The main objective of this study is to present a novel method for damage detection in plate-type structures using twodimensional (2D) continuous wavelet transforms. For this purpose, the 2D Mexican wavelet is employed to remold the equation of motion for transverse vibration of a plate. The remolded vibration equation of a plate can serve as a multiscale damage detection scheme that characterizes damage using an indicator of multiscale pseudo-load. Effects of multiscale pseudo-load can pinpoint the location of the damage as well as revealing its configuration; moreover, the strong solid mechanics foundation of the method results in the identified damage with an explicit physical implication. The performance of the proposed technique is validated through an experimental program of using a scanning laser vibrometer (SLV) to measure the transverse deflection of an aluminum plate bearing a cross-like notch and an added small mass. The results confirm the robustness and superior capability of the proposed method in detecting damage in plate-type structures.
Vibration-based nondestructive damage detection relying on modal curvatures has been investigated in various
applications. An intrinsic deficiency of a modal curvature is its susceptibility to the noise inevitably present in a
measured mode shape. This adverse effect of noise is likely to mask actual features of damage, resulting in false results
of damage detection. To circumvent this deficiency, a Teager energy operator (TEO), aided by a wavelet transform, is
adopted for the treatment of mode shapes to produce a new algorithm for damage identification. After wavelet-transform-
based preprocessing to separate the effective components of modal curvatures from noise interference, a TEO
is employed as a singularity detector, acting on the separated effective components, to reveal and characterize the
features of damage. The capacity of the TEO is demonstrated analytically in cases of cracked beams. The applicability of
the algorithm is experimentally validated using a scanning laser vibrometer to acquire mode shapes of an aluminum
beam bearing a crack. The analytical and experimental results show that the TEO, aided by wavelet transforms, has
stronger sensitivity to slight damage and greater robustness to noise than modal-curvature- and wavelet-transform-based
damage detection methods.
Fractal as a novel mathematical tool has a great potential to deal with transit events in a complex waveform. In this
paper, fractal is introduced to detect irregularity of vibration mode shapes without using a baseline requirement.
Different from the popular Katz's waveform fractal dimension (KWD), a novel approximate waveform capacity
dimension (AWCD) specialized in irregularity detection in vibration mode shapes is introduced, from which an AWCD-based
modal abnormality algorithm (AWCD-MAA) is established. The fundamental characteristics of AWCD-MAA,
such as crack location identification and size quantification, are investigated using an analytical crack model of
cantilever beams. An experimental modal shape evaluation of a cracked composite cantilever beam using smart
piezoelectric sensors/actuators (i.e., Piezoelectric
lead-zirconate-titanate (PZT) and polyvinylidene fluoride (PVDF)) is
conducted to confirm the feasibility of the proposed algorithm. The proposed AWCD-MAA is capable of locating and
quantifying the crack in a beam-type structure without prior requirement of baseline reference data.
In this study, a newly-developed technique, so-called "integrated wavelet transform (IWT)", is applied to damage
detection of laminated composite beams. The novel IWT technique combines advantages of stationary wavelet
transform (SWT) and continuous wavelet transform (CWT) to improve the robustness of wavelet-based modal analysis
in damage detection. Two progressive wavelet analysis steps are considered, in which the SWT-based multi-resolution
analysis (MRA) is first employed to refine the retrieved mode shapes, followed by the CWT-based multiscale analysis
(MSA) to magnify the effect of slight abnormality. The SWT-MRA is utilized to eliminate random noise and regular
interferences, separate multiple component signal, and thus extract purer damage information; while the CWT-MSA is
employed to smoothen, differentiate or suppress polynomial of mode shapes to magnify the effect of abnormality. The
effectiveness of IWT in damage detection is illustrated using the vibration mode shape data acquired from the
experimental testing of a cantilever laminated composite beam with a through-width crack. As demonstrated in the
successful detection of a crack in composite beams, the progressive wavelet transform analysis using IWT provides a
robust and viable technique to identify minor damage in a relatively lower signal-to-noise ratio environment.