Journal ArticleDOI
Approximate calculation of the fundamental frequency for bending vibrations of cracked beams
TLDR
In this article, a simplified method of evaluating the fundamental frequency for the bending vibrations of cracked Euler-Bernouilli beams is presented based on the well-known approach of representing the crack in a beam through a hinge and an elastic spring, but here the transverse deflection of the cracked beam is constructed by adding polynomial functions to that of the uncracked beam.About:
This article is published in Journal of Sound and Vibration.The article was published on 1999-08-12. It has received 132 citations till now. The article focuses on the topics: Fundamental frequency & Beam (structure).read more
Citations
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Journal ArticleDOI
Simplified models for the location of cracks in beam structures using measured vibration data
TL;DR: In this paper, a new simplified approach to modeling cracks in beams undergoing transverse vibration is presented, which uses Euler-Bernoulli beam elements with small modifications to the local flexibility in the vicinity of cracks.
Journal ArticleDOI
Natural frequencies for bending vibrations of Timoshenko cracked beams
TL;DR: In this paper, the natural frequencies for bending vibrations of Timoshenko cracked beams with simple boundary conditions have been obtained, where the beam is modelled as two segments connected by two massless springs (one extensional and another one rotational).
Journal ArticleDOI
Free vibration analysis of a cracked beam by finite element method
D.Y. Zheng,Nicole F Kessissoglou +1 more
TL;DR: In this paper, the stiffness matrix obtained using the overall additional flexibility matrix can give more accurate natural frequencies than those resulted from using the local additional flexibility matrices, and the authors constructed a shape function that can perfectly satisfy the local flexibility conditions at the crack locations.
Journal ArticleDOI
Free transverse vibrations of cracked nanobeams using a nonlocal elasticity model
TL;DR: In this article, the cracked-beam model is established using a proper modification of the classical crackedbeam theory consisting of dividing the cracked element into two segments connected by a rotational spring located at the cracked section.
Journal ArticleDOI
A transfer matrix method for free vibration analysis and crack identification of stepped beams with multiple edge cracks and different boundary conditions
TL;DR: In this article, the Euler-Bernoulli beam is modeled as an assembly of uniform sub-segments connected by massless rotational springs representing local flexibility induced by the non-propagating edge cracks and a simple transfer matrix method is utilized to obtain the general form of characteristic equation for the cracked beam, which is a function of frequency, the locations and sizes of the cracks, boundary conditions, geometrical and physical parameters of the beam.
References
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Book
The stress analysis of cracks handbook
TL;DR: The Stress Analysis of Cracks Handbook as mentioned in this paper provides a comprehensive, easy-to-access collection of elastic stress solutions for crack configurations, along with other relevant information, such as displacements, crack opening areas, basic stress functions source references, accuracy of solutions, and more.
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A Vibration Technique for Non-Destructively Assessing the Integrity of Structures:
TL;DR: In this paper, a method of non-destructively evaluating the integrity of structures is described and applied to structures for which a one dimensional analysis is satisfactory, and it is shown how vibration measureme...
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One-dimensional theory of cracked Bernoulli-Euler beams
S. Christides,A.D.S. Barr +1 more
TL;DR: In this paper, the authors derived the differential equation and associated boundary conditions for a nominally uniform Bernoulli-Euler beam containing one or more pairs of symmetric cracks and achieved the reduction to one spatial dimension using integrations over the cross-section after plausible stress, strain, displacement and momentum fields are chosen.
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Identification of Crack Location in Vibrating Simply Supported Beams
TL;DR: In this paper, a cracked, simply supported uniform beam is treated for either bending or axial vibrations, and the crack is simulated by an equivalent spring connecting the two segments of the beam.
Journal ArticleDOI
Natural modes of Bernoulli-Euler beams with symmetric cracks
M.-H. H. Shen,Christophe Pierre +1 more
TL;DR: In this paper, an approximate Galerkin solution to the one-dimensional cracked beam theory developed by Christides and Barr for the free bending motion of beams with pairs of symmetric open cracks is suggested.