Zhenhua Tian

Lamb wave frequency–wavenumber analysis and decomposition:

Lamb waves have shown great potentials in damage detection of thin-walled structures due to their long propagation capability and sensitivity to a variety of damage types. However, their practical adoption has been hindered due to the complexity caused by their multimodal nature. Various wave modes that propagate at various velocities in the structure make the interpretation of Lamb wave signals very difficult. It is desired that the modes can be separated for independent analysis or further employment. In this article, we present our studies on the multimodal Lamb wave propagation and wave mode decomposition using frequency–wavenumber analysis. Wave representation in the frequency–wavenumber domain is obtained using multidimensional Fourier transform, where various Lamb wave modes can be easily discerned. This allows for separating them or extracting a desired wave mode through a filtering process, thus making it possible to use a single-mode Lamb wave for the detection of a certain type of damage in structural health monitoring applications. To retain the temporal and spatial information that is lost during Fourier transformation, a novel wavenumber analysis is also presented. These concepts are illustrated through experimental testing where high spatial resolution wavefields are measured by a scanning laser Doppler vibrometer.

Lamb wave Structural Health Monitoring Using a Hybrid PZT-Laser Vibrometer Approach:

Lamb waves are dispersive and multi-modal, which makes the interpretation of Lamb wave signals very difficult in either the time or frequency domain. In the this article, we present our studies on Lamb wave propagation characterization and crack detection using a hybrid lead zirconate titanate (PZT)-laser vibrometer system and frequency–wave number analysis. A scanning laser Doppler vibrometer is used to acquiring high-resolution time–space Lamb wavefield excited by a PZT actuator. The recorded wavefield is then transformed to frequency–wave number domain by two-dimensional Fourier transform. Wave spectrum in the frequency–wave number domain shows clear distinction among Lamb wave modes being present. These concepts are illustrated through several experimental tests. However, the space information is lost during this transformation. A short-space two-dimensional Fourier transform is then adopted to obtain the frequency–wave number spectra at various spatial locations, resulting in the space–frequency–wave number representation, which can show how the frequency–wave number component varies with respect to space dimension. It provides a means to study the wave propagation from the perspective of wave number domain. The space–frequency–wave number analysis has successfully been used for the study of wave interaction with structural discontinuity and crack detection on an aluminum plate.

Delamination detection and quantification on laminated composite structures with Lamb waves and wavenumber analysis

Laminated composites are susceptible to delamination due to their weak transverse tensile and interlaminar shear strengths as compared to their in-plane properties. Delamination damage can occur internally, where it is not visible to the naked eye. Development of reliable, quantitative techniques for detecting delamination damage in laminated composite components will be imperative for safe and functional optimally designed next-generation composite structures. In this article, we study the potential of using Lamb waves for delamination detection and quantification, using model-assisted data acquisition. Novel wavenumber analysis approaches are developed and discussed to show how they can be used to investigate Lamb wave interactions with delaminated plies. Ultrasonic wave simulations are implemented to provide both in-plane and out-of-plane wave motion for the wavenumber studies. The out-of-plane results are verified against data obtained from experimental tests. It is found that the wavenumber methods can not only determine the delaminated region of the plate and its length, but can also identify the plies between which the delamination occurs. We envision that the wavenumber approaches can lead to a complete delamination quantification in the future.

Study on crack scattering in aluminum plates with Lamb wave frequency?wavenumber analysis

The multimodal characteristic of Lamb waves makes the interpretation of Lamb wave signals difficult in either the time or frequency domain. In this work, we present our study of Lamb wave propagation characterization and crack scattering using frequency–wavenumber analysis. The aim is to investigate three dimensional (3D) Lamb wave behavior in the presence of crack damage via the application of frequency–wavenumber analysis. The analysis techniques are demonstrated using simulation examples of an aluminum plate with a through-thickness crack. Both in-plane and out-of-plane components are acquired through a 3D elastodynamic finite integration technique (EFIT), while the out-of-plane component is also experimentally obtained using a scanning laser Doppler vibrometer for verification purposes. The time–space wavefield is then transformed to the frequency–wavenumber domain by a two dimensional (2D) Fourier transform and the out-of-plane EFIT results are compared to experimental measurements. The experimental and simulated results are found to be in close agreement. The frequency–wavenumber representation of in-plane and out-of-plane components shows clear distinction among various Lamb wave modes that are present. However, spatial information is lost during this 2D transformation. A short space 2D Fourier transform is therefore adopted to obtain the frequency–wavenumber spectra at various spatial locations, resulting in a space–frequency–wavenumber representation of the signal. The space–frequency–wavenumber analysis has shown its potential for indicating crack presence.

Visualization of solitary waves via laser Doppler vibrometry for heavy impurity identification in a granular chain

We study the propagation of highly nonlinear solitary waves in a one-dimensional granular chain composed of homogeneous spherical particles that includes a heavy impurity. We experimentally investigate the transmission and backscattering behavior of solitary waves in the region of the impurity by using a laser Doppler vibrometer. To assess the sensitivity of solitary waves to various impurity masses, this non-contact measurement technique is complemented by a conventional contact measurement method based on an instrumented sensor particle. By leveraging these two schemes, we find that the travelling time and attenuation of backscattered solitary waves are highly sensitive to the location and mass of an inserted impurity. The experimental results are found to be in satisfactory agreement with the numerical results obtained from a discrete element model and the theoretical predictions based on nonlinear wave dynamics and classical contact theory. This study demonstrates that laser Doppler vibrometry can be an efficient tool to visualize highly nonlinear wave propagation in granular media. With a view towards potential applications, highly nonlinear solitary waves can be employed as nondestructive probing signals to identify heavy impurities embedded in ordered granular architectures. (Some figures may appear in colour only in the online journal)

Rapid guided wave delamination detection and quantification in composites using global-local sensing

This paper presents a rapid guided ultrasonic wave inspection approach through global inspection by phased array beamforming and local damage evaluation via wavenumber analysis. The global-local approach uses a hybrid system consisting of a PZT wafer and a non-contact laser vibrometer. The overall inspection is performed in two steps. First, a phased array configured by a small number of measurements performs beamforming and beamsteering over the entire plate in order to detect and locate the presence of the damage. A local area is identified as target damage area for the second step. Then a high density wavefield measurement is taken over the target damage area and a spatial wavenumber imaging is performed to quantitatively evaluate the damage. The two-step inspection has been applied to locate and quantify impact-induced delamination damage in a carbon fiber reinforced polymer composite plate. The detected delamination location, size and shape agree well with those of an ultrasonic C-scan. For the test case studied in this work the global-local approach reduced the total composite inspection (damage detection and characterization) time by ~97% compared to using a full scan approach.

Guided wave phased array beamforming and imaging in composite plates

This paper describes phased array beamforming using guided waves in anisotropic composite plates. A generic phased array algorithm is presented, in which direction dependent guided wave parameters and the energy skew effect are considered. This beamforming at an angular direction is achieved based on the classic delay-and-sum principle by applying phase delays to signals received at array elements and adding up the delayed signals. The phase delays are determined with the goal to maximize the array output at the desired direction and minimize it otherwise. For array characterization, the beam pattern of rectangular grid arrays in composite plates is derived. In addition to the beam pattern, the beamforming factor in terms of wavenumber distribution is defined to provide intrinsic explanations for phased array beamforming. The beamforming and damage detection in a composite plate are demonstrated using rectangular grid arrays made by a non-contact scanning laser Doppler vibrometer. Detection images of the composite plate with multiple surface defects at various directions are obtained. The results show that the guided wave phased array method is a potential effective method for rapid inspection of large composite structures.

Guided wave imaging for detection and evaluation of impact-induced delamination in composites

In this paper, guided wavefield interactions with delamination damage in laminated composite panels are investigated. The frequency–wavenumber representations of the guided wavefields show that different wavenumbers are present in the delaminated plate, compared to a pristine case. The wavenumbers are correlated to trapped waves in the delamination region. Novel approaches for imaging the composite panels using guided waves are discussed and demonstrated for quantitative evaluation of the delamination damage. A filter reconstruction imaging method is shown to provide a rapid technique to locate delamination damage by showing where guided wave energy is trapped. A spatial wavenumber-based imaging algorithm is applied to calculate wavenumber values at each spatial location and highlights the delamination damage as regions with larger wavenumber values. The imaging approaches are demonstrated using experimental data from a plate with a simulated delamination (teflon insert) and from a plate containing impact-induced delamination damage. The methods are also applied to a multiple mode guided wave case to demonstrate application to complex wave cases.

Crack detection with Lamb wave wavenumber analysis

In this work, we present our study of Lamb wave crack detection using wavenumber analysis. The aim is to demonstrate the application of wavenumber analysis to 3D Lamb wave data to enable damage detection. The 3D wavefields (including vx, vy and vz components) in time-space domain contain a wealth of information regarding the propagating waves in a damaged plate. For crack detection, three wavenumber analysis techniques are used: (i) time-space Fourier transform which can transform the time-space wavefield into frequency-wavenumber representation while losing the spatial information; (ii) short space Fourier transform which can obtain the frequency-wavenumber spectra at various spatial locations, resulting in a space-frequency-wavenumber representation; (iii) local wavenumber analysis which can provide the distribution of the effective wavenumbers at different locations. All of these concepts are demonstrated through a numerical simulation example of an aluminum plate with a crack. The 3D elastodynamic finite integration technique (EFIT) was used to obtain the 3D wavefields, of which the vz (out-of-plane) wave component is compared with the experimental measurement obtained from a scanning laser Doppler vibrometer (SLDV) for verification purpose. The experimental and simulated results are found to be in close agreement. The application of wavenumber analysis on 3D EFIT simulation data shows the effectiveness of the analysis for crack detection.

Guided wave propagation study on laminated composites by frequency-wavenumber technique

Toward the goal of delamination detection and quantification in laminated composites, this paper examines guided wave propagation and wave interaction with delamination damage in laminated carbon fiber reinforced polymer (CFRP) composites using frequency-wavenumber (f-k) analysis. Three-dimensional elastodynamic finite integration technique (EFIT) is used to acquire simulated time-space wavefields for a CFRP composite. The time-space wavefields show trapped waves in the delamination region. To unveil the wave propagation physics, the time-space wavefields are further analyzed by using two-dimensional (2D) Fourier transforms (FT). In the analysis results, new f-k components are observed when the incident guided waves interact with the delamination damage. These new f-k components in the simulations are experimentally verified through data obtained from scanning laser Doppler vibrometer (SLDV) tests. By filtering the new f-k components, delamination damage is detected and quantified.