Free vibration analysis of uniform and stepped cracked beams with circular cross sections

Kısa, Murat; Gürel, M. Arif

doi:10.1016/j.ijengsci.2007.03.014

Cited by 65 publications

(19 citation statements)

References 38 publications

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“…The results obtained with the section method are herein compared with the ones of an uncracked beam or the ones obtained by Kisa and Gurel. 55 As visible from all the curves, the modal shapes of an uncracked or cracked beam are very close, in agreement with the findings of Ricci and Viola 47 for pure bending moments. An excellent agreement is also found between the two different methods here compared for the cracked beam.…”

Section: Differential Equations Of Motion For a Cracked Systemsupporting

confidence: 85%

“…Figure shows the first three dimensionless natural bending modes as a function of the beam length for a crack depth ratio L 1/ L = 0.4 and a crack position a / D = 0.4. The results obtained with the section method are herein compared with the ones of an uncracked beam or the ones obtained by Kisa and Gurel . As visible from all the curves, the modal shapes of an uncracked or cracked beam are very close, in agreement with the findings of Ricci and Viola for pure bending moments.…”

Section: Stiffness Matrix and Application To Fracture Specimensmentioning

confidence: 99%

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Analytical and numerical investigation of the stiffness matrix for edge‐cracked circular shafts

Cao

Dimitri

et al. 2016

Fatigue Fract Eng Mat Struct

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This paper examines two engineering methods of evaluating the stress intensity factors for cracked beams and bars subjected to a combined loading and proposes innovative formulations, as far as the circular cross section is concerned. Based on the definition of the stress intensity factors, the compliance matrix is determined as the inverse of the stiffness matrix, modelling the cracked section of a beam through a line‐spring approximation with interactive forces computed within fracture mechanics. A comparative evaluation of numerical predictions based on the proposed methods is also performed with methods available from the literature. Results for free vibration analyses of beams with transverse non‐propagating open cracks are presented and compared in order to estimate the accuracy and efficiency of the proposed methods, where a good agreement is generally found. More specifically, two different coupling effects are herein analysed for circular beams subjected to a combined bending, axial and shear loading, first, and a combined bending, shear and torsion loading, subsequently.

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Section: Differential Equations Of Motion For a Cracked Systemsupporting

confidence: 85%

Section: Stiffness Matrix and Application To Fracture Specimensmentioning

confidence: 99%

Analytical and numerical investigation of the stiffness matrix for edge‐cracked circular shafts

Cao

Dimitri

et al. 2016

Fatigue Fract Eng Mat Struct

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“…This strategy is able to detect the presence of cracks, however, it is hard to anticipate the location parameters and depth of the crack particularly while numerous cracks exist [9]. All together for identifying the parameters of the crack precisely through this methodology, initially a cracked-beam component is created for the cracked beams with express portrayals of the crack parameters, including the seriousness of the crack and its relative area inside a component [10,11].…”

Section: Introductionmentioning

confidence: 99%

Optimal Method for Identification of Cracks in Different Beams using Fuzzy with Elephant Based Neural Network

Pitchaiah*,

Rao

2019

IJITEE

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Failure of Structures i.e., beams can be avoided by identifying the damage in the structure at its beginning and proper retrofitting. Recently, the researchers created a structure to recognize crack damage using a cracked beam component model that originates from the fracture mechanics and local flexibility rules. The present work exhibits the analysis of cracked beam with a machine learning model to assess the stiffness of the structure. Here Fuzzy Optimal Neural Network (FONN) is considered, in addition, the stiffness reduction technique, especially concerning thick beams, is featured with a survey of other crack models. The extricated model data are utilized to conversely recognize the cracks with the cracked beam component model through a model updating technique. The optimal Neural Network based stiffness computation utilizes a global searching procedure using Adaptive Elephant Herding Optimization (AEHO) to identify the number of cracks in various beams. From the proposed model, the attained results are compared with the existing research work, and other optimization and machine learning models.

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“…Recently, extensive numerical studies were performed to study the characteristic of the vibrating cracked beams from the measurements of changes in resonant frequencies. It covers numerical studies on: the changes of structural stiffness with respect to the position of defects (12) , mode shapes of the cracked rotating tapered beam , multiple-crack damage detection and their possible orientation (13)(14) and modal analysis of multi-cracked beams with a circular cross section (15) . Despite the fact that enormous research has been conducted in the area of damage detection by using changes in modal responses (16)(17)(18) , changes in the natural frequencies (16,19,20) and changes in mode shapes (21)(22)(23) , but still the prediction of the operating cycles before catastrophic failure has not yet studied.…”

Section: Introductionmentioning

confidence: 99%

Fracture life estimation of Al-1050 thin beams using empirical data and a numerical approach

Khan¹,

Khan²,

Khan³

et al. 2018

insight

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A technique based on empirical data and finite element (FE) analysis to predict the fracture life of Al-1050 beam with the help of its fundamental mode is presented in this study. Experiments were performed on a non-prismatic beam vibrating with a constant value of the amplitude at the fixed end until the complete fracture of the specimen was achieved. The beam was vibrating on its fundamental mode to achieve fracture in less time. A power law model was used to acquire the possible trends in between the values of natural frequencies and the number of cycles recorded during these experiments. These trends were further compared with a numerically modeled specimen but with artificial cracks. FE modal analysis was used for this comparison. An error of less than 1% was observed in the estimated number of total cycles obtained through power law model before fracture as compare to those obtained from the numerical approach. Using this approach, fracture life of different length specimens was also predicted.

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Free vibration analysis of uniform and stepped cracked beams with circular cross sections

Cited by 65 publications

References 38 publications

Analytical and numerical investigation of the stiffness matrix for edge‐cracked circular shafts

Analytical and numerical investigation of the stiffness matrix for edge‐cracked circular shafts

Optimal Method for Identification of Cracks in Different Beams using Fuzzy with Elephant Based Neural Network

Fracture life estimation of Al-1050 thin beams using empirical data and a numerical approach

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