Identification of Damage in a Beam Structure by Using Mode Shape Curvature Squares

Abstract

During the last decades a great variety of methods have been proposed for damage detection by using the dynamic structure characteristics, however, most of them require modal data of the structure for the healthy state as a reference. In this paper the applicability of the mode shape curvature squares determined from only the damaged state of the structure for damage detection in a beam structure is studied. To establish the method, two aluminium beams containing different-size mill-cut damage at different locations are tested by using the experimentally measured modal data. The experimental modal frequencies and the corresponding mode shapes are obtained by using a scanning laser vibrometer with a PZT actuator. From the mode shapes, mode shape curvatures are obtained by using a central difference approximation. With the example of the beams with free-free and clamped boundary conditions, it is shown that the mode shape curvature squares can be used to detect damage in the structures. Further, the extent of a mill-cut damage is identified via modal frequencies by using a mixed numerical-experimental technique. The method is based on the minimization of the discrepancy between the numerically calculated and experimentally measured frequencies.

RETRACTED: Multiple damage detections in plate-like structures using curvature mode shapes and gapped smoothing method

“…The sum of squares of mode shape curvature was taken to minimize the noise from the modal data of the damaged part. 10 In this proposed work, we have focused on curvature mode shapes (CMSs), because in case of CMS, the changes in the rotation of mode shapes 11 are found to be more sensitive to identify the local changes in the irregular structure. CMS can also be directly or indirectly used to detect single or multiple damages.…”

Tikhonov's regularization approach in mode shape curvature analysis applied to damage detection

“…Some detailed literature reviews which describe the state of the art in the methods for damage detection, localization, and characterization, by examining changes in the dynamic response of a structure can be found in [1,2]. Many published results [3][4][5][6] confirm that mode shapes and corresponding mode shape curvatures are highly damage sensitive and can be used for its detection and evaluation. In these works the modulus of the difference in the mode shape data, between the healthy and the damaged state of a structure, is defined as a damage index, and its maximum value typically indicates the location of a certain defect.…”

“…Previous investigations of the present authors show that damage location and size can be assessed by employing exclusively the mode shape curvature data from the damaged structures. Damage index based on mode shape curvatures has successfully been applied to identify the location and the size of a mill-cut defect in a beam structure [5]. In [6] the efficiency and the robustness of the proposed method has been demonstrated on composite beams subjected to low-velocity impacts.…”

“…(4) ] So long as second derivatives (∂ 2 w n /∂x 2 ) ij and (∂ 2 w n /∂y 2 ) ij are calculated, one can calculate the damage index, Eq. (2), which is presented in figures (5). The color image of the detections presented below is not a result of any specific contouring algorithm (like in some inverseproblem identification algorithms) but is simply a discretely calibrated coloration of function DI i,j in Eq.…”

A multi-reference-based mode selection approach for the implementation of NExT-ERA in modal-based damage detection

“…Significant developments in sensor technologies to collect measurements and in algorithms to process the vast amount of data so collected make vibration‐based global damage detection significantly more convenient and cost effective than previously exercised visual inspection and local experimental techniques. Vibration‐based damage detection methods can be classified as modal‐based and signal‐based methods. In modal‐based damage detection methods, damage is indicated by changes in measured modal parameters or their derivatives or changes in physical properties determined by utilizing the identified modal parameters, whereas signal‐based damage detection methods involve statistical analysis of damage‐sensitive features extracted from the measured dynamic responses of the structure by employing parametric or non‐parametric time series algorithms.…”