39,676 research outputs found

    Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

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    A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient

    Finite element modeling of ultrasonic wave propagation with application to acoustic microscopy

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    The development of NDE techniques and the accurate interpretation of measurement signals require a firm understanding of the physical process of energy/defect interactions. This in turn demands an accurate model for the propagation of ultrasonic waves in acoustic and elastic media. Analytical approaches are restricted due to the arbitrary geometries of the discontinuities involved. In this work, a comprehensive numerical model based on the finite element method is developed to simulate ultrasonic wave propagation in ultrasonic NDE systems with emphasis on application to acoustic microscopy;Starting from the governing equations of dynamic elasticity, semi-discretized finite element equations in the space domain are derived according to the variational principle. Direct time integration is carried out through the explicit central difference scheme. Both linear and quadratic elements are implemented with comparison and verifications. Material properties, including anisotrophy, inhomogeneity, viscous damping and arbitrary discontinuities are handled successfully by the model. For ultrasonic systems containing a fluid/solid interface, the governing equations for both the solid and fluid media have to be solved simultaneously with the interfacing boundary conditions properly satisfied. In this case the solid and fluid media are formulated by the displacement vector and pressure scalar respectively. The coefficient matrices are rendered symmetric by introducing a new potential variable for the fluid medium;The transient fields of pulsed transducers in solids and their interaction with flaws are treated in detail. The fields of spherically focused transducers and time-delay arrays are examined. The wave field profiles are compared with those obtained by the classical impulse response method and good agreement is achieved. As an integral part of acoustic microscopy, the visualization of propagation properties of transient leaky Rayleigh waves is also presented. Wave propagation in an acoustic lens and focused waves probing a fluid/solid and solid/solid interfaces as situations in acoustic microscopy are characterized. The finite element model proves to be an effective tool for acoustic device design and ultrasonic NDE

    Numerical techniques in linear duct acoustics

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    Both finite difference and finite element analyses of small amplitude (linear) sound propagation in straight and variable area ducts with flow, as might be found in a typical turboject engine duct, muffler, or industrial ventilation system, are reviewed. Both steady state and transient theories are discussed. Emphasis is placed on the advantages and limitations associated with the various numerical techniques. Examples of practical problems are given for which the numerical techniques have been applied

    A time dependent difference theory for sound propagation in ducts with flow

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    A time dependent numerical solution of the linearized continuity and momentum equation was developed for sound propagation in a two dimensional straight hard or soft wall duct with a sheared mean flow. The time dependent governing acoustic difference equations and boundary conditions were developed along with a numerical determination of the maximum stable time increments. A harmonic noise source radiating into a quiescent duct was analyzed. This explicit iteration method then calculated stepwise in real time to obtain the transient as well as the steady state solution of the acoustic field. Example calculations were presented for sound propagation in hard and soft wall ducts, with no flow and plug flow. Although the problem with sheared flow was formulated and programmed, sample calculations were not examined. The time dependent finite difference analysis was found to be superior to the steady state finite difference and finite element techniques because of shorter solution times and the elimination of large matrix storage requirements

    Analysis of sound propagation in ducts using the wave envelope concept

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    A finite difference formulation is presented for sound propagation in a rectangular two-dimensional duct without steady flow for plane wave input. Before the difference equations are formulated, the governing Helmholtz equation is first transformed to a form whose solution does not oscillate along the length of the duct. This transformation reduces the required number of grid points by an order of magnitude, and the number of grid points becomes independent of the sound frequency. Physically, the transformed pressure represents the amplitude of the conventional sound wave. Example solutions are presented for sound propagation in a one-dimensional straight hard-wall duct and in a two-dimensional straight soft-wall duct without steady flow. The numerical solutions show evidence of the existence along the duct wall of a developing acoustic pressure diffusion boundary layer which is similar in nature to the conventional viscous flow boundary layer. In order to better illustrate this concept, the wave equation and boundary conditions are written such that the frequency no longer appears explicitly in them. The frequency effects in duct propagation can be visualized solely as an expansion and stretching of the suppressor duct

    Time-dependent difference theory for noise propagation in a two-dimensional duct

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    A time dependent numerical formulation was derived for sound propagation in a two dimensional straight soft-walled duct in the absence of mean flow. The time dependent governing acoustic-difference equations and boundary conditions were developed along with the maximum stable time increment. Example calculations were presented for sound attenuation in hard and soft wall ducts. The time dependent analysis were found to be superior to the conventional steady numerical analysis because of much shorter solution times and the elimination of matrix storage requirements

    Time dependent difference theory for sound propagation in axisymmetric ducts with plug flow

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    The time dependent governing acoustic-difference equations and boundary conditions are developed and solved for sound propagation in an axisymmetric (cylindrical) hard wall duct with a plug mean flow and spinning acoustic modes. The analysis begins with a harmonic sound source radiating into a quiescent duct. This explicit iteration method then calculates stepwise in real time to obtain the transient as well as the 'steady' state solutions of the acoustic field. The time dependent finite difference analysis has two advantages over the steady state finite difference and finite element techniques: (1)the elimination of large matrix storage requirements, and (2)shorter solution times under most conditions

    On the scattering of torsional elastic waves from axisymmetric defects in coated pipes

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    This is the post-print version of the Article - Copyright @ 2012 ElsevierLong range ultrasonic testing is now a well established method for examining in-service degradation in pipelines. In order to protect pipelines from the surrounding environment it is common for viscoelastic coatings to be applied to the outer surface. These coatings are, however, known to impact on the ability of long range ultrasonic techniques to locate degradation, or defects, within a coated pipe. The coating dissipates sound energy travelling along the pipe, attenuating both the incident and reflected signals making responses from defects difficult to detect. This article aims to investigate the influence of a viscoelastic coating on the ability of long range ultrasonic testing to detect a defect in an axisymmetric pipe. The article focuses on understanding the behaviour of the fundamental torsional mode and quantifying the effect of bitumen coatings on reflection coefficients generated by axisymmetric defects. Reflection coefficients are measured experimentally for coated and uncoated pipes and compared to theoretical predictions generated using numerical mode matching and a hybrid finite element technique. Good agreement between prediction and measurement is observed for uncoated pipes, and it is shown that the theoretical methods presented here are fast and efficient making them suitable for studying long pipe runs. However, when studying coated pipes agreement between theory and prediction is observed to be poor for predictions based on those bulk acoustic properties currently reported in the literature for bitumen. Good agreement is observed only after conducting a parametric study to identify more appropriate values for the bulk acoustic properties. Furthermore, the reflection coefficients obtained for the fundamental torsional mode in a coated pipe show that significant sound attenuation is present over relatively short lengths of coating, thus quantifying those problems commonly encountered with the use of long range ultrasonic testing on coated pipes in the field
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