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. Base...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 racliation. 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.展开更多
The use of the dipole force on atoms is a new technology that is used to build nanostructures. In this way, a high quality standard nano-grating can be obtained. Based on the semi-classical model, the motion equation ...The use of the dipole force on atoms is a new technology that is used to build nanostructures. In this way, a high quality standard nano-grating can be obtained. Based on the semi-classical model, the motion equation is investigated and the trajectories of atoms in double half Gaussian standing wave field are simulated. Compared with the Gaussian standing wave field, the double half Gaussian standing wave can well focus the Cr atoms. In order to obtain this kind of beam, a prism is designed and the experimental result shows that the beam is well generated.展开更多
The buried pipelines are widely used in oil transportation. The pipelines become suspended in the river with flushing of floodwater. If the frequency of vortex shedding is near to the nature frequency of pipelines, it...The buried pipelines are widely used in oil transportation. The pipelines become suspended in the river with flushing of floodwater. If the frequency of vortex shedding is near to the nature frequency of pipelines, it will cause resonance of the suspended pipeline and result in the damage of pipelines. In this paper, the buried parts of pipeline in soil are treated as the half unlimited long beam placed on the elastic foundations. The vibration partial differential equations of suspended pipe and the parts buried in soil are derived respectively. The iterative calculation method is then presented. The results obtained from the suggested method are proved to be identical with the measured values.展开更多
基金Project supported by the National Natural Science Foundation of China (No.50538010) the Doctoral Education of the State Education Ministry of China (No.20040335083) Encouragement Fund for Young Teachers in University of Ministry of Education.
文摘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 racliation. 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.
基金Project supported by the Shanghai Nanoscience Foundation,China (Grant Nos.0852nm07000 and 0952nm07000)the National Natural Science Foundation of China (Grant Nos.10804084 and 91123022)+1 种基金the National Key Technology R&D Program,China (Grant No.2006BAF06B08)the Specialized Research Fund for the Doctoral Program of Ministry of High Education of China (Grant No.200802471008)
文摘The use of the dipole force on atoms is a new technology that is used to build nanostructures. In this way, a high quality standard nano-grating can be obtained. Based on the semi-classical model, the motion equation is investigated and the trajectories of atoms in double half Gaussian standing wave field are simulated. Compared with the Gaussian standing wave field, the double half Gaussian standing wave can well focus the Cr atoms. In order to obtain this kind of beam, a prism is designed and the experimental result shows that the beam is well generated.
文摘The buried pipelines are widely used in oil transportation. The pipelines become suspended in the river with flushing of floodwater. If the frequency of vortex shedding is near to the nature frequency of pipelines, it will cause resonance of the suspended pipeline and result in the damage of pipelines. In this paper, the buried parts of pipeline in soil are treated as the half unlimited long beam placed on the elastic foundations. The vibration partial differential equations of suspended pipe and the parts buried in soil are derived respectively. The iterative calculation method is then presented. The results obtained from the suggested method are proved to be identical with the measured values.
