Analysis of Critical Velocities for an Infinite Timoshenko Beam Resting on an Elastic Foundation Subjected to a Harmonic Moving Load
Critical velocities are investigated for an infinite Timoshenko beam resting on a Winkler-type elastic foundation subjected to a harmonic moving load. The determination of critical velocities ultimately comes down to discrimination of the existence of multiple real roots of an algebraic equation wit...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2014/848536 |
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| author | Bin Zhen Wei Luo Jian Xu |
| author_facet | Bin Zhen Wei Luo Jian Xu |
| author_sort | Bin Zhen |
| collection | DOAJ |
| description | Critical velocities are investigated for an infinite Timoshenko beam resting on a Winkler-type elastic foundation subjected to a harmonic moving load. The determination of critical velocities ultimately comes down to discrimination of the existence of multiple real roots of an algebraic equation with real coefficients of the 4th degree, which can be solved by employing Descartes sign method and complete discrimination system for polynomials. Numerical calculations for the European high-speed rail show that there are at most four critical velocities for an infinite Timoshenko beam, which is very different from those gained by others. Furthermore, the shear wave velocity must be the critical velocity, but the longitudinal wave velocity is not possible under certain conditions. Further numerical simulations indicate that all critical velocities are limited to be less than the longitudinal wave velocity no matter how large the foundation stiffness is or how high the loading frequency is. Additionally, our study suggests that the maximum value of one group velocity of waves in Timoshenko beam should be one “dangerous” velocity for the moving load in launching process, which has never been referred to in previous work. |
| format | Article |
| id | doaj-art-97e4bc9374e64686b1eda023cfbf53d2 |
| institution | OA Journals |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-97e4bc9374e64686b1eda023cfbf53d22025-08-20T02:10:07ZengWileyShock and Vibration1070-96221875-92032014-01-01201410.1155/2014/848536848536Analysis of Critical Velocities for an Infinite Timoshenko Beam Resting on an Elastic Foundation Subjected to a Harmonic Moving LoadBin Zhen0Wei Luo1Jian Xu2School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443002, ChinaSchool of Aerospace Engineering and Mechanics, Tongji University, Shanghai 200092, ChinaCritical velocities are investigated for an infinite Timoshenko beam resting on a Winkler-type elastic foundation subjected to a harmonic moving load. The determination of critical velocities ultimately comes down to discrimination of the existence of multiple real roots of an algebraic equation with real coefficients of the 4th degree, which can be solved by employing Descartes sign method and complete discrimination system for polynomials. Numerical calculations for the European high-speed rail show that there are at most four critical velocities for an infinite Timoshenko beam, which is very different from those gained by others. Furthermore, the shear wave velocity must be the critical velocity, but the longitudinal wave velocity is not possible under certain conditions. Further numerical simulations indicate that all critical velocities are limited to be less than the longitudinal wave velocity no matter how large the foundation stiffness is or how high the loading frequency is. Additionally, our study suggests that the maximum value of one group velocity of waves in Timoshenko beam should be one “dangerous” velocity for the moving load in launching process, which has never been referred to in previous work.http://dx.doi.org/10.1155/2014/848536 |
| spellingShingle | Bin Zhen Wei Luo Jian Xu Analysis of Critical Velocities for an Infinite Timoshenko Beam Resting on an Elastic Foundation Subjected to a Harmonic Moving Load Shock and Vibration |
| title | Analysis of Critical Velocities for an Infinite Timoshenko Beam Resting on an Elastic Foundation Subjected to a Harmonic Moving Load |
| title_full | Analysis of Critical Velocities for an Infinite Timoshenko Beam Resting on an Elastic Foundation Subjected to a Harmonic Moving Load |
| title_fullStr | Analysis of Critical Velocities for an Infinite Timoshenko Beam Resting on an Elastic Foundation Subjected to a Harmonic Moving Load |
| title_full_unstemmed | Analysis of Critical Velocities for an Infinite Timoshenko Beam Resting on an Elastic Foundation Subjected to a Harmonic Moving Load |
| title_short | Analysis of Critical Velocities for an Infinite Timoshenko Beam Resting on an Elastic Foundation Subjected to a Harmonic Moving Load |
| title_sort | analysis of critical velocities for an infinite timoshenko beam resting on an elastic foundation subjected to a harmonic moving load |
| url | http://dx.doi.org/10.1155/2014/848536 |
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