Investigating the modal behaviors of a deep beam with a transverse open crack

• Published in: Journal of sound and vibration 2024-11, Vol.590, p.118613, Article 118613
• Main Authors: Lim, Taejeong, Park, Hyun Woo
• Format: Article
• Language: English
• Subjects: Axial-bending-shear modal coupling; Deep beam; Modal analysis; Mode I crack; Mode II crack; Transverse open crack
• ISSN: 0022-460X
• DOI: 10.1016/j.jsv.2024.118613

•The developed method accurately predicts modal frequency reduction in cracked deep beams (L/h < 5), unlike existing ones.•Axial-bending-shear modal coupling (ABSMC) is found to be a unique phenomenon in cracked deep beams.•Three compatibility equations considering modes I and II crack simultaneously are employed to address the ABSMC.•Experimental verification of the ABSMC of cracked deep beams by using piezoelectric wafers mounted on the beams.•Modes I and II crack are mutually exclusive in a free-free beam with a center crack depending on the vibration mode. This paper investigates the modal behaviors of a deep beam with a transverse open crack. Unlike cracked shallow beams with aspect ratio (L/h) > 10, cracked deep beams with aspect ratio < 5 simultaneously exhibit near the crack both axial-bending coupling mode caused by mode I crack and shear (or sliding) mode caused by mode II crack, referred to as axial-bending-shear modal coupling. Therefore, for accurate modal behaviors prediction, appropriate compatibility equations accounting for both modes I and II crack should be employed for deriving a frequency equation. Because the derived frequency equation is nonlinear with respect to modal frequency, the modal frequencies are calculated through the Newton–Raphson method. The corresponding mode shapes are determined by substituting the calculated modal frequencies into the spectral solutions for either side of the crack. The validity of the proposed method was demonstrated through comparison to the finite element analysis and experimental results. [Display omitted]