Elizabeth A. Skelton

Theoretical acoustics of underwater structures

This text provides an account of the linear acoustics of basic isotropic/anistropic structures excited by time-harmonic and transient mechanical forces and acoustic sources. Many numerical examples are given to aid physical insight and to provide benchmark computations of sound radiation and sound scattering.

Modeling Bulk and Guided Waves in Unbounded Elastic Media Using Absorbing Layers in Commercial Finite Element Packages

This paper presents solutions to achieve higher computational efficiency for the modeling of bulk and guided waves in unbounded elastic media using absorbing layers in commercially available FE packages. The aim is to provide an assessment to aid practical modeling of large wave propagation problems. The concept and implementation of perfectly matched layers and absorbing layers using increasing damping are explained. Analytical models enabling easy calculation of appropriate layer parameters for models are presented and validated. Demonstrator cases are used to prove that both techniques achieve a significant improvement in computational efficiency over classical techniques.

Acoustics of anisotropic planar layered media

Abstract The theory of a canonical problem of the acoustics of a planar system comprising triclinic anisotropic elastic layers and isotropic fluid layers is given. The special cases of orthorhombic or isotropic elastic layers are also included. Excitations are time-harmonic point forces, acoustic monopoles and plane waves. Quantities of interest are the far field sound radiation, and plane wave reflection and transmission coefficients. The theory may find useful application in the acoustic design of anisotropic composite materials.

A generic hybrid model for bulk elastodynamics, with application to ultrasonic nondestructive evaluation

Practical ultrasonic inspection requires modeling tools that enable rapid and accurate visualization; because of the increasing sophistication of practical inspection, it is becoming increasingly difficult to use a single modeling method to represent an entire inspection process. Hybrid models that utilize different or interacting numerical schemes in different regions, to use their relative advantages to maximal effect, are attractive in this context, but are usually custom-made for specific applications or sets of modeling methods. The limitation of hybrid schemes to particular modeling techniques is shown here to be related to their fundamental formulation. As a result, it becomes clear that a formalism to generalize hybrid schemes can be developed: an example of the construction of a generic hybrid modeling interface is given for the abstraction of bulk ultrasonic wave phenomena, common in practical inspection problems. This interface is then adapted to work within a prototype hybrid model consisting of two smaller finite element model-domains, and explicitly demonstrated for bulk ultrasonic wave propagation and scattering examples. Sources of error and ways to improve the accuracy of the interface are also discussed.

Acoustic scattering by a disc constraining an infinite fluid-loaded cylindrical shell

Abstract A plane sound wave is obliquely incident on an infinite cylindrical elastic shell which is constrained by a rigid internal disc and immersed in compressible fluid. A formal solution is obtained for the scattered pressure, and investigated asymptotically for the case of heavy exterior fluid loading.

Acoustic scattering by a disk or annulus linking two concentric cylindrical shells, part II: Results for heavy exterior fluid loading on both shells

Abstract A plane sound wave is incident upon a system of two concentric elastic shells. Linking the shells, in such a way that only reaction forces are transmitted to the shells, is a disk or annulus which can undergo rigid body motion only. The formal solution obtained in part I is investigated asymptotically for the case when the exterior fluid also occupies the region between the shells, and provides heavy fluid loading on both shells. In this case the additional limits of either large or small shell spacing are employed.

The validity of Kirchhoff theory for scattering of elastic waves from rough surfaces

The Kirchhoff approximation (KA) for elastic wave scattering from two-dimensional (2D) and three-dimensional (3D) rough surfaces is critically examined using finite-element (FE) simulations capable of extracting highly accurate data while retaining a fine-scale rough surface. The FE approach efficiently couples a time domain FE solver with a boundary integration method to compute the scattered signals from specific realizations of rough surfaces. Multiple random rough surfaces whose profiles have Gaussian statistics are studied by both Kirchhoff and FE models and the results are compared; Monte Carlo simulations are used to assess the comparison statistically. The comparison focuses on the averaged peak amplitude of the scattered signals, as it is an important characteristic measured in experiments. Comparisons, in both two dimensions and three dimensions, determine the accuracy of Kirchhoff theory in terms of an empirically estimated parameter σ2/λ0 (σ is the RMS value, and λ0 is the correlation length, of the roughness), being considered accurate when this is less than some upper bound c, (σ2/λ0<c). The incidence and scattering angles also play important roles in the validity of the Kirchhoff theory and it is found that for modest incidence angles of less than 30°, the accuracy of the KA is improved even when σ2/λ0>c. In addition, the evaluation results are compared using 3D isotropic rough surfaces and 2D surfaces with the same surface parameters.

A time-domain finite element boundary integration method for ultrasonic nondestructive evaluation.

A 2-D and 3-D numerical modeling approach for calculating the elastic wave scattering signals from complex stress-free defects is evaluated. In this method, efficient boundary integration across the complex boundary of the defect is coupled with a time-domain finite element (FE) solver. The model is designed to simulate time-domain ultrasonic nondestructive evaluation in bulk media. This approach makes use of the hybrid concept of linking a local numerical model to compute the near-field scattering behavior and theoretical mathematical formulas for postprocessing to calculate the received signals. It minimizes the number of monitoring signals from the FE calculation so that the computation effort in postprocessing decreases significantly. In addition, by neglecting the conventional regular monitoring box, the region for FE calculation can be made smaller. In this paper, the boundary integral method is implemented in a commercial FE code, and it is validated by comparing the scattering signals with results from corresponding full FE models. The coupled method is then implemented in real inspection scenarios in both 2-D and 3-D, and the accuracy and the efficiency are demonstrated. The limitations of the proposed model and future works are also discussed.

An asymptotic theory for waves guided by diffraction gratings or along microstructured surfaces

An effective surface equation, that encapsulates the detail of a microstructure, is developed to model microstructured surfaces. The equations deduced accurately reproduce a key feature of surface wave phenomena, created by periodic geometry, that are commonly called Rayleigh–Bloch waves, but which also go under other names, for example, spoof surface plasmon polaritons in photonics. Several illustrative examples are considered and it is shown that the theory extends to similar waves that propagate along gratings. Line source excitation is considered, and an implicit long-scale wavelength is identified and compared with full numerical simulations. We also investigate non-periodic situations where a long-scale geometrical variation in the structure is introduced and show that localized defect states emerge which the asymptotic theory explains.

Acoustic scattering by a closed semi-infinite fluid-loaded elastic cylindrical shell

A plane sound wave is obliquely incident upon a semi–infinite elastic circular cylindrical shell, closed at one end by a rigid but movable disk, with exterior fluid loading. Expanding the unknown pressure on the end plate as a Dini series and applying half–range Fourier transforms allows the problem to be formulated as a Wiener–Hopf equation with unknown coefficients which satisfy a system of simultaneous linear equations. The solution is presented for the axisymmetric, n = 0 harmonic, component of the scattered sound, which in the far–field consists of the cylindrically spreading waves, in appropriate regions, which would have been present if the shell had been infinitely long, together with a spherically spreading component which is due to the semi–infinite length of the shell. Some numerical results are presented for the spherically spreading component of the scattered field.