Perturbatıon Solution for a Cracked Euler-Bernoulli Beam
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol.26, no.6, pp.1233-1243, 2022 (TRDizin)
- Publication Type: Article / Article
- Volume: 26 Issue: 6
- Publication Date: 2022
- Doi Number: 10.16984/saufenbilder.1170458
- Journal Name: Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Journal Indexes: Academic Search Premier, Business Source Elite, Business Source Premier, TR DİZİN (ULAKBİM)
- Page Numbers: pp.1233-1243
- Istanbul University-Cerrahpasa Affiliated: Yes
Abstract
The natural frequencies and mode shapes of an Euler-Bernoulli beam with a rectangular cross- section, which has a surface crack, is investigated. The crack is modeled as a change (sudden or gradual) in the cross-section of the beam, and a modified perturbation approach is used assuming that the crack geometry is much smaller than the beam cross section. Computations of natural frequencies and mode shapes were carried out for various crack shapes and compared with a range of experiments and finite element analyses. It is concluded that the suggested modified perturbation approach gives reliable results with minimal effort for eigenfrequencies of cracked beams. Furthermore, as a new feature, the present perturbation method includes the shape of the crack in eigenfrequency computations and in principle, can work for any type of disturbance on the surface including a small bump for example.