A Continuous Cracked Beam Vibration Theory

Chondros, Thomas G.; Dimarogonas, Andrew D.; Yao, Ji

doi:10.1006/jsvi.1998.1640

Cited by 444 publications

(246 citation statements)

References 0 publications

Supporting

Mentioning

223

Contrasting

Unclassified

Order By: Relevance

“…Figure 6 shows the first natural frequency ratio ( c ω ω ) versus the crack depth ratio α for a simply supported beam with a surface crack at mid-span. Compared with the predictions obtained using the damage finite element by Potirniche et al [1], the first natural frequency reduction predicted by the proposed improved two-dimensional finite element matches very well with the experiments results by Chondros et al [7]. , is considered.…”

Section: Simply Supported Beam With a Surface Cracksupporting

confidence: 76%

See 1 more Smart Citation

Detection of crack location and size in structures using improved damaged finite element

Kalanad¹,

Rao²

2010

IOP Conf. Ser.: Mater. Sci. Eng.

View full text Add to dashboard Cite

Abstract. In this paper two-dimensional finite element with an embedded edge crack proposed by Potirniche et al [1] is improved further for crack depth ratios ranging up to 0.9 h ( h is the element depth) and for predicting natural frequency of a cracked beam more accurately. The element is implemented in the commercial finite element code ABAQUS as user element (UEL) subroutine. The accuracy of the UEL is verified by comparing the first natural frequency for the bending mode for several beam cases with different damage locations with available experimental data. Subsequently a methodology to detect crack location and size in conjunction the proposed improved cracked element with is presented for singularity problems like a cracked beam. The frequency response functions, function of crack location and size, are approximated by means of surface-fitting techniques. Measured natural frequencies are used in a crack detection process and the crack location and size can be identified by finding the point of intersection of three frequency contour lines. The experimental data from beams studied by other researchers is employed to verify the accuracy of the proposed methodology in the diagnosis of structural crack faults.

show abstract

Section: Simply Supported Beam With a Surface Cracksupporting

confidence: 76%

“…An aluminium beam [7] , is considered. In the numerical study the crack depth ratio α ( a H ) is varied from 0 to 0.5.…”

Section: Simply Supported Beam With a Surface Crackmentioning

confidence: 99%

Detection of crack location and size in structures using improved damaged finite element

Kalanad¹,

Rao²

2010

IOP Conf. Ser.: Mater. Sci. Eng.

View full text Add to dashboard Cite

show abstract

“…In both cases, a crack function representing the perturbation in the stress field induced by the crack is considered. Chondros et al [18] have developed a continuous cracked beam vibration theory. They considered that crack introduces a continuous change in the flexibility in its neighborhood and models it by incorporating a displacement field consistent with the singularity.…”

Section: Introductionmentioning

confidence: 99%

Natural frequencies for bending vibrations of Timoshenko cracked beams

Loya

Rubio

Fernández-Sáez

2006

Journal of Sound and Vibration

173

View full text Add to dashboard Cite

The natural frequencies for bending vibrations of Timoshenko cracked beams with simple boundary conditions have been obtained. The beam is modelled as two segments connected by two massless springs (one extensional and another one rotational). This model promotes discontinuities in both vertical displacement and rotation due to bending, which are proportional to shear force and bending moment transmitted by the cracked section, respectively. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section. The problem is also solved by the perturbation method and both procedures are applied to the case of a simply supported cracked beam. The results show that the perturbation method provides simple expressions for the natural frequencies of cracked beams and it gives good results for shallow cracks. E mail address: ppfer@ing.uc3m.es (J. Ferna´ndez Sa´ez).

show abstract

“…In 1978 Adams et al [2] investigated the case of damage that was modelled by an axial spring (axial damage model), but there is absent a calculating stiffness of the spring. Then transverse (rotational) model of damage has been developed and validated by a general theory of damaged beams [3] that makes it be possible to determine the stiffness of the equivalent spring as a function of damage depth. Using the transverse model of damage Rizos et al [4] have constructed the frequency equation for cantilever beam.…”

Section: Introductionmentioning

confidence: 99%

“…G . Chondros and A. D. Dimarogonas et al [3], we have If a parameter f3 = EI/KL is introduced for description of relative flexibility of the spring and called here damage magnitude, then (3=0 (K=oo) will correspond to the undamaged case and f3max =138.5 (h/ L), when a= h -to the completely damaged one. Furthermore, at the damage sit it's must be hold the condition…”

mentioning

confidence: 99%

Damage detection of beam by natural frequencies: General theory and procedure

Khiem¹

2006

Vietnam J. Mech.

View full text Add to dashboard Cite

Abstract. The frequency equation of single damaged beam has been established for arbitrary boundary conditions that is the main tool for analysis as well as identification of damaged beam by using measured natural frequencies. A procedure for damage detection problem presented in this paper consists of three steps. First, the modelling error is reduced by a model updating procedure, in which the material, geometrical parameters and boundary conditions are updated. Then , measurement data are corrected based on t he updated model. Finally, the damage parameters are identified using updated model and corrected measurement data. Theoretical investigation is illustrated by an example.

show abstract

A Continuous Cracked Beam Vibration Theory

Cited by 444 publications

References 0 publications

Detection of crack location and size in structures using improved damaged finite element

Detection of crack location and size in structures using improved damaged finite element

Natural frequencies for bending vibrations of Timoshenko cracked beams

Damage detection of beam by natural frequencies: General theory and procedure

Contact Info

Product

Resources

About