Approximate analytical method for damage detection in free–free beam by measurement of axial vibrations

Abstract

Nowadays, sophisticated structures and machinery parts are constructed by using metallic beams. Beams are widely used as structural element in civil, mechanical, naval, and aeronautical engineering. In structures and machinery, one undesirable phenomenon is crack initiation in which the impact cannot be seen overnight. Cracks develop gradually through time that lead finally to catastrophic failure. Therefore, crack should be monitored regularly with more care. This will lead to more effective preventive measure and ensure continuous operation of the structure and machine. Damage in structure alters its dynamic characteristics. The change is characterized by change in modal parameters, that is, modal frequencies. Thus, vibration technique can be suitably used as a nondestructive test for crack detection of component to be tested. Mostly modal frequencies are used for monitoring the crack because modal frequencies are properties of the whole structure component. In this paper, efforts are made to develop suitable methods that can serve as the basis to detection of crack location and crack size from measured axial vibration data. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure. The method is based on measurement of axial natural frequencies, which are global parameter and can be easily measured from any point on the structure and also indeed, the advantage in modeling complexity. In theoretical analysis, the relationship between the natural frequencies, crack location, and crack size has been developed. For identification of crack location and crack size, it was shown that data on the variation of the first two natural frequencies is sufficient. The experimental analysis is done to verify the practical applicability of the theoretical method developed.

Analysis and Damage Identification of a Moderately Thick Cracked Beam Using an Interdependent Locking-Free Element

“…It is easy to observe that in the thin beam limit, i.e. Ω → 0 (ζ → 1, ξ → 1, κ → 1), (20) reduces to the Euler-Bernoulli elementar stiffness matrix. This choice of finite element model based on the two-component form of the Timoshenko beam theory is powerful for the dynamic analysis, in fact, the mass matrix ensure a superconvergent method [6].…”

“…As suggested in many papers [19][20][21][22][23][24][25], this is relatively easy to do for various reasons: the simplicity of measuring natural frequencies, whereas mode shapes require a very large number of sensors and can be affected by measurement errors, and, under the assumption of linear behaviour, the opportunity to describe the diffused crack affecting a beam with only three parameters. These three parameters are the position, the extension and the coefficient of stiffness reduction (or magnitude), and very few frequencies are required to define their values.…”

Influence of multi-transverse crack on cantilever shaft

“…Saeed et al (2012) presented a crack diagnosis in the curvilinear beam using frequency functions and artificial neural network (ANN) and showed results with good agreement. Sayyad et al (2013) provided a proper procedure to verify the intensity of crack with its location regulating the data of axial vibration for different beam structure. The effectiveness of two first natural frequencies for determination of crack parameters is employed theoretically.…”

Vibration Analysis of a Cracked Beam Using Various Techniques - A Review

“…Saidiabdelkrim [11] has presented to analyse the vibration behaviour of concrete beams both experimentally and using FEM software ANSYS subjected to the crack under free vibration cases. FB Sayyad [12] has presented efforts are made to develop suitable methods that can serve as the basis to detection of crack location and crack size from measured axial vibration data. This method is used to address the inverse problem of assessing the crack location and crack size in various beam structure.…”