Exact Free Vibration Analysis for Plate Built-Up Structures under Comprehensive Combinations of Boundary Conditions
In this research, an exact dynamic stiffness model for spatial plate built-up structures under comprehensive combinations of different boundary conditions is newly proposed. Dynamic stiffness formulations for plate elements with 16 different types of supported opposite edges and arbitrarily supporte...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2020/5305692 |
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| _version_ | 1832558450730598400 |
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| author | Xiang Liu Chen Xie Han-cheng Dan |
| author_facet | Xiang Liu Chen Xie Han-cheng Dan |
| author_sort | Xiang Liu |
| collection | DOAJ |
| description | In this research, an exact dynamic stiffness model for spatial plate built-up structures under comprehensive combinations of different boundary conditions is newly proposed. Dynamic stiffness formulations for plate elements with 16 different types of supported opposite edges and arbitrarily supported boundary conditions along other edges are developed, which makes the dynamic stiffness method (DSM) more applicable to engineering problems compared to existing works. The Wittrick–Williams algorithm of the DSM is applied with the explicit expressions of the J0 count for plate elements under all above support conditions. In return, there is no need to refine the element in the DSM, and thus, it becomes immensely efficient. Moreover, the present theory is applied for exact free vibration analysis within the whole frequency range of three built-up structures which are commonly encountered in engineering. The results show that the DSM gives exact results with as much as 100-fold computational efficiency advantage over the commercial finite element method. Besides, benchmark results are also provided. |
| format | Article |
| id | doaj-art-61a1eff16fd04dcfa4b42f7a00b44736 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-61a1eff16fd04dcfa4b42f7a00b447362025-02-03T01:32:23ZengWileyShock and Vibration1070-96221875-92032020-01-01202010.1155/2020/53056925305692Exact Free Vibration Analysis for Plate Built-Up Structures under Comprehensive Combinations of Boundary ConditionsXiang Liu0Chen Xie1Han-cheng Dan2Key Laboratory of Traffic Safety on Track (Central South University), Ministry of Education, Central South University, Hunan, Changsha 410075, ChinaKey Laboratory of Traffic Safety on Track (Central South University), Ministry of Education, Central South University, Hunan, Changsha 410075, ChinaSchool of Civil Engineering, Central South University, Hunan, Changsha 410075, ChinaIn this research, an exact dynamic stiffness model for spatial plate built-up structures under comprehensive combinations of different boundary conditions is newly proposed. Dynamic stiffness formulations for plate elements with 16 different types of supported opposite edges and arbitrarily supported boundary conditions along other edges are developed, which makes the dynamic stiffness method (DSM) more applicable to engineering problems compared to existing works. The Wittrick–Williams algorithm of the DSM is applied with the explicit expressions of the J0 count for plate elements under all above support conditions. In return, there is no need to refine the element in the DSM, and thus, it becomes immensely efficient. Moreover, the present theory is applied for exact free vibration analysis within the whole frequency range of three built-up structures which are commonly encountered in engineering. The results show that the DSM gives exact results with as much as 100-fold computational efficiency advantage over the commercial finite element method. Besides, benchmark results are also provided.http://dx.doi.org/10.1155/2020/5305692 |
| spellingShingle | Xiang Liu Chen Xie Han-cheng Dan Exact Free Vibration Analysis for Plate Built-Up Structures under Comprehensive Combinations of Boundary Conditions Shock and Vibration |
| title | Exact Free Vibration Analysis for Plate Built-Up Structures under Comprehensive Combinations of Boundary Conditions |
| title_full | Exact Free Vibration Analysis for Plate Built-Up Structures under Comprehensive Combinations of Boundary Conditions |
| title_fullStr | Exact Free Vibration Analysis for Plate Built-Up Structures under Comprehensive Combinations of Boundary Conditions |
| title_full_unstemmed | Exact Free Vibration Analysis for Plate Built-Up Structures under Comprehensive Combinations of Boundary Conditions |
| title_short | Exact Free Vibration Analysis for Plate Built-Up Structures under Comprehensive Combinations of Boundary Conditions |
| title_sort | exact free vibration analysis for plate built up structures under comprehensive combinations of boundary conditions |
| url | http://dx.doi.org/10.1155/2020/5305692 |
| work_keys_str_mv | AT xiangliu exactfreevibrationanalysisforplatebuiltupstructuresundercomprehensivecombinationsofboundaryconditions AT chenxie exactfreevibrationanalysisforplatebuiltupstructuresundercomprehensivecombinationsofboundaryconditions AT hanchengdan exactfreevibrationanalysisforplatebuiltupstructuresundercomprehensivecombinationsofboundaryconditions |