Gaussian-DPSM (G-DPSM) and Element Source Method (ESM) modifications to DPSM for ultrasonic field modeling

In the last few years, Distributed Point Source Method (DPSM) a mesh-free semi-analytical technique has been developed. In spite of its many advantages, one shortcoming of the conventional DPSM method is that the field obtained by conventional DPSM method needs to be scaled to match the theoretical solutions. Two modification techniques called Gaussian-DPSM (G-DPSM) and Element Source Method (ESM) are developed here to avoid the scaling need. G-DPSM technique introduces additional fictitious point sources around every parent point source. Gaussian weight functions determine the strength of these additional fictitious point sources that are denoted as child point sources. ESM replaces discrete point sources used in the conventional DPSM by continuous sources. In the ESM formulation individual point sources are denoted as nodes. Special elements are formed on the boundary by connecting these nodes. The source strength inside the element can vary linearly or non-linearly depending on the order of the interpolation function used inside the element. Results generated by both these methods are compared with the conventional DPSM solution and analytical solution. It is shown that the ultrasonic field in front of the transducer computed by G-DPSM and ESM matches very well with the theory without using any scaling factor.     

Elastic wave propagation in sinusoidally corrugated waveguides

The ultrasonic wave propagation in sinusoidally corrugated waveguides is studied in this paper. Periodically corrugated waveguides are gaining popularity in the field of vibration control and for designing structures with desired acoustic band gaps. Currently only numerical method (Boundary Element Method or Finite Element Method) based packages (e.g., PZFlex) are in principle capable of modeling ultrasonic fields in complex structures with rapid change of curvatures at the interfaces and boundaries but no analyses have been reported. However, the packages are very CPU intensive; it requires a huge amount of computation memory and time for its execution. In this paper a new semi-analytical technique called Distributed Point Source Method (DPSM) is used to model the ultrasonic field in sinusoidally corrugated waveguides immersed in water where the interface curvature changes rapidly. DPSM results are compared with analytical solutions. It is found that when a narrow ultrasonic beam hits the corrugation peaks at an angle, the wave propagates in the backward direction in waveguides with high corrugation depth. However, in waveguides with small corrugation the wave propagates in the forward direction. The forward and backward propagation phenomenon is found to be independent of the signal frequency and depends on the degree of corrugation.     

DPSM technique for ultrasonic field modelling near fluid-solid interface

Distributed point source method (DPSM) is gradually gaining popularity in the field of non-destructive evaluation (NDE). DPSM is a semi-analytical technique that can be used to calculate the ultrasonic fields produced by transducers of finite dimension placed in homogeneous or non-homogeneous media. This technique has been already used to model ultrasonic fields in homogeneous and multi-layered fluid structures. In this paper the method is extended to model the ultrasonic fields generated in both fluid and solid media near a fluid-solid interface when the transducer is placed in the fluid half-space near the interface. Most results in this paper are generated by the newly developed DPSM technique that requires matrix inversion. This technique is identified as the matrix inversion based DPSM technique. Some of these results are compared with the results produced by the Rayleigh-Sommerfield integral based DPSM technique. Theory behind both matrix inversion based and Rayleigh-Sommerfield integral based DPSM techniques is presented in this paper. The matrix inversion based DPSM technique is found to be very efficient for computing the ultrasonic field in non-homogeneous materials. One objective of this study is to model ultrasonic fields in both solids and fluids generated by the leaky Rayleigh wave when finite size transducers are inclined at Rayleigh critical angles. This phenomenon has been correctly modelled by the technique. It should be mentioned here that techniques based on paraxial assumptions fail to model the critical reflection phenomenon. Other advantages of the DPSM technique compared to the currently available techniques for transducer radiation modelling are discussed in the paper under Introduction.     

Extension of the distributed point source method for ultrasonic field modeling

The distributed point source method (DPSM) was recently proposed for ultrasonic field modeling and other applications. This method uses distributed point sources, placed slightly behind transducer surface, to model the ultrasound field. The acoustic strength of each point source is obtained through matrix inversion that requires the number of target points on the transducer surface to be equal to the number of point sources. In this work, DPSM was extended and further developed to overcome the limitations of the original method and provide a solid mathematical explanation of the physical principle behind the method. With the extension, the acoustic strength of the point sources was calculated as the solution to the least squares minimization problem instead of using direct matrix inversion. As numerical examples, the ultrasound fields of circular and rectangular transducers were calculated using the extended and original DPSMs which were then systematically compared with the results calculated using the theoretical solution and the exact spatial impulse response method. The numerical results showed the extended method can model ultrasonic fields accurately without the scaling step required by the original method. The extended method has potential applications in ultrasonic field modeling, tissue characterization, nondestructive testing, and ultrasound system optimization.     

Numerical simulation of electromagnetic acoustic transducers using distributed point source method

In spite of many advances in analytical and numerical modeling techniques for solving different engineering problems, an efficient solution technique for wave propagation modeling of an electromagnetic acoustic transducer (EMAT) system is still missing. Distributed point source method (DPSM) is a newly developed semi-analytical technique developed since 2000 by Placko and Kundu (2007) [12] that is very powerful and straightforward for solving various engineering problems, including acoustic and electromagnetic modeling problems. In this study DPSM has been employed to model the Lorentz type EMAT with a meander line and flat spiral type coil. The problem of wave propagation has been solved and eddy currents and Lorentz forces have been calculated. The displacement field has been obtained as well. While modeling the Lorentz force the effect of dynamic magnetic field has been considered that most current analyses ignore. Results from this analysis have been compared with the finite element method (FEM) based predictions. It should be noted that with the current state of knowledge this problem can be solved only by FEM.     

Spectral-energy characteristics of sound fields scattered by fine-structured inhomogeneities of sound velocity into the geometrical shadow zone

In analyzing experimental results obtained with explosive sources in the tropical zone of the Indian Ocean, a good agreement was obtained for spectral-energy characteristics of signals observed in the first geometrical shadow zone with computer calculations of the sound field scattered by fine structure inhomogeneities of the fractal type. From the comparison of the results of calculating the frequency characteristics of sound fields in the shadow zone by the wave code and by the method combining ray acoustics with the wave theory of sound scattering, it was found that both methods are appropriate for describing the real processes of scattering and propagation of sound in the ocean with fine-structured stratification and that these methods can be used for solving inverse problems.     

Wave envelopes method for description of nonlinear acoustic wave propagation

A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach (based on a Fourier series representation of the propagating wave) are given for circular source geometry, which represents the most challenging case from the computational time point of view. For two cases, short (2 cycle) and long (8 cycle) 2 MHz bursts, the computational times were 10 min and 15 min versus 2 h and 8 h for the TAWE method versus the conventional method, respectively.     

Behavior of block boundaries during ultrasonic vibration in alkali halide crystals at temperatures 20–300°C

The behavior of block boundaries was investigated in alkali halide crystals of various orientations deformed by ultrasound at frequencies 40–73 kHz in the temperature interval 20–300°C. The specimen orientation was defined by the angle between the fourfold axis and the propagation direction of the ultrasonic wave. The initial stage of plastic deformation at room temperature is due to the generation of sources at the block boundaries in KCl and KBr, and by the heterogeneous nucleation of dislocation in NaCl and LiF. In the temperature interval 200–300°C, in NaCl and LiF dislocation multiplication begins already with the generation of sources at the block boundaries. In 30° orientation specimens the beginning of multiplication is preceded by the motion initiated by the ultrasound of sections of the block boundaries in the {1 0 0} <110> secondary glide system.Translated from Izvestiya Vysshika Uchebnykh Zavedenii, Fizika, No. 1, pp. 49–53, January, 1986.     

深海中利用单水听器的影区声源无源测距测深方法

在典型深海情况下当声源与接收水听器位于海水表层时,在影区内由声源海底接收器、声源海面海底接收器、声源海底海面接收器和声源海面海底海面接收器4条声线形成声场干涉结构,声强随着频率具有两种干涉周期,随着收发距离的增加而增大,分别随着声源深度、接收水听器深度的增加而减小。因此由单水听器记录的声场干涉结构即可实现宽带声源目标的无源测距测深,仿真分析验证了其有效性。在南海深海声学实验中观测到海面宽带噪声源在声场影区所形成的声场干涉结构,数据分析结果验证了深海声场干涉结构用于声源无源定位的有效性。与传统无源定位方法相比,该方法不需要宽带引导声源、精确的海底声学参数和大规模的拷贝场计算。      

Lamb waves propagation in elastic plane layers with a joint strip

The Lamb waves are used for the ultrasonic characterization of welds because of their relative long-range propagation. In this paper, a simplified model of a weld-strip between two identical semi-infinite elastic layers is investigated. The reflected and transmitted ultrasonic fields are expressed by modal series whose coefficients are obtained by application of orthogonality relation. Comparisons with solutions obtained by finite elements wave propagation simulations are made. The energy balance between the incident and the scattered waves is also used to verify the accuracy of the obtained modal amplitudes.     

A Wavelet-Based Processing method for simultaneously determining ultrasonic velocity and material thickness

Methods of measuring ultrasonic wave velocity in an elastic sample require data on the thickness of the sample and/or the distances between the transducers and the sample. The uncertainty of the ultrasonic wave velocity measurements generally depends on that of the data available. Conversely, to determine the thickness of a material, it is necessary to have a priori information about the wave velocity. This problem is particularly hard to solve when measuring the parameters of biological specimens such as bones having a greater acoustical impedance contrast (typically 3-5 MRayl) than that of the surrounding soft tissues (typically 1.5 MRayl). Measurements of this kind cannot easily be performed. But obtaining the thickness of a bone structure and/or the ultrasonic wave velocity is a important problem, for example, in biomechanical field for the calculation of elastic modulus, or in acoustical imaging field to parameterize the images, and to reference the grey or color level set to a physical parameter.The aim of the present study was to develop a method of simultaneously and independently determining the velocity of an ultrasonic wave in an elastic sample and the wave path across the thickness of this sample, using only one acquisition in pure transmission mode. The new method, which we have called the “Wavelet-Based Processing” method, is based on the wavelet decomposition of the signals and on a suitable transmitted incident wave correlated with the experimental device, and the mathematical properties such as orthonormality, of which lend themselves well to the time-scale approach. By following an adapted algorithm, ultrasonic wave velocities in parallelepipedic plates of elastic manufactured material and the apparent thicknesses were both measured using a water tank, a mechanical device and a matched pair of 1 MHz ultrasonic focused transducers having a diameter of 3 mm, a focal length of 150 mm and beam width of 2 × 2 mm at the focus (mean temperature 22°). The results were compared with those obtained with a conventional Pulse-mode method and with the control values, to check their validity. Measurements performed on bovine and human dry cortical bone samples are also presented to assess the limitations of the method when it is applied to elastic biological samples, including those of an equal-wavelength size (≈1.5 mm). The thicknesses and the ultrasonic wave velocities were then measured in this kind of (quasi-) parallelepipedic elastic materials with an mean estimated error ranged from 1% to 3.5% compared to the referenced values.     

Solution of the scalar wave equation over very long distances using nonlinear solitary waves: Relation to finite difference methods

The linear wave equation represents the basis of many linear electromagnetic and acoustic propagation problems. Features that a computational model must have, to capture large scale realistic effects (for over the horizon or “OTH” radar communication, for example), include propagation of short waves with scattering and partial absorption by complex topography. For these reasons, it is not feasible to use Green’s Function or any simple integral method, which neglects these intermediate effects and requires a known propagation function between source and observer. In this paper, we describe a new method for propagating such short waves over long distances, including intersecting scattered waves. The new method appears to be much simpler than conventional high frequency schemes: Lagrangian “particle” based approaches, such as “ray tracing” become very complex in 3-D, especially for waves that may be expanding, or even intersecting. The other high frequency scheme in common use, the Eikonal, also has difficulty with intersecting waves.Our approach, based on nonlinear solitary waves concentrated about centroid surfaces of physical wave features, is related to that of Whitham [1], which involves solving wave fronts propagating on characteristics. Then, the evolving electromagnetic (or acoustic) field can be approximated as a collection of propagating co-dimension one surfaces (for example, 2-D surfaces in three dimensions). This approach involves solving propagation equations discretely on an Eulerian grid to approximate the linear wave equation. However, to propagate short waves over long distances, conventional Eulerian numerical methods, which attempt to resolve the structure of each wave, require far too many grid cells and are not feasible on current or foreseeable computers. Instead, we employ an “extended” wave equation that captures the important features of the propagating waves. This method is first formulated at the partial differential equation (PDE) level, as a wave equation with an added “confining” term that involves both a positive and a negative dissipation. Once we have the stable PDE, the discrete formulation is simply a multidimensional PDE with (stable) perturbations caused by the discretization. The resulting discrete solution can then be low order and very simple and yet remain stable over arbitrarily long times. When discretized and solved on an Eulerian grid, this new method allows far coarser grids than required by conventional resolution considerations, while still accounting for the effects of varying atmospheric and topographic features. An important point is that the new method is in the same form as conventional discrete wave equation methods. However, the conventional solution eventually decays, and only the “intermediate asymptotic” solution can be used. Simply by adding an extra term, we show that a nontrivial true asymptotic solution can be obtained. A similar solitary wave based approach has been used successfully in a different problem (involving “Vorticity Confinement”), for a number of years.     

Laser ultrasonic propagation imaging method in the frequency domain based on wavelet transformation

A wavelet-transformed ultrasonic propagation imaging method capable of ultrasonic propagation imaging in the frequency domain was developed and applied as a new structural damage or flaw visualization algorithm. Since the wavelet-transformed ultrasonic propagation imaging method has strong frequency selectivity, it can visualize the propagation of ultrasonic waves of a specific frequency (for example, to isolate ultrasonic mode of interest and a damage-related ultrasonic wave). The strong frequency selectivity of the wavelet-transformed ultrasonic propagation imaging method was demonstrated, isolating only the zeroth-order asymmetrical mode of the fundamental Lamb wave modes in an anisotropic carbon fiber-reinforced plastic plate with a thickness of 5 mm. The wavelet-transformed ultrasonic propagation imaging method can also convert a complex time domain multiple wavefield into a simple frequency domain single wavefield. This feature enables easy interpretation of the results, and facilitates the precise evaluation of the location and size of structural damage or flaws. We demonstrated this capability by detecting a disbond in a sandwich structure made of Al-alloy skins and a foam core. A disbond with a diameter of 20 mm, which is representative of a common manufacturing flaw, was successfully detected, localized, and evaluated. Since a method to determine the allowable maximum pulse repetition frequency depending on target materials and structures was found by investigating the residual wave caused from the previous laser impinging, our laser ultrasonic system can scan rapidly the target with an optimal pulse repetition rate. In addition, the proposed wavelet-transformed ultrasonic propagation imaging method can visualize damage or flaw without the need for reference data from the intact state of the structure. Hence, we propose the wavelet-transformed ultrasonic propagation imaging approach for automatic inspection of in-service engineering structures, or in-process quality inspection in manufacturing.     

Faster 360° domain wall motion in nanostrip induced by spin-polarized current with out-of-plane magnetic field

By micromagnetic simulation, we show that faster propagation of 360° domain wall in magnetic nanostrips under spin-polarized currents in conjunction with out-of-plane magnetic fields can be obtained. Without magnetic field, the annihilation process of 360° domain wall is irreversible when spin-polarized current velocity above about 220 m/s. The annihilation of 360° domain wall can be suppressed by an out-of -plane magnetic field and domain wall speed can exceed 1500 m/s at large current density. This is different from the case exhibited in 180° domain wall. The underlying mechanism is investigated by changing the state of 360° domain wall and the direction of out-of-plane field.     

Scattering of focused ultrasonic beams by cavities in a solid half-space

The ultrasonic field generated by a point focused acoustic lens placed in a fluid medium adjacent to a solid half-space, containing one or more spherical cavities, is modeled. The semi-analytical distributed point source method (DPSM) is followed for the modeling. This technique properly takes into account the interaction effect between the cavities placed in the focused ultrasonic field, fluid-solid interface and the lens surface. The approximate analytical solution that is available in the literature for the single cavity geometry is very restrictive and cannot handle multiple cavity problems. Finite element solutions for such problems are also prohibitively time consuming at high frequencies. Solution of this problem is necessary to predict when two cavities placed in close proximity inside a solid can be distinguished by an acoustic lens placed outside the solid medium and when such distinction is not possible.     

Analytical methods for modeling of ultrasonic nondestructive testing of anisotropic media

Many modern structural materials exhibit anisotropic elastic behavior leading to complicated wave propagation phenomena. To ensure the reliability of ultrasonic nondestructive testing techniques, these material properties as well as the influence of microstructural inhomogeneities and the effects of interfaces on ultrasonic wave propagation have to be taken into account. In this respect, mathematical modeling provides an efficient method of assisting analysis. Two computationally efficient analytical approaches--a Gaussian beam and a point source superposition technique--are presented, which are well-suited for performing ultrasonic wave propagation and scattering simulations for anisotropic media. Results for homogeneous as well as inhomogeneous anisotropic media like composites and weld material are presented.     

An improved automated ultrasonic NDE system by wavelet and neuron networks

Despite of the widespread and increasing use of digitized signals, the ultrasonic testing community has not realized yet the full potential of the electronic processing. The performance of an ultrasonic flaw detection method is evaluated by the success of distinguishing the flaw echoes from those scattered by microstructures. So, de-noising of ultrasonic signals is extremely important as to correctly identify smaller defects, because the probability of detection usually decreases as the defect size decreases, while the probability of false call does increase. In this paper, the wavelet transform has been successfully experimented to suppress noise and to enhance flaw location from ultrasonic signal, with a good defect localization. The obtained result is then directed to an automatic Artificial Neuronal Networks classification and learning algorithm of defects from A-scan data. Since there is some uncertainty connected with the testing technique, the system needs a numerical modelling. So, knowing the technical characteristics of the transducer, we can preview which are the defects that experimental inspection should find. Indeed, the system performs simulation of the ultrasonic wave propagation in the material, and gives a very helpful tool to get information and physical phenomena understanding, which can help to a suitable prediction of the service life of the component.     

The field theory two-body problem in acoustics

We address the problem of determining effective equations of motion for sources in field theories, where finite propagation speeds lead to radiation reaction and runaway solutions. Acoustics is used to illustrate a solution of this problem: The effective equation of motion is obtained by reduction to an inertial manifold. This equation can be approximated to any desired accuracy by expansion (and truncation) in powers of the reciprocal of the wave propagation speed and reduction to a slow manifold of a singular perturbation problem. This research is supported by a grant from the National Science Foundation NSF DMS-0604331.