Free Vibrations of an Elastically Restrained Euler Beam Resting on a Movable Winkler Foundation
The traditional theory of beam on elastic foundation implies a hypothesis that the elastic foundation is static with respect to the inertia reference frame, so it may not be applicable when the foundation is movable. A general model is presented for the free vibration of a Euler beam supported on a...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2019/2724768 |
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| author | Qiang Zhou Tong Wang |
| author_facet | Qiang Zhou Tong Wang |
| author_sort | Qiang Zhou |
| collection | DOAJ |
| description | The traditional theory of beam on elastic foundation implies a hypothesis that the elastic foundation is static with respect to the inertia reference frame, so it may not be applicable when the foundation is movable. A general model is presented for the free vibration of a Euler beam supported on a movable Winkler foundation and with ends elastically restrained by two vertical and two rotational springs. Frequency equations and corresponding mode shapes are analytically derived and numerically solved to study the effects of the movable Winkler foundation as well as elastic restraints on beam’s natural characteristics. Results indicate that if one of the beam ends is not vertically fixed, the effect of the foundation’s movability cannot be neglected and is mainly on the first two modes. As the foundation stiffness increases, the first wave number, sometimes together with the second one, firstly decreases to zero at the critical foundation stiffness and then increases after this point. |
| format | Article |
| id | doaj-art-ec415af9bb4e49058b0b532327978ba5 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-ec415af9bb4e49058b0b532327978ba52025-02-03T01:32:05ZengWileyShock and Vibration1070-96221875-92032019-01-01201910.1155/2019/27247682724768Free Vibrations of an Elastically Restrained Euler Beam Resting on a Movable Winkler FoundationQiang Zhou0Tong Wang1Research Center for Wind Engineering, Southwest Jiaotong University, Chengdu, ChinaCollege of Civil Engineering, Shanghai Normal University, Shanghai, ChinaThe traditional theory of beam on elastic foundation implies a hypothesis that the elastic foundation is static with respect to the inertia reference frame, so it may not be applicable when the foundation is movable. A general model is presented for the free vibration of a Euler beam supported on a movable Winkler foundation and with ends elastically restrained by two vertical and two rotational springs. Frequency equations and corresponding mode shapes are analytically derived and numerically solved to study the effects of the movable Winkler foundation as well as elastic restraints on beam’s natural characteristics. Results indicate that if one of the beam ends is not vertically fixed, the effect of the foundation’s movability cannot be neglected and is mainly on the first two modes. As the foundation stiffness increases, the first wave number, sometimes together with the second one, firstly decreases to zero at the critical foundation stiffness and then increases after this point.http://dx.doi.org/10.1155/2019/2724768 |
| spellingShingle | Qiang Zhou Tong Wang Free Vibrations of an Elastically Restrained Euler Beam Resting on a Movable Winkler Foundation Shock and Vibration |
| title | Free Vibrations of an Elastically Restrained Euler Beam Resting on a Movable Winkler Foundation |
| title_full | Free Vibrations of an Elastically Restrained Euler Beam Resting on a Movable Winkler Foundation |
| title_fullStr | Free Vibrations of an Elastically Restrained Euler Beam Resting on a Movable Winkler Foundation |
| title_full_unstemmed | Free Vibrations of an Elastically Restrained Euler Beam Resting on a Movable Winkler Foundation |
| title_short | Free Vibrations of an Elastically Restrained Euler Beam Resting on a Movable Winkler Foundation |
| title_sort | free vibrations of an elastically restrained euler beam resting on a movable winkler foundation |
| url | http://dx.doi.org/10.1155/2019/2724768 |
| work_keys_str_mv | AT qiangzhou freevibrationsofanelasticallyrestrainedeulerbeamrestingonamovablewinklerfoundation AT tongwang freevibrationsofanelasticallyrestrainedeulerbeamrestingonamovablewinklerfoundation |