An Analytical Investigation on Nonlinear Free Vibrations of Beam with a Fatigue-Crack
DOI:
https://doi.org/10.14311/CEJ.2025.01.0002Keywords:
Nonlinear Vibration, Fatigue-Crack, Bilinear stiffness, natural frequency, Analytical methodAbstract
This study examines the nonlinear free vibration behavior of beams affected by a fatigue crack. Initially, transverse vibrations of a cantilevered beam are demonstrated as a single-degree-of-freedom system with equivalent mass and stiffness in the first mode. Subsequently, a novel bilinear stiffness model for beams with breathing cracks is introduced. Utilizing this model, the governing differential equation is formulated analytically using the Lindest-Poincaré perturbation method. The results indicate that the response derived through the perturbation method comprises 2 distinct components. With stiffness equal to the mean of the crack's completely open and fully closed states, the first component depicts the system's reaction. The additional correction terms, supplementing the initial response, account for variations in stiffness resulting from crack opening and closing dynamics. These corrections elucidate the impact of changing equivalent stiffness on the system's response due to crack dynamics. Indeed, the correction terms encompass higher harmonic components that emerge in the response, stemming from the nonlinear behavior of the structure. These additional terms capture the intricate interplay between crack dynamics and system response, providing a comprehensive understanding of the system's nonlinear characteristics.
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