scholarly journals Modeling and Imaging of Ultrasonic Array Inspection of Side Drilled Holes in Layered Anisotropic Media

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4640
Author(s):  
Chirag Anand ◽  
Roger M. Groves ◽  
Rinze Benedictus
Keyword(s):  
Anisotropic Medium ◽  
Stiffness Matrix ◽  
Composite Structures ◽  
Layered Medium ◽  
Plane Waves ◽  
Anisotropic Media ◽  
Full Matrix ◽  
Inherent Anisotropy ◽  
Transmission And Reflection Coefficients ◽  
Modeling Techniques

There has been an increase in the use of ultrasonic arrays for the detection of defects in composite structures used in the aerospace industry. The response of a defect embedded in such a medium is influenced by the inherent anisotropy of the bounding medium and the layering of the bounding medium and hence poses challenges for the interpretation of the full matrix capture (FMC) results. Modeling techniques can be used to understand and simulate the effect of the structure and the defect on the received signals. Existing modeling techniques, such as finite element methods (FEM), finite difference time domain (FDTD), and analytical solutions, are computationally inefficient or are singularly used for structures with complex geometries. In this paper, we develop a novel model based on the Gaussian-based recursive stiffness matrix approach to model the scattering from a side-drilled hole embedded in an anisotropic layered medium. The paper provides a novel method to calculate the transmission and reflection coefficients of plane waves traveling from a layered anisotropic medium into a semi-infinite anisotropic medium by combining the transfer matrix and stiffness matrix methods. The novelty of the paper is the developed model using Gaussian beams to simulate the scattering from a Side Drilled Hole (SDH) embedded in a multilayered composite laminate, which can be used in both immersion and contact setups. We describe a method to combine the scattering from defects with the model to simulate the response of a layered structure and to simulate the full matrix capture (FMC) signals that are received from an SDH embedded in a layered medium. The model-assisted correction total focusing method (MAC-TFM) imaging is used to image both the simulated and experimental results. The proposed method has been validated for both isotropic and anisotropic media by a qualitative and quantitative comparison with experimentally determined signals. The method proposed in this paper is modular, computationally inexpensive, and is in good agreement with experimentally determined signals, and it enables us to understand the effects of various parameters on the scattering of a defect embedded in a layered anisotropic medium.

scholarly journals A Gaussian Beam Based Recursive Stiffness Matrix Model to Simulate Ultrasonic Array Signals from Multi-Layered Media

Sensors ◽  
2020 ◽  
Vol 20 (16) ◽  
pp. 4371
Author(s):  
Chirag Anand ◽  
Roger Groves ◽  
Rinze Benedictus
Keyword(s):  
Gaussian Beam ◽  
Stiffness Matrix ◽  
Composite Structures ◽  
Finite Size ◽  
Modeling Technique ◽  
Beam Model ◽  
Inherent Anisotropy ◽  
Reinforced Plastic ◽  
Fdtd Methods ◽  
Difference Time

Ultrasonic testing using arrays is becoming widely used to test composite structures in the Aerospace industry. In recent years, the Full Matrix Capture (FMC) technique has been implemented to extract the signals for post-processing to form an image. The inherent anisotropy and the layering of the structure pose challenges for the interpretation of this FMC data. To overcome this challenge, modeling techniques are required that take into account the diffraction caused by finite-size transducers and the response of the structure to these bounded beams. Existing models either homogenize the entire structure, use computationally expensive finite difference time domain (FDTD) methods, or do not consider the shape of the bounded beam, which is used to test such structures. This paper proposes a modeling technique based on combining the Multi-Gaussian beam model with the recursive stiffness matrix method to simulate the FMC signals for layered anisotropic media. The paper provides the steps required for the modeling technique, the extraction of the system efficiency factor, and validation of the model with experimentally determined signals for aluminum as an isotropic material such as aluminum and Carbon Fiber Reinforced Plastic (CFRP) laminate as a layered material. The proposed method is computationally inexpensive, shows good agreement with the experimentally determined FMC data, and enables us to understand the effects of various transducer and material parameters on the extracted FMC signals.

scholarly journals Modelling of the wave fields by the modification of the matrix method in anisotropic media

2014 ◽  
Vol 6 (1) ◽  
pp. 467-485
Author(s):  
A. Pavlova
Keyword(s):  
Free Surface ◽  
Anisotropic Medium ◽  
Matrix Method ◽  
Layered Medium ◽  
Displacement Vector ◽  
Moment Tensor ◽  
Anisotropic Media ◽  
Seismic Moment Tensor ◽  
Arbitrary Boundary ◽  
The Matrix

Abstract. The modification of the matrix method of construction of wave field on the free surface of an anisotropic medium is presented. The earthquake source represented by a randomly oriented force or a seismic moment tensor is placed on an arbitrary boundary of a layered anisotropic medium. The theory of the matrix propagator in a homogeneous anisotropic medium by introducing a "wave propagator" is presented. It is shown that, for an anisotropic layered medium, the matrix propagator can be represented by a "wave propagator" in each layer. The matrix propagator P (z, z0 = 0) acts on the free surface of the layered medium and generates stress-displacement vector at depth z. The displacement field on the free surface of an anisotropic medium is obtained from the received system of equations considering the radiation condition and that the free surface is stressless. The approbation of the modification of the matrix method for isotropic and anisotropic media with TI symmetry is done. A comparative analysis of our results with the synthetic seismic records obtained by other methods and published in foreign papers is executed.

Physical Ultrasonics of Composites

2011 ◽  
Author(s):  
Dale Chimenti ◽  
Stanislav Rokhlin ◽  
Peter Nagy
Keyword(s):  
Composite Laminates ◽  
Stiffness Matrix ◽  
Composite Plates ◽  
Anisotropic Media ◽  
Anisotropic Materials ◽  
Ultrasonic Waves ◽  
Laminated Plates ◽  
Structure Characteristic ◽  
Major Advance

Physical Ultrasonics of Composites is a rigorous introduction to the characterization of composite materials by means of ultrasonic waves. Composites are treated here not simply as uniform media, but as inhomogeneous layered anisotropic media with internal structure characteristic of composite laminates. The objective here is to concentrate on exposing the singular behavior of ultrasonic waves as they interact with layered, anisotropic materials, materials which incorporate those structural elements typical of composite laminates. This book provides a synergistic description of both modeling and experimental methods in addressing wave propagation phenomena and composite property measurements. After a brief review of basic composite mechanics, a thorough treatment of ultrasonics in anisotropic media is presented, along with composite characterization methods. The interaction of ultrasonic waves at interfaces of anisotropic materials is discussed, as are guided waves in composite plates and rods. Waves in layered media are developed from the standpoint of the "Stiffness Matrix", a major advance over the conventional, potentially unstable Transfer Matrix approach. Laminated plates are treated both with the stiffness matrix and using Floquet analysis. The important influence on the received electronic signals in ultrasonic materials characterization from transducer geometry and placement are carefully exposed in a dedicated chapter. Ultrasonic wave interactions are especially susceptible to such influences because ultrasonic transducers are seldom more than a dozen or so wavelengths in diameter. The book ends with a chapter devoted to the emerging field of air-coupled ultrasonics. This new technology has come of age with the development of purpose-built transducers and electronics and is finding ever wider applications, particularly in the characterization of composite laminates.

3D mapping of kinematic attributes in anisotropic media

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. C159-C170 ◽  
Author(s):  
Yuriy Ivanov ◽  
Alexey Stovas
Keyword(s):  
Anisotropic Medium ◽  
Heterogeneous Media ◽  
Homogeneous Medium ◽  
Anisotropic Media ◽  
Transformation Matrix ◽  
3D Mapping ◽  
Slowness Surface ◽  
Point Correspondence ◽  
Geometric Spreading ◽  
Point To Point

Based on the rotation of a slowness surface in anisotropic media, we have derived a set of mapping operators that establishes a point-to-point correspondence for the traveltime and relative-geometric-spreading surfaces between these calculated in nonrotated and rotated media. The mapping approach allows one to efficiently obtain the aforementioned surfaces in a rotated anisotropic medium from precomputed surfaces in the nonrotated medium. The process consists of two steps: calculation of a necessary kinematic attribute in a nonrotated, e.g., orthorhombic (ORT), medium, and subsequent mapping of the obtained values to a transformed, e.g., rotated ORT, medium. The operators we obtained are applicable to anisotropic media of any type; they are 3D and are expressed through a general form of the transformation matrix. The mapping equations can be used to develop moveout and relative-geometric-spreading approximations in rotated anisotropic media from existing approximations in nonrotated media. Although our operators are derived in case of a homogeneous medium and for a one-way propagation only, we discuss their extension to vertically heterogeneous media and to reflected (and converted) waves.

Anisotropic Born scattering for the qP scalar wavefield using a low-rank symbol approximation

Geophysics ◽  
2021 ◽  
pp. 1-74
Author(s):  
Iury Araújo ◽  
Murillo Nascimento ◽  
Jesse Costa ◽  
Alan Souza ◽  
Jörg Schleicher
Keyword(s):  
Anisotropic Medium ◽  
Mathematical Formulation ◽  
Hamiltonian Formulation ◽  
Anisotropic Media ◽  
Low Rank ◽  
Direct Access ◽  
S Wave ◽  
Evolution Operators ◽  
Individual Parameter ◽  
Reflection Data

We present a procedure to derive low-rank evolution operators in the mixed space-wavenumber domain for modeling the qP Born-scattered wavefield at perturbations of an anisotropic medium under the pseudo-acoustic approximation. To approximate the full wavefield, this scattered field is then added to the reference wavefield obtained with the corresponding low-rank evolution operator in the background medium. Being built upon a Hamiltonian formulation using the dispersion relation for qP waves, this procedure avoids pseudo-S-wave artifacts and provides a unified approach for linearizing anisotropic pseudo-acoustic evolution operators. Therefore it is immediately applicable to any arbitrary class of anisotropy. As an additional asset, the scattering operators explicitly contain the sensitivity kernels of the Born-scattered wavefield with respect to the anisotropic medium parameters. This enables direct access to important information like its offset dependence or directional characteristics as a function of the individual parameter perturbations. For our numerical tests, we specify the operators for a mildly anisotropic tilted transversly isotropic (TTI) medium. We validate our implementation in a simple model with weak contrasts and simulate reflection data in the BP TTI model to show that the procedure works in a more realistic scenario. The Born-scattering results indicate that our procedure is applicable to strongly heterogeneous anisotropic media. Moreover, we use the analytical capabilities of the kernels by means of sensitivity tests to demonstrate that using two different medium parameterizations leads to different results. The mathematical formulation of the method is such that it allows for an immediate application to least-squares migration in pseudo-acoustic anisotropic media.

Predictive analysis of stitched aerospace structures for advanced aircraft

2019 ◽  
Vol 124 (1271) ◽  
pp. 44-54
Author(s):  
B. Horton ◽  
Y. Song ◽  
D. Jegley ◽  
F. Collier ◽  
J. Bayandor
Keyword(s):  
Composite Structures ◽  
Experimental Validation ◽  
Aviation Industry ◽  
Body Structure ◽  
Element Analysis ◽  
Aerospace Structures ◽  
New Approach ◽  
Leading Role ◽  
Modeling Techniques ◽  
Analysis Environment

ABSTRACTIn recent years, the aviation industry has taken a leading role in the integration of composite structures to develop lighter and more fuel efficient aircraft. Among the leading concepts to achieve this goal is the Pultruded Rod Stitched Efficient Unitized Structure (PRSEUS) concept. The focus of most PRSEUS studies has been on developing an hybrid wing body structure, with only a few discussing the application of PRSEUS to a tube-wing fuselage structure. Additionally, the majority of investigations for PRSEUS have focused on experimental validation of anticipated benefits rather than developing a methodology to capture the behavior of stitched structure analytically. This paper presents an overview of a numerical methodology capable of accurately describing PRSEUS’ construction and how it may be implemented in a barrel fuselage platform resorting to high-fidelity mesoscale modeling techniques. The methodology benefits from fresh user defined strategies developed in a commercially available finite element analysis environment. It further proposes a new approach for improving the ability to predict deformation in stitched composites, allowing for a better understanding of the intricate behavior and subtleties of stitched aerospace structures.

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