Natural Frequencies of a Beam With an Arbitrary Number of Cracks

Shifrin, E. I.; Ruotolo, Romualdo

doi:10.1006/jsvi.1998.2083

Cited by 216 publications

(122 citation statements)

References 9 publications

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“…Number of unknown parameters is generally decreased by removing some of them which can have negligibly small effects. Theories of most studies are based upon the analytical method including local flexibility model which uses the conditions of compatibility and continuity at crack locations (Bakhtiari-Nejad et al 2014;Caddemi and Calio 2009;Dado 1997;Khiem and Lien 2001;Nandwana and Maiti 1997;Ostachowicz and Krawczuk 1991;Shifrin and Ruotolo 1999). Local flexibility model neglects the distributed energy effects of crack and accumulates the effects of dynamical changes into rotational springs considered at the crack locations.…”

Section: Latin American Journal Of Solids and Structures 12 (2015) 24mentioning

confidence: 99%

“…With this method, to construct linear system is not a simple task for the beams with n cracks. Shifrin and Ruotolo (1999) extend this base approach by defining 2 + n equations for simplifying the vibration analysis of the beams with n cracks. However, their method can have the lack of exactness due to the some simplifications and linearization done for decreasing the matrix size.…”

Section: Latin American Journal Of Solids and Structures 12 (2015) 24mentioning

confidence: 99%

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A Novel Methodology Using Simplified Approaches for Identification of Cracks in Beams

Mazanoglu

2015

Lat. Am. j. solids struct.

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In this paper, natural frequency based forward and inverse methods are proposed for identifying multiple cracks in beams. Forward methods include simplified definition of the natural frequency drops caused by the cracks. The ratios between natural frequencies obtained from multi-cracked and un-cracked beams are determined by an approach that uses the local flexibility model of cracks. This approach does not consider nonlinear crack effects that can be easily neglected when the number of cracks is not excessive. In addition, an expression, which removes the necessity of repeating natural frequency analyses, is given for identifying the connection between the crack depths and natural frequency drops. These simplified approaches play crucial role in solving inverse problem using constituted crack detection methodology. Solution needs a number of measured modal frequency knowledge two times more than the number of cracks to be detected. Efficiencies of the methods are verified using the natural frequency ratios obtained by the finite element package. The crack detection methodology is also validated using some experimental natural frequency ratios given in current literature. Results show that the locations and depths ratios of cracks are successfully predicted by using the methods presented.

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Section: Latin American Journal Of Solids and Structures 12 (2015) 24mentioning

confidence: 99%

Section: Latin American Journal Of Solids and Structures 12 (2015) 24mentioning

confidence: 99%

A Novel Methodology Using Simplified Approaches for Identification of Cracks in Beams

Mazanoglu

2015

Lat. Am. j. solids struct.

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“…Using these notations for the vector of the nodal displacements and vector of the nodal forces given from above, in connection with the expression (13) we obtain the relation between the end forces and the nodal displacements:…”

Section: The Dynamic Stiffness Matrix Of a Multiple Cracked Beammentioning

confidence: 99%

Determination of the Shape Function of a Multiple Cracked Beam Element and Its Application for the Free Vibration Analysis of a Multiple Cracked Frame Structure

Lien¹,

Hao²

2014

AJCEA

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Assessment of the behavior of damaged structures as well as determination of the locations and the depths of cracks in multiple cracked structures are very important and attractive for many researchers. This article presents some results on the determination of the vibration shape function of a multiple cracked elastic beam element, which is modeled as an assembly of intact sub-segments connected by massless rotational springs. Algorithms and computer programs to analyse changes of natural mode shapes of multiple cracked beams have been determined. Numerical analysis of natural mode shapes of cracked simple support beams using the obtained expression shows a good agreement in comparison with the well-known analytical methods. The methodology approach and results presented in this article are new and the basis for building an efficient method to identify cracks in frame structures using wavelet analysis of mode shapes.

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“…The reality of affecting a crack or local defect on structural member dynamic response is recognized since years ago [1][2][3][4][5]. Defects in a structure can cause changes in mass distribution and damping properties.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Analysis of a cracked beam subjected to a moving load with Piezoelectric patches

2015

2015 International Conference on Advances in Software, Control and Mechanical Engineering (ICSCME'2015) Sept. 7-8, 2015 Antalya

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Natural Frequencies of a Beam With an Arbitrary Number of Cracks

Cited by 216 publications

References 9 publications

A Novel Methodology Using Simplified Approaches for Identification of Cracks in Beams

A Novel Methodology Using Simplified Approaches for Identification of Cracks in Beams

Determination of the Shape Function of a Multiple Cracked Beam Element and Its Application for the Free Vibration Analysis of a Multiple Cracked Frame Structure

Finite Element Analysis of a cracked beam subjected to a moving load with Piezoelectric patches

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