When cracks start to surface in the surrounding areas of the structure, they create a local softness zone and influences on the dynamic response of the structure. The beams are more susceptible to shear and flexural cracks because of being subjected to shear and bending stress. In this study, the dynamic response of the single-span and multi-span damped beam under moving load with multi-crack and elastic boundary condition is studied based on Timoshenko’s theory. The Green’s function method is used to calculate the dynamic response of the cracked beam. In addition, the Green’s function method provides a solution for the differential equations. Moreover, the effects of the crack on the essential characteristics of the multi-span beams, especially the natural frequencies, are investigated. In this study, crack by itself is modeled in different situations and its effect on the behavior of the beam is analyzed. Also, the elastically restrained beam is modeled and its effect on the behavior of the beam is assessed. Because of the fact that the Euler–Bernoulli theory is also used in most beams, in this study, the results of the numerical examples are compared with the Euler–Bernoulli theory. Several examples are analyzed for a better understanding of the Timoshenko cracked beam.

当裂缝开始在结构的周围区域中浮出水面时，它们会形成局部柔软区域并影响结构的动力响应。由于梁承受剪切应力和弯曲应力，因此更容易产生剪切裂纹和弯曲裂纹。在这项研究中，基于蒂莫申科的理论，研究了具有多裂纹和弹性边界条件的移动荷载下单跨和多跨阻尼梁的动力响应。格林函数法用于计算裂纹梁的动力响应。此外，格林函数方法为微分方程提供了解决方案。此外，研究了裂纹对多跨梁的基本特性，尤其是固有频率的影响。在这个研究中，在不同情况下对裂纹本身进行建模，并分析其对梁行为的影响。同样，对受弹性约束的梁进行建模，并评估其对梁性能的影响。由于大多数光束也使用了Euler–Bernoulli理论，因此在本研究中，将数值示例的结果与Euler–Bernoulli理论进行了比较。分析了几个示例，以更好地理解Timoshenko裂纹梁。