A problem of reconstruction of multiple cracks in a beam by means of the natural frequencies corresponding to transverse vibration of the beam is considered. The cracks are simulated by massless rotational springs. It is proved that the cracks can be uniquely identified by three spectra corresponding to three different types of the end conditions. The problem is solved by reducing it to the inverse spectral problem for an ordinary differential equation of fourth order. A method for identifying damage caused by cracks has been developed. The method is based on minimization of the objective function, built with the knowledge of the three spectra. Numerical examples are considered.

考虑了通过与梁的横向振动相对应的固有频率来重构梁中的多个裂纹的问题。裂纹由无质量的旋转弹簧模拟。证明了可以通过对应于三种不同类型的最终条件的三个光谱来唯一地识别裂纹。通过将其简化为四阶常微分方程的逆谱问题来解决该问题。已经开发出一种用于识别由裂纹引起的损坏的方法。该方法基于目标函数的最小化，并利用三个光谱的知识进行构建。考虑了数值示例。