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**Simplified stress correction factor to study the dynamic behavior of a cracked beam.**
*(English)*
Zbl 1167.74572

Summary: A simplified formula for the stress correction factor in terms of the crack depth to the beam height ratio, \(f(a/h)\), is presented. The modified formula is compared to a well-known similar factor in the literature, and shows a good agreement for \(a/h\) lower than 0.5. The modified formula is used to examine the lateral vibration of an Euler-Bernoulli beam with a single-edge open crack. This is done through introducing the flexibility scalar. This scalar can be generated from the Irwins’s relationship using the modified factor \(f(a/h)\). The crack in this case is represented as rotational spring. With the modified model, beam configurations with classical and non-classical support conditions could be studied.The mode shapes for the cracked and the uncracked beam are obtained using this model. They are displayed graphically for selected values of the system parameters; the crack depth ratio \(a/h\), and the crack location ratio \(s/L\). The shift in the mode shape due to the existence of a crack is highlighted. The obtained results showed good agreement with similar published studies.

### MSC:

74R99 | Fracture and damage |

74H45 | Vibrations in dynamical problems in solid mechanics |

74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |

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\textit{A. S. Y. Alsabbagh} et al., Appl. Math. Modelling 33, No. 1, 127--139 (2009; Zbl 1167.74572)

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