A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory
The spectral element matrix is derived for a straight and uniform beam element having an arbitrary cross-section. The general higher-order beam theory is used, which accurately accounts for the transverse shear deformation out of the cross-sectional plane and antielastic-type deformation within the...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2008/953639 |
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| _version_ | 1832545490280906752 |
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| author | Jiao Sujuan Li Jun Hua Hongxing Shen Rongying |
| author_facet | Jiao Sujuan Li Jun Hua Hongxing Shen Rongying |
| author_sort | Jiao Sujuan |
| collection | DOAJ |
| description | The spectral element matrix is derived for a straight and uniform beam element having an arbitrary cross-section. The general higher-order beam theory is used, which accurately accounts for the transverse shear deformation out of the cross-sectional plane and antielastic-type deformation within the cross-sectional plane. Two coupled equations of motion are derived by use of Hamilton's principle along with the full three-dimensional constitutive relations. The theoretical expressions of the spectral element matrix are formulated from the exact solutions of the coupled governing equations. The developed spectral element matrix is directly applied to calculate the exact natural frequencies and mode shapes of the illustrative examples. Numerical results of the thick isotropic beams with rectangular and elliptical cross-sections are presented for a wide variety of cross-section aspect ratios. |
| format | Article |
| id | doaj-art-2804040dee56478ea543aa8811414b3c |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-2804040dee56478ea543aa8811414b3c2025-02-03T07:25:37ZengWileyShock and Vibration1070-96221875-92032008-01-0115217919210.1155/2008/953639A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order TheoryJiao Sujuan0Li Jun1Hua Hongxing2Shen Rongying3Vibration, Shock & Noise Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, ChinaVibration, Shock & Noise Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, ChinaVibration, Shock & Noise Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, ChinaVibration, Shock & Noise Institute, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, ChinaThe spectral element matrix is derived for a straight and uniform beam element having an arbitrary cross-section. The general higher-order beam theory is used, which accurately accounts for the transverse shear deformation out of the cross-sectional plane and antielastic-type deformation within the cross-sectional plane. Two coupled equations of motion are derived by use of Hamilton's principle along with the full three-dimensional constitutive relations. The theoretical expressions of the spectral element matrix are formulated from the exact solutions of the coupled governing equations. The developed spectral element matrix is directly applied to calculate the exact natural frequencies and mode shapes of the illustrative examples. Numerical results of the thick isotropic beams with rectangular and elliptical cross-sections are presented for a wide variety of cross-section aspect ratios.http://dx.doi.org/10.1155/2008/953639 |
| spellingShingle | Jiao Sujuan Li Jun Hua Hongxing Shen Rongying A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory Shock and Vibration |
| title | A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory |
| title_full | A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory |
| title_fullStr | A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory |
| title_full_unstemmed | A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory |
| title_short | A Spectral Finite Element Model for Vibration Analysis of a Beam Based on General Higher-Order Theory |
| title_sort | spectral finite element model for vibration analysis of a beam based on general higher order theory |
| url | http://dx.doi.org/10.1155/2008/953639 |
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