| STEADY-STATE RESPONSE OF A TIMOSHENKO BEAM ON AN ELASTIC HALF-SPACE UNDER A MOVING LOAD |
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| 作者姓名： | Chen Vunmin Wang Changjing |
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| 作者单位： | Chen Yumnin Wang Changjing (Department of Civil Engineering，Zhejiang University，Hangzhou 310027，China) ( City College，Zhejiang University，Hangzhou 310015，China) |
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| 基金项目： | 中国科学院资助项目
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The Doctoral Education of The State Education Ministry of China
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Encouragement Fund for Young Teachers in University of Ministry of Education |
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| 摘 要： | By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Based on the relative relation of wave velocities of the half-space and the beam, four cases with the combination of different parameters of the half-space and the beam, the system of soft beam and hard half-space, the system of sub-soft beam and hard half-space, the system of sub-hard beam and soft half-space, and the system of hard beam and soft half-space are considered. The critical velocities of the moving load are studied using dispersion curves. It is found that critical velocities of the moving load on the Timoshenko beam depend on the relative relation of wave velocities of the half-space and the beam. The Rayleigh wave velocity in the half-space is always a critical velocity and the response of the system will be infinite when the load velocity reaches it. For the system of soft beam and hard half-space, wave velocities of the beam are also critical velocities. Besides the shear wave velocity of the beam, there is an additional minimum critical velocity for the system of sub-soft beam and hard half-space. While for systems of (sub-) hard beams and soft half-space, wave velocities of the beam are no longer critical ones. Comparison with the Euler-Bernoulli beam shows that the critical velocities and response of the two types of beams are much different for the system of (sub-) soft beam and hard half-space but are similar to each other for the system of (sub-) hard beam and soft half space. The largest displacement of the beam is almost at the location of the load and the displacement along the beam is almost symmetrical if the load velocity is smaller than the minimum critical velocity (the shear wave velocity of the beam for the system of soft beam and hard half-space). The largest displacement of the beam shifts behind the load and the asymmetry of the displacement along the beam increases with the increase of the load velocity due to the damping and wave radiation. The displacement of the beam at the front of the load is very small if the load velocity is larger than the largest wave velocity of the beam and the half space. The results of the present study provide attractive theoretical and practical references for the analysis of ground vibration induced by the high-speed train.
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| 关 键 词： | 临界流速 等效硬度 半空间 色散曲线 |
| 收稿时间： | 2004-12-21 |
| 修稿时间： | 2005-11-28 |
STEADY-STATE RESPONSE OF A TIMOSHENKO BEAM ON AN ELASTIC HALF-SPACE UNDER A MOVING LOAD |
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| Chen Vunmin Wang Changjing.STEADY-STATE RESPONSE OF A TIMOSHENKO BEAM ON AN ELASTIC HALF-SPACE UNDER A MOVING LOAD[J].Acta Mechanica Solida Sinica,2006,19(1):26-39. |
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| Authors: | Chen Yunmin Wang Changjing |
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| Institution: | 1. Department of Civil Engineering, Zhejiang University, Hangzhou 310027, China;2. City College, Zhejiang University, Hangzhou 310015, China;1. School of Mechanical Engineering, Tianjin University, Tianjin 300072, PR China;2. Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin 300072, PR China;1. Department of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, PR China;2. Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai 200240, PR China;1. Structural Mechanics Laboratory, Railway Technical Research Institute, 2-8-38, Hikari-cho, Kokubunji-shi, 185-8540 Tokyo, Japan;2. Design and Technology Department, Japan Railway Construction, Transport and Technology Agency, 6-50-1, Honcho, Naka-Ku, Yokohama-shi, 231-0005 Kanagawa, Japan;3. Department of Civil Engineering, Osaka University, 2-1, Yamadaoka, Suita-shi, 565-0871 Osaka, Japan;1. College of Civil Eng., Fuzhou University, 2, Xueyuan-road, Minhou, Fuzhou 350108, China;2. Dept. of Civil and Environmental Eng., Nagasaki University, 1-14, Bunkyo-machi, Nagasaki 852-8521, Japan |
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| Abstract: | By introducing the equivalent stiffness of an elastic half-space interacting with a Timoshenko beam, the displacement solution of the beam resting on an elastic half-space subjected to a moving load is presented. Based on the relative relation of wave velocities of the half-space and the beam, four cases with the combination of different parameters of the half-space and the beam, the system of soft beam and hard half-space, the system of sub-soft beam and hard half-space, the system of sub-hard beam and soft half-space, and the system of hard beam and soft half-space are considered. The critical velocities of the moving load are studied using dispersion curves. It is found that critical velocities of the moving load on the Timoshenko beam depend on the relative relation of wave velocities of the half-space and the beam. The Rayleigh wave velocity in the half-space is always a critical velocity and the response of the system will be infinite when the load velocity reaches it. For the system of soft beam and hard half-space, wave velocities of the beam are also critical velocities. Besides the shear wave velocity of the beam, there is an additional minimum critical velocity for the system of sub-soft beam and hard half-space. While for systems of (sub-) hard beams and soft half-space, wave velocities of the beam are no longer critical ones. Comparison with the Euler-Bernoulli beam shows that the critical velocities and response of the two types of beams are much different for the system of (sub-) soft beam and hard half-space but are similar to each other for the system of (sub-) hard beam and soft half space. The largest displacement of the beam is almost at the location of the load and the displacement along the beam is almost symmetrical if the load velocity is smaller than the minimum critical velocity (the shear wave velocity of the beam for the system of soft beam and hard half-space). The largest displacement of the beam shifts behind the load and the asymmetry of the displacement along the beam increases with the increase of the load velocity due to the damping and wave radiation. The displacement of the beam at the front of the load is very small if the load velocity is larger than the largest wave velocity of the beam and the half space. The results of the present study provide attractive theoretical and practical references for the analysis of ground vibration induced by the high-speed train. |
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| Keywords: | critical velocities equivalent stiffness Timoshenko beam half-space moving load dispersion curve |
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