移动质量与梁耦合系统固有频率的计算与分析

建立了在移动质量减速运动情况下，通过获取梁的挠度响应曲线，数值仿真实验获得耦合系统的基频；在移动质量匀速运动情况下，通过获取梁的跨中挠度响应曲线，数值仿真实验获得梁的基频；以及用来计算耦合系统各阶固有频率的特征值方法的理论。数值算例结果表明，这类耦合系统的各阶固有频率不仅与质量比有关，而且与位置比也有关，若用梁的固有频率取代耦合系统的固有频率或用实验值代替理论值有时会产生较大的误差．

Calculation and analysis on natural frequency of a moving mass and beam's coupled system

The formula to calculate the natural frequencies of a moving mass and beam coupled system was established. First, in the case of a moving mass made decelerated motion, the fundamental frequency of the coupled system can be gained by getting the deflection response curve of beam through the numerical simulation experimental method. Second, in the case of the moving mass made uniform motion, the fundamental frequency of the beam can be gained by getting the mid span deflection response curve of the beam through the numerical simulation experimental method. Third, the eigenvalue computation method can be used to get the various steps natural frequencies of the coupled system. The results of numerical examples show that the natural frequencies of the coupled system, not only have relation to the mass ratio, but also to the location ratio. Sometimes there will be bigger error if the natural frequencies of beam are used instead of the natural frequencies in coupled system or the theoretical values are substituted by the experimental values.