DOI: 10.55581/ejeas.1967401 ISSN: 2651-3412

Natural-Frequency Uncertainty of Cracked Microbeams with Random Crack Flexibility

Serpil Yılmaz Kutluay, Duygu Atcı
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Uncertainty in crack flexibility can significantly affect the vibration characteristics of cracked microbeams, particularly in microscale structures. This study investigates the stochastic free vibration behavior of cracked microbeams with random crack flexibility within the framework of modified couple stress theory. The crack is modeled as a torsional spring; its position defines the crack location, while its rotational flexibility characterizes the crack severity. In the stochastic formulation, the crack location is kept deterministic, and the crack flexibility is modeled as a random variable. Natural frequencies are obtained for simply supported and clamped-clamped microbeams using a numerical procedure based on the characteristic equation. Deterministic frequency maps are first generated in the crack parameter plane to identify regions where the modal response is most sensitive to crack location and crack flexibility. Monte Carlo simulation is then used to propagate the uncertainty in crack flexibility, and the resulting samples of the first mode natural frequency are evaluated using the mean, standard deviation, coefficient of variation, and percentile intervals. The results show that the coefficient of variation increases as the crack location moves toward the midspan, and the simply supported microbeam exhibits larger uncertainty than the clamped-clamped microbeam. A sensitivity analysis of the uncertainty level further confirms that greater dispersion in crack flexibility leads to greater uncertainty in the natural frequency.

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