Modified and Simplified Sectional Flexibility of a Cracked Beam

Abstract

This paper presents a new sectional flexibility factor to simulate the reduction of the stiffness of a single-edge open cracked beam. The structural model for crack of the beam is considered as a rotational spring which is related to the ratio of crack depth to the beam height,a/h. The mathematical model of this single-edge open crack beam is considered as an Euler-Bernoulli beam. The modified factor,f(a/h), derived in this paper is in good agreement with previous researchers' results for crack depth ratioa/hless than 0.5. The natural frequencies and corresponding mode shapes for lateral vibration with different types of single-edge open crack beams can then be evaluated by applying this modified factorf(a/h). Using the compatibility conditions on the crack and the analytical transfer matrix method, the numerical solutions for natural frequencies of the cracked beam are obtained. The natural frequencies and the mode shapes with crack at different locations are obtained and compared with the latest research literature. The numerical results of the proposed cracked beam model obtained by this method can be extended to construct frequency contour. The natural frequencies measured from field can be used in solving the inverse problem to identify cracks in structures.

Parametric Vibrations of Axially Moving Beams with Multiple Edge Cracks

“…See Wang and Lee for further information related with K I,w . 15 Additionally, for cantilever beam, opening mode SIFs resulting from axial force and bending moment could be seen from the study presented by Majkut. 20 SIFs in Eq.…”

“…If one browses the study done by Wang and Lee, it would be seen that the procedures we follow are the same. 15 In this study, axial force has been considered in addition to bending moment.…”

“…13 Yokoyama et al studied beams having edge cracks of different depths at different positions. 14 15 Fernández-Sáez et al studied fundamental frequencies of cracked Euler-Bernoulli beams. 16 The effect of mass attachment on the free vibrations of cracked beams carrying a point mass has been discussed by Mermertas et al 17 By using the nonlinear spring model, Mendelshon et al studied nonlinear free-vibration analysis of an Euler-Bernoulli beam with an edge crack.…”

A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips

“…The change in the strain energy caused by the horizontal crack is [19] 0 () a rr c U J a da   (29) By Castigliano's theorem [22,23,61,62], the additional rotation θ caused by the horizontal crack at the cross-section at X 2 can be obtained:…”

“…As one of accurate and comprehensive methods, a modeling and simulation method can predict the dynamic characteristics of a cracked structure and provide some guidance to early detection of crack failure. Many previous works focused on an edge crack [9,[12][13][14][15][16][17][18][19][20][21][22][23][24] and multiple edge cracks [3,10,[25][26][27][28][29][30] in cantilever or simply supported beams. Some researchers have studied delaminations in beam structures [16, 31 -46 ].…”