José M. Galán

Lamb mode conversion at edges. A hybrid boundary element–finite-element solution

Two general and flexible numerical techniques based on the finite-element and boundary element methods developed by the authors in a previous paper are applied to study Lamb wave propagation in multilayered plates and Lamb mode conversion at free edges for frequencies beyond the first cutoff frequency. Both techniques are supported by a meshing criterion which guarantees the accuracy of the results when a condition is fulfilled. A finite-element formulation is directly applicable to study Lamb wave propagation and reflection by simple obstacles such as a flat edge. In order to tackle Lamb wave diffraction problems by defects with more complex geometries, a hybrid boundary element-finite-element formulation is used. This technique provides a major improvement with respect to the only previous boundary element application on Lamb waves: the connecting boundary might be placed as close to the reflector as desired, reducing greatly the requirement on mesh size. Two main application problems on practical metallic plates are studied and compared with reported numerical, theoretical, and experimental results: (1) Lamb wave propagation in degraded titanium diffusion bonds, and (2) Lamb mode conversion at inclined or perpendicular free edges of steel plates for frequencies beyond the first cutoff frequency.

Ultrasonic guided wave scattering in a plate overlap

Guided wave scattering in a plate overlap is investigated by numerical calculations and experimental measurements of transmission and reflection factors from the overlap region. In the numerical study, a hybrid boundary element-finite element method is used to calculate the guided wave scattered field from the overlap region. Transmission and reflection factors are calculated for incident A0 and S0 Lamb and n0 shear horizontal waves, including higher modes generated through mode conversion phenomena. In addition, parametric studies of transmission and reflection factors in this problem are performed numerically over various incident modes, frequencies, and overlap lengths. For verification and comparison with numerical results, experiments were conducted to measure the transmission and reflection factors for incident Lamb and shear horizontal waves in steel plates with two different overlap areas. The experimental results agree well with the numerical calculations. The numerical and experimental results show that it is highly feasible to carry out efficient Lamb wave nondestructive evaluation (NDE) in overlapped plates and in multilayer structures with various lap joints by selecting various modes and tuning frequency.

Ultrasonic guided wave propagation across waveguide transitions: energy transfer and mode conversion.

Ultrasonic guided wave inspection of structures containing adhesively bonded joints requires an understanding of the interaction of guided waves with geometric and material discontinuities or transitions in the waveguide. Such interactions result in mode conversion with energy being partitioned among the reflected and transmitted modes. The step transition between an aluminum layer and an aluminum-adhesive-aluminum multi-layer waveguide is analyzed as a model structure. Dispersion analysis enables assessment of (i) synchronism through dispersion curve overlap and (ii) wavestructure correlation. Mode-pairs in the multi-layer waveguide are defined relative to a prescribed mode in a single layer as being synchronized and having nearly perfect wavestructure matching. Only a limited number of mode-pairs exist, and each has a unique frequency range. A hybrid model based on semi-analytical finite elements and the normal mode expansion is implemented to assess mode conversion at a step transition in a waveguide. The model results indicate that synchronism and wavestructure matching is associated with energy transfer through the step transition, and that the energy of an incident wave mode in a single layer is transmitted almost entirely to the associated mode-pair, where one exists. This analysis guides the selection of incident modes that convert into transmitted modes and improve adhesive joint inspection with ultrasonic guided waves.

Transmission and Reflection of A0 Mode Lamb Wave in a Plate Overlap

Lamb wave propagation in a plate overlap is investigated. Transmission and reflection coefficients for incident Lamb waves of A0 mode across the overlap region are numerically calculated using a hybrid BE‐FE method. Transmission and reflection coefficients of the Lamb wave across the overlap region are studied as a function of frequency and overlap length. In addition, mode conversion phenomena from the incident waves within the overlap region are also included in the numerical study. A few experiments were also conducted for measurements of transmission and reflection coefficients for incident A0 mode wave in overlap‐shaped steel plates with two different overlap areas. The experimental results are in good agreement with the numerical calculations. The numerical and experimental results can be used to establish guidelines for NDE in overlapped plates and in multilayer structures with various joints by selecting modes and tuning frequency.

Lamb wave scattering by defects: A hybrid boundary element-finite element formulation

A hybrid Boundary Element (FE)-Finite Element (BE) Formulation is applied to study Lamb wave scattering by defects in homogeneous isotropic plates. A BE model of the neighborhood of the defect is combined with a semi-analytical FE non-reflecting boundary condition which accurately models the radiation condition in the plate. A meshing criterion guarantees the accuracy of the results. The numerical results satisfy energy flux conservation and reciprocity within a very tight margin. The accuracy of the code is verified by a series of benchmark problems.

Analysis of ultrasonic guided wave interaction with a waveguide transition

The mode conversion of ultrasonic guided waves at transitions in plate-like structures is investigated analytically through wavestructure correlation and numerically with a hybrid semi-analytical finite element/normal mode expansion model. This analysis enables selection of modes and frequencies for nondestructive evaluation or structural health monitoring that are effectively transmitted across transitions and are sensitive to a damage mode of interest. Experimental results demonstrate that the method is valuable for an adhesively bonded skin-stringer aluminum plate structure.

Nonreflecting Boundary Conditions for the Nonlinear Euler Equations

Computationally efficient nonreflecting boundary conditions are derived for time-dependent internal flows. The formulation linearizes the Euler equations near the inlet/outlet boundaries and expands the solution in terms of the Fourier-Bessel modes. This leads to a onedimensional convected wave equation for the perturbation pressure for which an ‘exact’ nonreflecting boundary condition, local in space but nonlocal in time, has been derived. The perturbation velocity and density are then calculated using acoustic, entropic and vortical mode splitting. The boundary conditions are implemented for the nonlinear Euler equations which are solved in space using the finite volume approximation and integrated in time using a MacCormack scheme. Four test problems were carried out: propagation of acoustic, vortical and entropic waves and the scattering of a vortical wave by a cascade of flat plates. Comparison between the present exact conditions and commonly used approximate local boundary conditions is made. Results show that unlike the local boundary conditions, whose accuracy depends on the group velocity of the scattered or propagating waves, the present conditions give accurate solutions for a range of problems that have a wide array of group velocities.

Investigation of Guided Wave Scattering in Curved Waveguides

This paper aims at investigating guided wave scattering phenomena in curved waveguides. The use of hybrid numerical technique combining interior boundary element solutions with the finite element method for a semi-infinite waveguide is proposed for investigating guided wave scattering from a doubly bent section. Some sample results of numerical parametric study are also given with a physical interpretation of the variation of guided wave scattering profiles with respect to the bend geometry and the corresponding modes. Introduction Recently, the use of ultrasonic guided wave has been well known as a promising alternative in various NDE applications especially for a long range inspection [1-5]. This is mainly because it has a unique acoustic character that its propagation path is guided by a certain geometry of structures to be tested while bulk waves can interact only with local zone [1, 2]. As an example, corrosion in pipework is a major problem in the oil, chemical and other industries. Many pipes are insulated which means that quite often, approaching to desired inspection area is not even possible without removing the insulation. A significant advance has established in modeling of various guided wave scattering problems though the vigorous efforts in recent years [6]. The more practical implementation of the guided waves is attempted for NDE applications [3-5], modeling studies take the more crucial role for optimization of inspection scheme and quantification of signal interpretation. In 80’s, the guided waves modeling works have been carried out mainly by either pure analytical or semi-analytical approaches with the assumption to simplify their complicate “mode conversion” [6, 7]. In 90’s, the breakthrough to employ the various hybrid techniques in conjunction with either FEM [8, 9] or BEM [10, 11] allows us to handle more realistic models with sophisticate geometry and consequently, the various mode conversions turned to be rather unique promising features for the guided wave technique which can be physically predicted and readily used for tuning experimental schemes. Although a number of earlier works have been reported in the modeling of guided wave scatterings from various defects [6], the studies on waveguide shape changes such as the curved ones are still relatively rare. A lack of physical interpretation for the data is also a room for improvement and some pioneering efforts has just recently begun to focus on the issue. Consequently, the establishment of more detailed data library with physical explanation on guided wave scattering profiles is still highly demanded. In this study, the hybrid modeling technique combining the semi-analytical finite element method and the boundary element method is proposed and the detailed data library with some physical explanation on the S0 Lamb mode interaction with a doubly bent waveguide joint is illustrated varying incident modes, frequency and joint configuration. Descriptions on Numerical Scheme and Models Our goal is to study the feasibility of transmitting the Lamb waves with satisfactory penetration efficiency through an S bending in a plate. Therefore, the motivation of this study is to investigate if Key Engineering Materials Online: 2004-08-15 ISSN: 1662-9795, Vols. 270-273, pp 447-452 doi:10.4028/www.scientific.net/KEM.270-273.447