
The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwi...
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| Veröffentlicht in: | Applied mathematics and mechanics 2017-10, Vol.38 (10), p.1425-1438 |
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| creator | Yang, Xiaodong Wang, Shaowen Zhang, Wei Qin, Zhaohong Yang, Tianzhi |
| description | The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees. |
| doi_str_mv | 10.1007/s10483-017-2249-6 |
| format | Article |
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The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. 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Math. Mech.-Engl. Ed</addtitle><addtitle>Applied Mathematics and Mechanics（English Edition）</addtitle><description>The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees.</description><subject>Applications of Mathematics</subject><subject>Cantilever beams</subject><subject>Classical Mechanics</subject><subject>Differential equations</subject><subject>Fluid- and Aerodynamics</subject><subject>Functions (mathematics)</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><subject>Power series</subject><subject>Resonant frequencies</subject><subject>Stiffening</subject><subject>Tapering</subject><subject>Timoshenko梁</subject><subject>偏微分方程</subject><subject>固有频率</subject><subject>幂级数法</subject><subject>悬臂梁</subject><subject>数学模型</subject><subject>旋转</subject><subject>锥形</subject><issn>0253-4827</issn><issn>1573-2754</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kE1P3DAQhi0EEsvCD-BmtTekUH8lTo7Vlhaklbjs3Zok401gYy926JJ_j1dBlFMPo7k87zuah5Brzm45Y_pH5EyVMmNcZ0KoKitOyILnWmZC5-qULJjIZaZKoc_JRYxPjDGllVqQ-tfkYOgbCg52U-wj9ZYCDX6EsXdbOsIeA7a0ATf2O_yLgW76wccO3bOnNcJAa4gJ8I6OHdK9PyQkYugx0gHHzreX5MzCLuLVx16Sze-7zeo-Wz_-eVj9XGeN1OWYFZXUFYg2l7KolQRWtm2BHGxtS6wLKEEw1BKkyitr60ZVIte1VTxN2wi5JDdz7QGcBbc1T_41pKeimab41u3eDIqkJ9liRYK_z_A--JdXjOM_mlc5U4ViokwUn6km-BgDWrMP_QBhMpyZo3Yzazep1xy1m2OzmDMxsW6L4Uvzf0LfPg513m1fUu7zUqGl4KKSpXwH4u2RhQ</recordid><startdate>20171001</startdate><enddate>20171001</enddate><creator>Yang, Xiaodong</creator><creator>Wang, Shaowen</creator><creator>Zhang, Wei</creator><creator>Qin, Zhaohong</creator><creator>Yang, Tianzhi</creator><general>Shanghai University</general><general>Springer Nature B.V</general><general>Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China%Science and Technology on Reliability and Environment Engineering Laboratory, Beijing Institute of Structure and Environment Engineering, Beijing 100176, China%Department of Engineering Mechanics, Shenyang Aerospace University,Shenyang 110136, China</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20171001</creationdate><title>Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method</title><author>Yang, Xiaodong ; Wang, Shaowen ; Zhang, Wei ; Qin, Zhaohong ; Yang, Tianzhi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c378t-69379a2d5336b43a08dd6e1afbf8eb6a8a20e73a3459ffbc49257bf41bf4dc23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Applications of Mathematics</topic><topic>Cantilever beams</topic><topic>Classical Mechanics</topic><topic>Differential equations</topic><topic>Fluid- and Aerodynamics</topic><topic>Functions (mathematics)</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><topic>Power series</topic><topic>Resonant frequencies</topic><topic>Stiffening</topic><topic>Tapering</topic><topic>Timoshenko梁</topic><topic>偏微分方程</topic><topic>固有频率</topic><topic>幂级数法</topic><topic>悬臂梁</topic><topic>数学模型</topic><topic>旋转</topic><topic>锥形</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Yang, Xiaodong</creatorcontrib><creatorcontrib>Wang, Shaowen</creatorcontrib><creatorcontrib>Zhang, Wei</creatorcontrib><creatorcontrib>Qin, Zhaohong</creatorcontrib><creatorcontrib>Yang, Tianzhi</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Applied mathematics and mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Yang, Xiaodong</au><au>Wang, Shaowen</au><au>Zhang, Wei</au><au>Qin, Zhaohong</au><au>Yang, Tianzhi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method</atitle><jtitle>Applied mathematics and mechanics</jtitle><stitle>Appl. Math. Mech.-Engl. Ed</stitle><addtitle>Applied Mathematics and Mechanics（English Edition）</addtitle><date>2017-10-01</date><risdate>2017</risdate><volume>38</volume><issue>10</issue><spage>1425</spage><epage>1438</epage><pages>1425-1438</pages><issn>0253-4827</issn><eissn>1573-2754</eissn><abstract>The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees.</abstract><cop>Shanghai</cop><pub>Shanghai University</pub><doi>10.1007/s10483-017-2249-6</doi><tpages>14</tpages><edition>English ed.</edition></addata></record> |
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| source | SpringerNature Journals; Alma/SFX Local Collection |
| subjects | Applications of Mathematics Cantilever beams Classical Mechanics Differential equations Fluid- and Aerodynamics Functions (mathematics) Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Partial Differential Equations Power series Resonant frequencies Stiffening Tapering Timoshenko梁 偏微分方程 固有频率 幂级数法 悬臂梁 数学模型 旋转 锥形 |
| title | Dynamic analysis of a rotating tapered cantilever Timoshenko beam based on the power series method |
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