The nonlinear vibration analysis of cracked structures could be a suitable indicator for diagnosing defects. When breathing cracks appear on the beam, its behavior can be modeled as a bilinear oscillator. In this paper, the nonlinear vibration behavior of a cantilever beam with multiple breathing cracks is investigated. For this purpose, the multi-cracked beam’s stiffness is calculated by introducing the effective length for the local stiffness reduction in the vicinity of cracks. Furthermore, owing to the importance of the damping variation in a cracked beam, its exact value is evaluated through theoretical expressions. A continuous polynomial function with the Weierstrass approximation is exploited to simulate the bilinear behavior of breathing cracks. By performing nonlinear analysis using the perturbation technique, the cracked beam’s dynamic behavior is studied. Moreover, the sensitivity of the response to the crack parameters in the primary resonance of the structure is analyzed. Finally, the sensitivity of the beam’s nonlinear response to the different number of breathing cracks and various crack depths is investigated. It is shown that the beam with a higher number of cracks or deeper ones has obvious softening behavior, and hence a more significant jumping can appear in the response.

裂纹结构的非线性振动分析可能是诊断缺陷的合适指标。当梁上出现呼吸裂纹时，其行为可以建模为双线性振荡器。本文研究了具有多个呼吸裂纹的悬臂梁的非线性振动行为。为此，通过引入裂纹附近局部刚度降低的有效长度来计算多裂纹梁的刚度。此外，由于裂纹梁中阻尼变化的重要性，其精确值通过理论表达式进行评估。利用具有 Weierstrass 近似的连续多项式函数来模拟呼吸裂缝的双线性行为。通过使用微扰技术进行非线性分析，研究了裂纹梁的动力行为。此外，分析了对结构主共振中裂纹参数响应的敏感性。最后，研究了梁的非线性响应对不同数量的呼吸裂纹和各种裂纹深度的敏感性。结果表明，裂纹数量较多或更深的梁具有明显的软化行为，因此响应中会出现更显着的跳跃。