The paper addresses the frequency response of beams in presence of open cracks with interval parameters. On adopting the standard Euler–Bernoulli beam theory, every crack is modelled as a linearly-elastic rotational spring whose stiffness and position are treated as uncertain-but-bounded parameters. A two-step method is proposed to calculate the bounds of all response variables. First, the sensitivity functions of the response are calculated as every uncertain parameter varies within the respective interval. Next, the bounds of the response are computed by either a sensitivity-based method or a global optimization technique, the former if the response is monotonic with respect to all uncertain parameters and the latter if the response is non-monotonic with respect to even one parameter only. The method relies on analytical forms for all response variables and the associated sensitivity functions. The applications focus on the frequency response of multi-cracked beams equipped with tuned mass dampers, showing potential and accuracy of the method.

本文讨论了带有间隔参数的开放裂纹存在时梁的频率响应。在采用标准的Euler–Bernoulli梁理论时，每个裂纹都被建模为线性弹性旋转弹簧，其刚度和位置被视为不确定但有界的参数。提出了一种两步法来计算所有响应变量的边界。首先，在每个不确定参数在相应间隔内变化时，计算响应的灵敏度函数。接下来，通过基于灵敏度的方法或全局优化技术来计算响应的界限，如果响应相对于所有不确定参数都是单调的，则前者；如果响应相对于甚至一个都不是单调的，则前者仅参数。该方法依赖于所有响应变量和相关灵敏度函数的分析形式。这些应用专注于配备了调谐质量阻尼器的多裂纹梁的频率响应，显示了该方法的潜力和准确性。