Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams
Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approxim...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2005/824616 |
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| _version_ | 1832563743452561408 |
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| author | Menglin Lou Qiuhua Duan Genda Chen |
| author_facet | Menglin Lou Qiuhua Duan Genda Chen |
| author_sort | Menglin Lou |
| collection | DOAJ |
| description | Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are discussed in detail. |
| format | Article |
| id | doaj-art-f72fcefdd3d342988b6f48f2346a1e8a |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-f72fcefdd3d342988b6f48f2346a1e8a2025-02-03T01:12:41ZengWileyShock and Vibration1070-96221875-92032005-01-0112642543410.1155/2005/824616Modal Perturbation Method for the Dynamic Characteristics of Timoshenko BeamsMenglin Lou0Qiuhua Duan1Genda Chen2State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, ChinaState Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, ChinaDepartment of Civil, Architectural, and Environmental Engineering, University of Missouri-Rolla, Rolla, MO 65409, USATimoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are discussed in detail.http://dx.doi.org/10.1155/2005/824616 |
| spellingShingle | Menglin Lou Qiuhua Duan Genda Chen Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams Shock and Vibration |
| title | Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams |
| title_full | Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams |
| title_fullStr | Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams |
| title_full_unstemmed | Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams |
| title_short | Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams |
| title_sort | modal perturbation method for the dynamic characteristics of timoshenko beams |
| url | http://dx.doi.org/10.1155/2005/824616 |
| work_keys_str_mv | AT menglinlou modalperturbationmethodforthedynamiccharacteristicsoftimoshenkobeams AT qiuhuaduan modalperturbationmethodforthedynamiccharacteristicsoftimoshenkobeams AT gendachen modalperturbationmethodforthedynamiccharacteristicsoftimoshenkobeams |