Pawel Packo

Lamb wave propagation modelling and simulation using parallel processing architecture and graphical cards

This paper demonstrates new parallel computation technology and an implementation for Lamb wave propagation modelling in complex structures. A graphical processing unit (GPU) and computer unified device architecture (CUDA), available in low-cost graphical cards in standard PCs, are used for Lamb wave propagation numerical simulations. The local interaction simulation approach (LISA) wave propagation algorithm has been implemented as an example. Other algorithms suitable for parallel discretization can also be used in practice. The method is illustrated using examples related to damage detection. The results demonstrate good accuracy and effective computational performance of very large models. The wave propagation modelling presented in the paper can be used in many practical applications of science and engineering.

GPU-based local interaction simulation approach for simplified temperature effect modelling in Lamb wave propagation used for damage detection

Temperature has a significant effect on Lamb wave propagation. It is important to compensate for this effect when the method is considered for structural damage detection. The paper explores a newly proposed, very efficient numerical simulation tool for Lamb wave propagation modelling in aluminum plates exposed to temperature changes. A local interaction approach implemented with a parallel computing architecture and graphics cards is used for these numerical simulations. The numerical results are compared with the experimental data. The results demonstrate that the proposed approach could be used efficiently to produce a large database required for the development of various temperature compensation procedures in structural health monitoring applications. (Some figures may appear in colour only in the online journal)

Generalized semi-analytical finite difference method for dispersion curves calculation and numerical dispersion analysis for Lamb waves

The paper presents an efficient and accurate method for dispersion curve calculation and analysis of numerical models for guided waves. The method can be used for any arbitrarily selected anisotropic material. The proposed approach utilizes the wave equation and through-thickness-only discretization of anisotropic, layered plates to obtain the Lamb wave characteristics. Thus, layered structures, such as composites, can be analyzed in a straightforward manner. A general framework for the proposed analysis is given, along with application examples. Although these examples are based on the local interaction simulation approach for elastic waves propagation, the proposed methodology can be easily adopted for other methods (e.g., finite elements). The method can be also used to study the influence of discretization parameters on dispersion curves estimates.

CUDA technology for Lamb wave simulations

Guided ultrasonic waves are widely used in Structural Health Monitoring applications for inspections of large plate-like structures. Wave propagation phenomena associated with guided ultrasonic waves are difficult to model for complex engineering structures. Various simulation algorithms used in practice are not accurate and very expensive computationally. The paper demonstrates new parallel computation technology offered by modern Graphics Processing Units (GPUs) and Compute Unified Device Architecture (CUDA) used in low-cost graphical cards available in standard PCs. Such systems enable calculations of very large models in minutes. The Local Interaction Simulation Approach (LISA) algorithm have been implemented and used for wave propagation modelling. Application examples are related to structural damage detection. The results demonstrate good accuracy and effective computational performance.

Time–distance domain transformation for Acoustic Emission source localization in thin metallic plates

Acoustic Emission used in Non-Destructive Testing is focused on analysis of elastic waves propagating in mechanical structures. Then any information carried by generated acoustic waves, further recorded by a set of transducers, allow to determine integrity of these structures. It is clear that material properties and geometry strongly impacts the result. In this paper a method for Acoustic Emission source localization in thin plates is presented. The approach is based on the Time-Distance Domain Transform, that is a wavenumber-frequency mapping technique for precise event localization. The major advantage of the technique is dispersion compensation through a phase-shifting of investigated waveforms in order to acquire the most accurate output, allowing for source-sensor distance estimation using a single transducer. The accuracy and robustness of the above process are also investigated. This includes the study of Youngs modulus value and numerical parameters influence on damage detection. By merging the Time-Distance Domain Transform with an optimal distance selection technique, an identification-localization algorithm is achieved. The method is investigated analytically, numerically and experimentally. The latter involves both laboratory and large scale industrial tests.

Amplitude-dependent Lamb wave dispersion in nonlinear plates

The paper presents a perturbation approach for calculating amplitude-dependent Lamb wave dispersion in nonlinear plates. Nonlinear dispersion relationships are derived in closed form using a hyperelastic stress-strain constitutive relationship, the Green-Lagrange strain measure, and the partial wave technique integrated with a Lindstedt-Poincaré perturbation approach. Solvability conditions are derived using an operator formalism with inner product projections applied against solutions to the adjoint problem. When applied to the first- and second-order problems, these solvability conditions lead to amplitude-dependent, nonlinear dispersion corrections for frequency as a function of wavenumber. Numerical simulations verify the predicted dispersion shifts for an example nonlinear plate. The analysis and identification of amplitude-dependent, nonlinear Lamb wave dispersion complements recent research focusing on higher harmonic generation and internally resonant waves, which require precise dispersion relationships for frequency-wavenumber matching.

Modelling nonlinearity of guided ultrasonic waves in fatigued materials using a nonlinear local interaction simulation approach and a spring model

HighlightsA diagnostic method can be utilised with present two sources of nonlinearity.Embryo stages of crack can be observed using high‐frequency Lamb wave pair.The developing stages of crack can be monitored using low‐frequency Lamb wave pair.Strong dependence of cumulative synchronism on numerical parameters is observed.New numerical tool NL‐LISA/SM to model nonlinear material and crack is presented. ABSTRACT Modelling and numerical simulation – based on the framework of the Local Interaction Simulation Approach – was developed to have more insight into nonlinear attributes of guided ultrasonic waves propagating in fatigued metallic materials. Various sources of nonlinearity were considered in this modelling work, with particular emphases on higher‐order harmonic generation and accumulation of nonlinearity along wave propagation. The material hyper‐elasticity was considered in the model using an energy density approach based on the Landau–Lifshitz formulation; and the “breathing” motion pattern of a fatigue crack in the material was interrogated using a spring model. Upon the successful validation with the model prepared in the commercial software based on the Finite Element Methods, two scenarios were comparatively investigated, i.e. the lower and higher frequency regime. In the first case propagation of a basic symmetric mode pair was simulated using the model to observe a cumulative characteristic of the second harmonic mode with nonlinear hyper‐elastic material definition upon appropriate selection of excitation frequency. In the second case, the higher‐order symmetric mode pair was excited according to the “internal resonance” conditions, revealing a strong dependence of manifested nonlinearity on numerical parameters. Moreover, it was shown that with the use of the wave from the low frequency regime it was easier to differentiate later stages of the crack development, being in contrary to waves in the high frequency regime, which allowed to clearly observe early stages of the crack expansion. Such outcome lays the foundation to develop the damage detection and monitoring scheme in the field of Structural Health Monitoring based on utilising the nonlinear features of guided ultrasonic waves.

Actuation stress modelling of piezoceramic transducers under variable temperature field

The article presents a two-dimensional temperature-dependent model of piezoceramic transducers used for Lamb wave–based damage detection applications. The effect of temperature on shear stress and normal stress components influencing wave actuation is analysed. Three models are analysed and compared, that is, static theoretical model and two numerical models, that is, static and dynamic. These models are analysed for two different piezoceramic transducers’ thicknesses. The results demonstrate that the effective transducer’s length is smaller than its physical in-plane dimension. The influence of the normal actuation stress component is significant for wave actuation. This component is dependent on temperature and transducer’s dimension.

Local computational strategies for predicting wave propagation in nonlinear media

Two local computational strategies for modeling elastic wave propagation, namely the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE), are compared and contrasted in analyzing bulk waves in two-dimensional nonlinear media. Each strategy formulates the problem from the perspective of a cell and its local interactions with other cells, leading to robust treatments of anisotropy, heterogeneity, and nonlinearity. The local approach also enables straight-forward parallelization on high performance computing clusters. While the two share a common local perspective, they differ in two major respects. The first is that CAFE employs both rectangular and triangular cells, while LISA considers only rectangular. The second is that LISA appeared much earlier than CAFE (early 1990’s versus late 2000’s), and as such has been developed to a much greater degree with a multitude of material models, cell-to-cell interactions, loading possibilities, and boundary treatments. A hybrid approach which combines the two is of great interest since the non-uniform mesh capability of the CAFE triangular cell can be readily coupled to LISA’s rectangular grids, taking advantage of the built-in LISA features on the uniform portion of the domain. For linear material domains, the hybrid implementation appears straight-forward since both methods have been shown to recover the same equations in the rectangular case. For nonlinear material domains, the formulations cannot be put into a one-to-one correspondence, and hybrid implementation may be more problematic. This paper addresses these differences by first presenting the underlying formulations, and then computing results for growth of a second harmonic in an introduced bulk pressure wave. Rectangular cells are used in both LISA and CAFE. Results from both approaches are compared to an approximate, analytical solution based on a two-scale field representation. Differences in the LISA and CAFE computed solutions are discussed and recommendations are made for a follow-on hybrid implementation.

Local Interaction Simulation Approach vs. Finite Element Modelling for Fault Detection in Medical Ultrasonic Transducer

Ultrasonic transducers are extensively used in medical applications. Any deterioration in their performance can lead to poor quality images. The Local Interaction Simulation Approach (LISA) and Finite Elements are used to model medical ultrasonic transducers. The entire analysis attempts to find out whether the LISA-based methodology could be used for transducer modelling in fault detection applications based on in-air reverberation patterns.