Crack identification in beams by coupled response measurements

Free vibrations of cracked prestressed concrete beams

“…(2). While the first variation of the external energy, read (5) and (6). Hence, after integration by parts and after some algebraic manipulations, the static incremental equations take the following form:…”

“…The governing incremental equations of motion and the associated boundary and continuity conditions are derived using Eqs. (1) to (4), along with the use of the kinematic relations (5) and (6). Hence, after some algebraic manipulations and integration by parts, the incremental equations of motion read: …”

“…They have determined the influence of the load cycling on the stress transfer, the stiffness and the crack width by analytical and experimental studies that compare well. Other authors (Chondros et al [5]; Gounaris et al [6]; Murphy & Zhang [7]) have mainly focused on the effect of fatigue cracks on the vibrations of metal beams, adopting this approach. The second approach uses bilinear behavior of the cracked beam, where the beam behaves as an uncracked beam when it is displaced upwards and as a cracked beam when it is displaced downwards.…”

Nonlinear dynamic response of an edge-cracked functionally graded Timoshenko beam under parametric excitation

“…The dynamic behavior of cracked structures has been a topic of active research over the last few decades. A large number of studies on the free and forced vibration of cracked structures, using analytical or numerical methods or both, are available in open literature [1][2][3][4][5][6][7][8]. For Timoshenko beams in which the effect of transverse shear deformation is nonnegligible, Kisa et al [9] analyzed the free vibration of cracked Timoshenko beam using a combination of finite element and mode synthesis method.…”

On the use of non-linear vibrations and the anti-resonances of Higher-Order Frequency Response Functions for crack detection in pipeline beam

“…In recent years a lot of effort has been devoted to the detection of cracks in mechanical structures and many researchers have proposed various developments of non-destructive techniques based on changes in the structural vibrations [1][2][3][4]. Basic methods based on linear condition monitoring techniques have been extensively developed by considering not only changes in natural frequencies and modes shapes [5], but also the appearances of resonant peaks due to vibration coupling [6,7], different changes in the measurements of the Frequency Responses Functions and the motion of anti-resonances [8][9][10].…”