Identification of a crack in a beam based on the finite element method of a B-spline wavelet on the interval

Xiang, Jiawei; Chen, X.F.; Li, B.; He, Yanfei; He, Zong-Syun

doi:10.1016/j.jsv.2006.02.019

Cited by 50 publications

(19 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The results for various crack locations and depths, given in Table 2, show a reasonable agreement between the two methods results and those achieved by [19] for all cases of the cracked beam, but the difference between natural frequencies increases for higher order modes. Figure 2 represents plots of the corresponding mode shapes, using the two methods.…”

Section: Direct Problemsupporting

confidence: 71%

“…The lowest three natural frequencies of transverse vibration are calculated by the two methods, and compared with what reported by [19] for the damaged beam with one crack. The results for various crack locations and depths, given in Table 2, show a reasonable agreement between the two methods results and those achieved by [19] for all cases of the cracked beam, but the difference between natural frequencies increases for higher order modes.…”

Section: Direct Problemmentioning

confidence: 99%

“…The inverse problem is solved by using the exact first three frequencies used in [19] as inputs from various cases. and actual (  , ) crack parameters using any two of these three frequencies.…”

Section: Inverse Problemmentioning

confidence: 99%

See 2 more Smart Citations

Comparative study of direct and inverse problems of cracked beams

Mahieddine

Lassoued

2018

MATEC Web Conf.

View full text Add to dashboard Cite

Abstract. In recent decades, the analysis and evaluation of the cracked structures were hot spots in several engineering fields and has been the subject of great interest with important and comprehensive surveys covering various methodologies and applications, in order to obtain reliable and effective methods to maintain the safety and performance of structures on a proactive basis. The presence of a crack, not only causes a local variation in the structural parameters (e.g., the stiffness of a beam) at its location, but it also has a global effect which affects the overall dynamic behavior of the structure (such as the natural frequencies). For this reason, the dynamic characterization of the cracked structures can be used to detect damage from non-destructive testing. The objective of this paper is to compare the accuracy and ability of two methods to correctly predict the results for both direct problem to find natural frequencies and inverse problem to find crack's locations and depths of a cracked simply supported beam. Several cases of crack depths and crack locations are investigated. The crack is supposed to remain open. The Euler-Bernoulli beam theory is employed to model the cracked beam and the crack is represented as a rotational spring with a sectional flexibility. In the first method, the transfer matrix method is used; the cracked beam is modeled as two uniform sub-segments connected by a rotational spring located at the cracked section. In the second method which is based on the Rayleigh's method, the mode shape of the cracked beam is constructed by adding a cubic polynomial function to that of the undamaged beam. By applying the compatibility conditions at crack's location and the corresponding boundary conditions, the general forms of characteristic equations for this cracked system are obtained. The two methods are then utilized to determine the locations and depths by using any two natural frequencies of a cracked simply supported beam obtained from measurements as inputs. The two approaches are compared with a number of numerical examples for simply supported beams including one crack. The theoretical results show that the accuracy of the Rayleigh's method to predict natural frequencies decreases for higher modes when crack depth increases. It is also found that for the inverse problem, the transfer matrix method show a good agreement with those obtained from previous works done in this field.

show abstract

Section: Direct Problemsupporting

confidence: 71%

Section: Direct Problemmentioning

confidence: 99%

See 1 more Smart Citation

Comparative study of direct and inverse problems of cracked beams

Mahieddine

Lassoued

2018

MATEC Web Conf.

View full text Add to dashboard Cite

show abstract

“…In addition, on a bounded interval, BSWI basis has the good characteristics of compact support, symmetry, smoothness, and explicit expression [41,42]. Moreover, B-spline wavelets have the best approximation properties among all the known wavelets of a given order L [43].…”

Section: Wavelet Basis Expansion-based Volterra Kernels Identificationmentioning

confidence: 99%

Wavelet basis expansion-based spatio-temporal Volterra kernels identification for nonlinear distributed parameter systems

et al. 2014

View full text Add to dashboard Cite

In practical industries, there are many systems belong to nonlinear distributed parameter systems (DPS); unfortunately, modeling of nonlinear DPS is a challenging task because of the infinite-dimensional and nonlinear properties. To model the nonlinear DPS, a spatio-temporal Volterra model is presented with a series of spatio-temporal kernels. It can be considered as a spatial extension of the traditional Volterra model. One question involved in modeling a spatiotemporal functional relationship between the input and output of nonlinear distributed parameter systems using spatio-temporal Volterra series is to identify the spatiotemporal Volterra kernel functions. In addition, in order to derive a low-order model, the Karhunen-Loève (KL) decomposition is used for the time/space separation. The basic routine of the approach is that, first, from the system outputs, KL decomposition is used for the time/space separation, where the spatio-temporal output is decomposed into a few dominant spatial basis functions with temporal coefficients. Second, according to temporal coefficients of outputs under multilevel excitations, the Volterra series outputs of different orders are estimated with the wavelet balance method. Third, the Volterra kernel functions of different orders are separately estimated through their

show abstract

“…And the development trends of structural damage detection are also put forward. Xiang et al (2006), studied the model-based forward and inverse problems in the diagnosis of structural crack location and size by using the Finite Element Method of a B-Spline Wavelet on the Interval (FEM BSWI). Zhu and Law (2005) presented a new method for crack identification of bridge beam structures under a moving load based on wavelet analysis.…”

Section: Introductionmentioning

confidence: 99%

Examining the function of wavelet packet transform (WPT) and continues wavelet transform (CWT) in recognizing the crack specification

Lotfollahi-Yaghin

Koohdaragh

2011

KSCE J Civ Eng

View full text Add to dashboard Cite

Modern and efficient methods focus on signal analysis and have drawn researchers' attention to it in recent years. These methods mainly include Continuous Wavelet and Wavelet Packet transforms. The main advantage of the application of these Wavelets is their ability to analyze the signal position in different times and places. The frequency decomposition of this transform in location with high frequencies is very poor. Wavelet packet transform is more advanced form of continuous wavelet and can make a perfect level by level resolution for each signal. However, very few studies have been done in this field. In the present study, first there was an attempt to do a modal analysis on the structure by the ANSYS finite elements software, then using MATLAB, the wavelet was investigated through a continuous wavelet analysis. Finally, the results were displayed in 2-D location-coefficient figures. In the second form, transient dynamic analysis was done on the structure and to find out the characteristics of the crack, wavelet packet energy rate index was suggested. The results revealed that suggested index in the second form is both practical and applicable.

show abstract

Identification of a crack in a beam based on the finite element method of a B-spline wavelet on the interval

Cited by 50 publications

References 11 publications

Comparative study of direct and inverse problems of cracked beams

Comparative study of direct and inverse problems of cracked beams

Wavelet basis expansion-based spatio-temporal Volterra kernels identification for nonlinear distributed parameter systems

Examining the function of wavelet packet transform (WPT) and continues wavelet transform (CWT) in recognizing the crack specification

Contact Info

Product

Resources

About