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
针对风电机组出力的间歇性和波动性,提出了基于等效电量频率法(equiva1ent energy and frequency function method,EEFF)的电力系统随机生产模拟方法。将等效电量函数法(equiva1ent energy function method,EEF)与频率持续法(frequency ...针对风电机组出力的间歇性和波动性,提出了基于等效电量频率法(equiva1ent energy and frequency function method,EEFF)的电力系统随机生产模拟方法。将等效电量函数法(equiva1ent energy function method,EEF)与频率持续法(frequency and duration,FD)相结合,用来评估风电场接入对电力系统生产运行的影响。该方法在生产模拟中保留了负荷和风电机组的时变特性,除了可以得到常规算法所能得到的生产模拟结果外,还可以评估风电场对常规机组造成的开停机影响,以及与火电机组开机、暖机等因素相关的动态费用。EPRI36机组随机生产模拟结果验证了所提方法的正确性和有效性。展开更多
等效电量函数法是电力系统随机生产模拟的实用高效方法,但在计算失负荷概率(Loss Of Load Probability,LOLP)指标时可能存在精度不高的问题。利用实际电力系统中持续负荷曲线的台阶状特征,引入基准单位将拐点横坐标整数化,提出了用于电...等效电量函数法是电力系统随机生产模拟的实用高效方法,但在计算失负荷概率(Loss Of Load Probability,LOLP)指标时可能存在精度不高的问题。利用实际电力系统中持续负荷曲线的台阶状特征,引入基准单位将拐点横坐标整数化,提出了用于电力系统随机生产模拟的稀疏卷积递推法。该方法采用变宽度矩形描述持续负荷曲线,充分利用了拐点横坐标在整数空间中分布的稀疏性,计算时间对基准单位的取值不敏感,比较适用于系统规模较大、对LOLP指标计算精度要求较高的场合。最后通过对IEEE-RTS79系统及其修正和扩大系统的仿真测试验证了所提方法的准确性及效率。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.
文摘针对风电机组出力的间歇性和波动性,提出了基于等效电量频率法(equiva1ent energy and frequency function method,EEFF)的电力系统随机生产模拟方法。将等效电量函数法(equiva1ent energy function method,EEF)与频率持续法(frequency and duration,FD)相结合,用来评估风电场接入对电力系统生产运行的影响。该方法在生产模拟中保留了负荷和风电机组的时变特性,除了可以得到常规算法所能得到的生产模拟结果外,还可以评估风电场对常规机组造成的开停机影响,以及与火电机组开机、暖机等因素相关的动态费用。EPRI36机组随机生产模拟结果验证了所提方法的正确性和有效性。
文摘等效电量函数法是电力系统随机生产模拟的实用高效方法,但在计算失负荷概率(Loss Of Load Probability,LOLP)指标时可能存在精度不高的问题。利用实际电力系统中持续负荷曲线的台阶状特征,引入基准单位将拐点横坐标整数化,提出了用于电力系统随机生产模拟的稀疏卷积递推法。该方法采用变宽度矩形描述持续负荷曲线,充分利用了拐点横坐标在整数空间中分布的稀疏性,计算时间对基准单位的取值不敏感,比较适用于系统规模较大、对LOLP指标计算精度要求较高的场合。最后通过对IEEE-RTS79系统及其修正和扩大系统的仿真测试验证了所提方法的准确性及效率。
