Dynamic response of a beam to a random train of moving forces moving with the same velocity is considered. Unlike a widely used Poisson process model, a more adequate Erlang renewal process is used as a process driving the train of forces. Normal-mode approach is used to convert the problem into that of a renewal driven train of general pulses. Consequently the modal responses are the filtered renewal processes and are expressed as integrals with respect to the response to a single pulse (passage of a force) and to the increments of the counting renewal process. The expressions for the mean values and cross-correlations of modal responses are obtained as single and double integrals, respectively. The results are presented in terms of the renewal density of the underlying Erlang counting process. Mean value and variance of the mid-span deflection of the beam are determined by numerical evaluation of the pertinent integrals. Numerical analysis is carried out for the Erlang processes with integer parameter $k=2$, $k=3$ and 4 and, for comparison, also for a Poisson process. Different traffic conditions such as the velocity and the mean arrival rate of vehicles are taken into account.

考虑了梁对以相同速度移动的随机移动力序列的动态响应。与广泛使用的泊松过程模型不同，使用更合适的 Erlang 更新过程作为驱动力列的过程。正常模式方法用于将问题转换为更新驱动的一般脉冲序列的问题。因此，模态响应是过滤后的更新过程，并表示为相对于对单个脉冲（力的传递）的响应和计数更新过程的增量的积分。模态响应的平均值和互相关的表达式分别作为单积分和双积分获得。结果以底层 Erlang 计数过程的更新密度表示。梁跨中挠度的平均值和方差由相关积分的数值计算确定。对带整数参数的Erlang进程进行数值分析$克=2$, $克=3$和 4 并且，为了比较，也是泊松过程。考虑了不同的交通条件，例如车辆的速度和平均到达率。