Purpose

This work aims to investigate a cracked cantilever beam subjected to a moving point force using the Discrete Element Method (DEM).

Contribution and Method

A novel approach to mathematically include a moving force in discrete element formulation of a cracked beam is the main contribution of this paper. The local reduction in the stiffness of the cantilever beam due to the presence of a crack has been accounted for by a popularly used result from fracture mechanics. Hence, the present work provides an alternative approach to numerically evaluate the forced vibration of cracked beams under the application of a moving point force.

Conclusion

The methodology has been verified by comparing some of the results obtained here to those obtained using an already published analytical method. In the end, the effects of crack length, crack location, and force-velocity on the dynamic behavior of the cracked beam are studied using the proposed methodology. The proposed method can provide an effective alternative for the analysis of cracked beams subjected to a moving point force.

中文翻译：

---

离散元法研究裂隙悬臂梁受移动点力的动力学

目的

这项工作旨在利用离散元方法（DEM）研究受到移动点力作用的破裂悬臂梁。

贡献与方法

本文的主要贡献是一种新的数学方法，该方法将移动力包含在裂纹梁的离散元素公式中。由于裂缝的存在，悬臂梁刚度的局部降低是由于裂纹的存在所造成的。因此，本工作提供了一种替代方法，以在移动点力的作用下数值评估裂纹梁的强迫振动。

结论

通过将此处获得的某些结果与使用已发布的分析方法获得的结果进行比较，已验证了该方法。最后，利用所提出的方法研究了裂纹长度，裂纹位置和力速度对裂纹梁动力特性的影响。所提出的方法可以为分析受移动点力作用的裂纹梁提供有效的替代方法。