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Free vibration analysis of a double tapered beam with multiple cracks
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DOI：10.1080/15376494.2026.2690196.png)
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Abstract
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This study presents the free vibration analysis of a double-tapered Euler–Bernoulli beam containing two and three cracks, using finite element and component mode synthesis methods. The double-tapered beam varies linearly in both thickness and width. The crack in the beam is modeled as a massless spring, and the beam is divided into n + 1 sub-components for n crack sections. The stiffness of the spring is derived as the inverse of the compliance matrix, which is calculated from the expressions for stress intensity factors and strain energy release rate using linear elastic fracture mechanics theory. By combining the finite element method with component mode synthesis, natural frequency ratios for the first three bending modes have been calculated for a wide range of taper ratios (α = 0.5–0.9), crack depth ratios (a/b = 0.2–0.8), and various crack locations. The effects of the number of cracks, crack location, crack depth, and geometric tapering on natural frequencies have been obtained for cantilever-free and pinned–pinned boundary conditions.
Keywords:
Double tapered beam
multiple cracks
free vibration
finite element method
component mode synthesis
taper ratio
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