Journal Articles

Lamb waves have been widely explored as a promising inspection tool for non-destructive evaluation (NDE) and structural health monitoring (SHM). This article presents a combined analytical finite element model (FEM) approach (CAFA) for the accurate, efficient, and versatile simulation of 2-D Lamb wave propagation and interaction with damage. CAFA used a global analytical solution to model wave generation, propagation, scattering, mode conversion, and detection, while the wave-damage interaction coefficients (WDICs) were extracted from harmonic analysis of local FEM with non-reflective boundaries (NRB). The analytical procedure was coded using MATLAB, and a predictive simulation tool called WaveFormRevealer 2-D was developed. The methodology of obtaining WDICs from local FEM was presented. Case studies were carried out for Lamb wave propagation in a pristine plate and a damaged plate. CAFA predictions compared well with full scale multi-physics FEM simulations and experiments with scanning laser Doppler vibrometry (SLDV), while achieving remarkable performance in computational efficiency and computer resource saving compared with conventional FEM.

This paper presents an efficient and accurate analytical method to calculate the scattering of straight-crested Lamb waves from geometric discontinuities. In this method, the scattered field is expanded in terms of complex Lamb wave modes with unknown amplitudes. These unknown amplitudes are obtained from the boundary conditions using a vector projection utilizing the power expression. The process works by projecting the stress conditions onto the displacement eigen-spaces of complex Lamb wave modes and vice-versa. We call this technique “complex modes expansion with vector projection” (CMEP). Unlike other methods, the CMEP approach is versatile and can be readily applied to notches, cracks, or disbonds. In this paper, the methodology is illustrated by applying the CMEP method to a benchmark problem — the geometric discontinuity created by a step in the thickness of a plate. For method verification, the finite element method (FEM) and the axial–flexural analytical model were used. The FEM analysis was conducted in the frequency domain with non-reflecting boundaries. It was found that the CMEP results correspond very well with the FEM results over a wide frequency–thickness range up to 1.5 MHz-mm. The axial–flexural model was used to verify only the CMEP asymptotic behavior toward zero frequency where frequency-domain FEM encounters difficulties. Our study shows that the computational efficiency of CMEP is orders of magnitude higher than FEM. The paper ends with a discussion of how the CMEP method may be extended to the fast and accurate analysis of realistic damage situations.

In this article, ultrasonic guided wave propagation and interaction with the rivet hole cracks has been formulated using closed-form analytical solution while the local damage interaction, scattering, and mode conversion have been obtained from finite element analysis. The rivet hole cracks (damage) in the plate structure gives rise to the non-axisymmetric scattering of Lamb wave, as well as shear horizontal (SH) wave, although the incident Lamb wave source (primary source) is axisymmetric. The damage in the plate acts as a non-axisymmetric secondary source of Lamb wave and SH wave. The scattering of Lamb and SH waves are captured using wave damage interaction coefficient (WDIC). The scatter cubes of complex-valued WDIC are formed that can describe the 3D interaction (frequency, incident direction, and azimuth direction) of Lamb waves with the damage. The scatter cubes are fed into the exact analytical framework to produce the time domain signal. This analysis enables us to obtain the optimum design parameters for better detection of the cracks in a multiple-rivet-hole problem. The optimum parameters provide the guideline of the design of the sensor installation to obtain the most noticeable signals that represent the presence of cracks in the rivet hole.

In this article, gauge condition in elastodynamics is explored more to revive its potential capability of simplifying wave propagation problems in elastic medium. The inception of gauge condition in elastodynamics happens from the Navier-Lame equations upon application of Helmholtz theorem. In order to solve the elastic wave problems by potential function approach, the gauge condition provides the necessary conditions for the potential functions. The gauge condition may be considered as the superposition of the separate gauge conditions of Lamb waves and shear horizontal (SH) guided waves respectively, and thus, it may be resolved into corresponding gauges of Lamb waves and SH waves. The manipulation and proper choice of the gauge condition does not violate the classical solutions of elastic waves in plates; rather, it simplifies the problems. The gauge condition allows to obtain the analytical solution of complicated problems in a simplified manner.

This paper presents an inexpensive but accurate analytical method to calculate the scattering of straight-crested Lamb waves from cracks parallel to the plate surface. The same method is applicable for the disbond problem. In this method, the scatter field is expanded in terms of complex Lamb wave modes with unknown amplitudes. These unknown amplitudes are obtained from the boundary conditions using vector projection utilizing the power expression. The process works by projecting the stress conditions onto the displacement eigen-spaces of complex Lamb wave modes and vice versa. The authors call this technique "complex modes expansion with vector projection" (CMEP). The CMEP approach is versatile and can be readily applied to corrosion, cracks, or disbonds. In this paper, the CMEP method is applied to a horizontal crack in a plate. For verification of the results the authors compared them with the results obtained by using the finite element method (FEM) and literature. The FEM analysis was conducted in the frequency domain with non-reflecting boundaries. It was found that CMEP results correspond very well with FEM results over a wide frequency-thickness range up to 1.5 MHz mm with CMEP being orders of magnitude faster than FEM.

The paper deals with the development of low-cost tools for fast computer simulation of guided wave propagation and diffraction in plate-like structures of variable thickness. It is focused on notched surface irregularities, which are the basic model for corrosion damages. Their detection and identification by means of active ultrasonic structural health monitoring technologies assumes the use of guided waves generated and sensed by piezoelectric wafer active sensors as well as the use of laser Doppler vibrometry for surface wave scanning and visualization. To create a theoretical basis for these technologies, analytically based computer models of various complexity have been developed. The simplest models based on the Euler–Bernoulli beam and Kirchhoff plate equations have exhibited a sufficiently wide frequency range of reasonable coincidence with the results obtained within more complex integral equation based models. Being practically inexpensive, they allow one to carry out a fast parametric analysis revealing characteristic features of wave patterns that can be then made more exact using more complex models. In particular, the effect of resonance wave energy transmission through deep notches has been revealed within the plate model and then validated by the integral equation based calculations and experimental measurements.

This article presents a new approach to designing non-reflective boundary (NRB) for inhibiting Lamb wave reflections at structural boundaries. Our NRB approach can be effectively and conveniently implemented in commercial finite element (FE) codes. The paper starts with a review of the state of the art: (a) the absorbing layers by increasing damping (ALID) approach; and (b) the Lysmer–Kuhlemeyer absorbing boundary conditions (LK ABC) approach is briefly presented and its inadequacy for Lamb wave applications is explained. Hence, we propose a modified Lysmer–Kuhlemeyer approach to be used in the NRB design for Lamb wave problems; we call our approach MLK NRB. The implementation of this MLK NRB was realized using the spring–damper elements which are available in most commercial FE codes. Optimized implementation parameters are developed in order to achieve the best performance for Lamb wave absorption. Our MLK NRB approach is compared with the state of the art ALID and LK ABC methods. Our MLK NRB shows better performance than ALID and LK ABC for all Lamb modes in the thin-plate structures considered in our examples. Our MLK NRB approach is also advantageous at low frequencies and at cut-off frequencies, where extremely long wavelengths exist. A comprehensive study with various design parameters and plate thicknesses which illustrates the advantages and limitations of our MLK NRB approach is presented. MLK NRB applications for both transient analysis in time domain and harmonic analysis in frequency domain are illustrated. The article finishes with conclusions and suggestions for future work.

This paper addresses theoretical and experimental work on thickness-mode electromechanical (E/M) impedance spectroscopy (EMIS) of proof-mass piezoelectric wafer active sensors (PMPWAS). The proof-mass (PM) concept was used to develop a new method for tuning the ultrasonic wave modes and for relatively high frequency local modal sensing by the PM affixed on PWAS. In order to develop the theoretical basis of the PMPWAS tuning concept, analytical analyses were conducted by applying the resonator theory to derive the EMIS of a PWAS constrained on one and both surfaces by isotropic elastic materials. The normalized thickness-mode shapes were obtained for the normal mode expansion (NME) method to eventually predict the thickness-mode EMIS using the correlation between PMPWAS and the structural dynamic properties of the substrate. Proof-masses of different sizes and materials were used to tune the system resonance towards an optimal frequency point. The results were verified by coupled-field finite element analyses (CF-FEA) and experimental results. An application of the tuning effect of PM on the standing wave modes was discussed as the increase in PM thickness shifts the excitation frequency of the wave mode toward the surface acoustic wave (SAW) mode.

This study aimed to develop theoretical models to accurately predict the in-plane (longitudinal) and out-of-plane (thickness-wise) modes of the electromechanical impedance spectroscopy (EMIS) of a piezoelectric wafer active sensor (PWAS). Two main electrical assumptions are applied for both in-plane and thickness mode PWAS-EMIS in one-dimensional simplified analytical models. These assumptions are 1) constant electrical field assumption and 2) constant electrical displacement assumption. The analytical models with two assumptions are compared with one another to understand the prediction accuracy of the models in different vibration modes. Coupled field finite element analysis (CF-FEA) is also conducted with 2D PWAS model under stress-free boundary conditions. The simulations of the simplified analytical models for free PWAS-EMIS under these two assumptions are carried out. The analytical models are validated by corresponding finite element simulations as well as experimental measurements

This article presents an analytical model for power and energy transfer between excited piezoelectric wafer active sensors and host structure. This model is based on exact multimodal Lamb waves, normal mode expansion technique, and orthogonality of Lamb waves. Modal participation factors are presented to show the contribution of every mode to the total energy transfer. The model assumptions include the following: (1) straight-crested multimodal ultrasonic guided wave propagation, (2) propagating waves only, (3) ideal bonding (pin-force) connection between piezoelectric wafer active sensors and structure, and (4) ideal excitation source at the transmitter piezoelectric wafer active sensors. Constrained piezoelectric wafer active sensor admittance is reviewed. Electrical active power, mechanical converted power, and Lamb wave kinetic and potential energies are derived in closed-form formulae. Numerical simulations are performed for the case of symmetric and antisymmetric excitation of thin aluminum structure. The simulation results are compared with axial and flexural approximation for the case of low-frequency Lamb waves. In addition, a thick steel structure example is considered to illustrate the case of multimodal guided waves. A parametric study for different excitation frequencies and different transducer sizes is performed to show the best match of frequency and piezoelectric wafer active sensor size to achieve maximum energy transfer into the excited structure.