Lamb Wave Propagation In Plate Research Articles

Effect of viscoelastic coating on Lamb wave propagation in plates

Dispersion curves for elastic multilayer plates are useful to describe the behavior of guided wave modes in composite materials. They provide information to set up the appropriate launching conditions of the guided waves for assuring high scanning distances with sensitivity. This paper applies an efficient Gauss-Lobatto-Legendre (GLL) collocation method to formulate the Scaled Boundary Finite Element Method SBFEM to estimate the dispersion curves and wave structure in metallic plates with viscoelastic coatings. This formulation is quite efficient because it discretize the cross-section of each layer with only one spectral element. As a result, a global stiffness matrix is obtained by assembling the stiffness matrices of each layer. The formulation leads to a first-order eigenvalue problem by implementing the Z coefficient matrix that can be efficiently solved to compute the (ω, k) couples that guarantee the wave modes propagating in the structure. The estimated phase velocity and group velocity curves for coated and free plates show a small frequency shifting exhibited in some modes, with predominant displacement in the viscoelastic layer of the wave displacement profile.

Control of low-frequency Lamb wave propagation in plates by boundary condition manipulation

Locally resonant metasurfaces can control the propagation of Lamb wave modes in a plate. The resonator is typically designed through frequency matching: adjusting its geometry and/or materials properties by trial and error until its resonance frequency matches the frequency of the target Lamb wave mode. We demonstrate that although frequency matching appears effective for controlling the A0 wave mode, it may fail in the case of the S0 mode. This paper proposes a fundamentally different approach to design a specific metasurface to forbid the propagation of a prescribed Lamb wave mode in a plate. The proposed approach is based upon manipulating the boundary conditions on the top surface of the plate. Different types of Cauchy boundary conditions applied to the surface are shown to control the reflections and mode conversions of low-frequency A0 and S0 Lamb waves. Even a small patch with the modified boundary conditions can be effective. Finally, we show that a local “clamping” resonator that assimilates Cauchy boundary conditions on the surface of the plate changes the plate dispersion characteristics resulting in mode conversion and reflection. This finding provides a rational procedure to design a specific metasurface. The surface-mounted resonators enable control of wave propagation in plates without compromising structural integrity, are easily installed, and can be retrofit to the existing planar structures. The numerical results agree well with the experimental results reported in the literature.

Finite element prediction of acoustoelastic effect associated with Lamb wave propagation in pre-stressed plates

The paper presents outcomes of a finite element (FE) study of acoustoelastic effect associated with Lamb wave propagation in plates subjected to homogeneous bi-axial and bending stresses. In particular, the change of the phase velocity of the fundamental Lamb wave modes is obtained for different stress levels, bi-axial stress ratios and wave propagation angles. A comparison of the obtained numerical results with an analytical solution demonstrates a very good agreement. Moreover, the influence of bending stress on the wave velocities and wave front profile is further investigated numerically. There are currently no analytical results for this case. The developed and verified FE modelling approach can help to address several issues in the current non-destructive inspections including: in the investigation of changing stress conditions on the defect detection as well as in an adaptation of the existing Lamb wave-based defect evaluation systems to monitoring of stress too. The latter may have many benefits from sharing the same hardware for the purpose of maintaining structural integrity of thin-walled structural components.

Multimodal sparse reconstruction in guided wave imaging of defects in plates

A multimodal sparse reconstruction approach is proposed for localizing defects in thin plates in Lamb wave-based structural health monitoring. The proposed approach exploits both the sparsity of the defects and the multimodal nature of Lamb wave propagation in plates. It takes into account the variation of the defects’ aspect angles across the various transducer pairs. At low operating frequencies, only the fundamental symmetric and antisymmetric Lamb modes emanate from a transmitting transducer. Asymmetric defects scatter these modes and spawn additional converted fundamental modes. Propagation models are developed for each of these scattered and spawned modes arriving at the various receiving transducers. This enables the construction of modal dictionary matrices spanning a two-dimensional array of pixels representing potential defect locations in the region of interest. Reconstruction of the region of interest is achieved by inverting the resulting linear model using the group sparsity constraint, where the groups extend across the various transducer pairs and the different modes. The effectiveness of the proposed approach is established with finite-element scattering simulations of the fundamental Lamb wave modes by crack-like defects in a plate. The approach is subsequently validated with experimental results obtained from an aluminum plate with asymmetric defects.

Semi-analytical finite element method for modeling of lamb wave propagation

Lamb wave propagation in plates is multi-modal, dispersive and highly dependent on the material properties. In homogeneous isotropic plates, Lamb modes can be grouped into symmetric and anti-symmetric modes, and they are decoupled from the shear modes. Due to the material isotropy, Lamb wave propagation behavior is independent from the propagation direction. This property can be used to find analytical solutions for the field of displacements in the frequency domain. However, in composite plates having anisotropic material properties, Lamb wave propagation behavior depends on the propagation direction. For this reason, the complexity of Lamb wave propagation modes increases, and no direct analytical solutions are available. Thus, numerical methods need to be used. In this paper, the semi-analytical finite element (SAFE) method is applied as it is suitable for both isotropic homogeneous plates and anisotropic composite laminated plates. Dispersion curves for these complex materials are calculated using SAFE. The effect of obstacles on the reflection and transmission of Lamb waves is considered. SAFE is also used for 2D point force response analysis. By applying the 2D point response analysis for perfectly bonded strip actuators, mode tuning behavior is calculated for general composite plates. A method to consider plate edge reflections in the 2D force response analysis is also presented.

Lamb wave propagation using Wave Finite Element Method

AbstractSome of the available techniques for Lamb wave propagation simulation are the Finite Element Method (FEM), the Boundary Element Method and the Finite Difference Method. The FEM is the best method when complex damage, geometry or boundary is involved. However, high Lamb wave frequency requires very small element size thus high computational cost in FEM analysis. By using the existence of periodicity in plates, an attempt to reduce this computational cost is done using Wave FEM. The applicability of this method to model Lamb wave propagation in plate is first assessed in this paper for the 1‐D wave propagation and compared with FEM explicit method. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling of Lamb wave propagation in plate with two-dimensional phononic crystal layer coated on uniform substrate using plane-wave-expansion method

We show that the conversional three-dimensional plane wave expansion method can be revised to investigate the lamb wave propagation in the plate with two-dimensional phononic crystal layer coated on uniform substrate. We find that an imaginary three-dimensional periodic system can be constructed by stacking the studied plates and vacuum layers alternately, and then the Fourier series expansion can be performed. The difference between our imaginary periodic system and the true three-dimensional one is that, in our system, the Bloch feature of the wave along the thickness direction is broken. Three different systems are investigated by the proposed method as examples. The principle and reliability of the method are also discussed.

Wave boundary element to study Lamb wave propagation in plates

By using analytical mode shapes as the interpolating functions for both displacements and stresses on the reference edges of a plate, a wave element is formulated for use in the boundary element method to study Lamb wave propagation and interaction in plates, to achieve both accuracy and computational efficiency. Lamb wave interaction with a notch is investigated using this method. The results with respect to wave transmission, reflection and mode conversion are consistent with physical considerations of Lamb mode shape and energy conservation. It is shown through the reflection coefficients that S 0 Lamb wave is more sensitive than A 0 wave for detecting a shallow notch in a plate. These coefficients can be used to aid the characterization of the presence of a notch and contribute to quantitative non-destructive evaluation methodology for plate structures. Time history results are obtained by conducting Fourier transform on the coefficients solved in frequency domain. Comparison with experiment results shows the suitability of the method for wave propagation studies in relation to damage detection.

Calculation of the Acoustic Channel in Acoustic Emission Testing of Bottoms of Vertical Steel Tanks

On the basis of theoretical and experimental studies of the fundamental laws of Lamb wave propagation in plates, the acoustic channel is calculated for possible paths of propagation of acoustic-emission waves in the bottom of vertical steel tanks and losses in the acoustic channel are quantitatively estimated.

Acoustic Emission Source Location Using Lamb Wave Modes

This paper describes the development of a technique based on acoustic emission (AE) technology that can be used for global nondestructive evaluation (NDE) of steel structures. This will also be useful for the subsequent local inspection used to further monitor cracking, defective connections, retrofit measures, and so forth. The dispersive nature of Lamb wave propagation in plates makes it possible to perform a linear source location of AE events based on the arrival of different frequency components (Lamb wave modes) of an AE event at a single transducer. Experiments on steel beams and plates in the laboratory explored the theory of wave propagation and digital signal processing needed to pursue this objective. Subsequent field investigation on a real bridge substantiated the applicability of this technique. This new technique could allow AE inspection to locate structural problems better, and with a reduced number of transducers.