Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method
The modal analysis method (MAM) is very useful for obtaining the dynamic responses of a structure in analytical closed forms. In order to use the MAM, accurate information is needed on the natural frequencies, mode shapes, and orthogonality of the mode shapes a priori. A thorough literature survey r...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2017/3924921 |
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| _version_ | 1832549749054504960 |
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| author | Taehyun Kim Ilwook Park Usik Lee |
| author_facet | Taehyun Kim Ilwook Park Usik Lee |
| author_sort | Taehyun Kim |
| collection | DOAJ |
| description | The modal analysis method (MAM) is very useful for obtaining the dynamic responses of a structure in analytical closed forms. In order to use the MAM, accurate information is needed on the natural frequencies, mode shapes, and orthogonality of the mode shapes a priori. A thorough literature survey reveals that the necessary information reported in the existing literature is sometimes very limited or incomplete, even for simple beam models such as Timoshenko beams. Thus, we present complete information on the natural frequencies, three types of mode shapes, and the orthogonality of the mode shapes for simply supported Timoshenko beams. Based on this information, we use the MAM to derive the forced vibration responses of a simply supported Timoshenko beam subjected to arbitrary initial conditions and to stationary or moving loads (a point transverse force and a point bending moment) in analytical closed form. We then conduct numerical studies to investigate the effects of each type of mode shape on the long-term dynamic responses (vibrations), the short-term dynamic responses (waves), and the deformed shapes of an example Timoshenko beam subjected to stationary or moving point loads. |
| format | Article |
| id | doaj-art-c9021d1f099c4cc5a7a0c7232cba28e5 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-c9021d1f099c4cc5a7a0c7232cba28e52025-02-03T06:08:48ZengWileyShock and Vibration1070-96221875-92032017-01-01201710.1155/2017/39249213924921Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis MethodTaehyun Kim0Ilwook Park1Usik Lee2Department of Mechanical Engineering, Inha University, 100 Inha-ro, Nam-gu, Incheon 402-751, Republic of KoreaDepartment of Mechanical Engineering, Inha University, 100 Inha-ro, Nam-gu, Incheon 402-751, Republic of KoreaDepartment of Mechanical Engineering, Inha University, 100 Inha-ro, Nam-gu, Incheon 402-751, Republic of KoreaThe modal analysis method (MAM) is very useful for obtaining the dynamic responses of a structure in analytical closed forms. In order to use the MAM, accurate information is needed on the natural frequencies, mode shapes, and orthogonality of the mode shapes a priori. A thorough literature survey reveals that the necessary information reported in the existing literature is sometimes very limited or incomplete, even for simple beam models such as Timoshenko beams. Thus, we present complete information on the natural frequencies, three types of mode shapes, and the orthogonality of the mode shapes for simply supported Timoshenko beams. Based on this information, we use the MAM to derive the forced vibration responses of a simply supported Timoshenko beam subjected to arbitrary initial conditions and to stationary or moving loads (a point transverse force and a point bending moment) in analytical closed form. We then conduct numerical studies to investigate the effects of each type of mode shape on the long-term dynamic responses (vibrations), the short-term dynamic responses (waves), and the deformed shapes of an example Timoshenko beam subjected to stationary or moving point loads.http://dx.doi.org/10.1155/2017/3924921 |
| spellingShingle | Taehyun Kim Ilwook Park Usik Lee Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method Shock and Vibration |
| title | Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method |
| title_full | Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method |
| title_fullStr | Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method |
| title_full_unstemmed | Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method |
| title_short | Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method |
| title_sort | forced vibration of a timoshenko beam subjected to stationary and moving loads using the modal analysis method |
| url | http://dx.doi.org/10.1155/2017/3924921 |
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