Ehsan Kabiri Rahani

Ultrasonic field modeling: a comparison of analytical, semi-analytical, and numerical techniques

Modeling ultrasonic fields in front of a transducer in the presence and absence of a scatterer is a fundamental problem that has been attempted by different techniques: analytical, semi-analytical, and numerical. However, a comprehensive comparison study among these techniques is currently missing in the literature. The objective of this paper is to make this comparison for different ultrasonic field modeling problems with various degrees of difficulty. Four fundamental problems are considered: a flat circular transducer, a flat square transducer, a circular concave transducer, and a point focused transducer (concave lens) in the presence of a cavity. The ultrasonic field in front of a finite-sized transducer can be obtained by Huygens-Fresnel superposition principle that integrates the contributions of several point sources distributed on the transducer face. This integral which is also known as the Rayleigh integral or Rayleigh-Sommerfeld integral (RSI) can be evaluated analytically for obtaining the pressure field variation along the central axis of the transducer for simple geometries, such as a flat circular transducer. The semi-analytical solution is a newly developed mesh-free technique called the distributed point source method (DPSM). The numerical solution is obtained from finite element analysis. Note that the first three problems study the effect of the transducer size and shape, whereas the fourth problem computes the field in presence of a scatterer.

Mechanical Damage Detection in Polymer Tiles by THz Radiation

Today the ultrasonic inspection technique is probably the most popular method for nondestructive evaluation and structural health monitoring. However, ultrasonic waves are not very effective in detecting internal defects in some materials such as ceramic foam tiles used in the thermal protection system (TPS) of the space shuttle, thick polymer composites, and polymer tiles used in various applications. Ultrasonic energy is attenuated very fast in these materials. On the other hand the electromagnetic radiation in THz (1000 GHz) frequency range can penetrate deep inside these materials. Its wavelength is small enough to detect internal defects. To understand the limits of structural damage detection capability of THz electromagnetic radiation or T-ray, mechanical damage in polymer tiles is introduced by drilling holes. Then T-ray is passed through the damaged and defect-free tiles. The received signal strength is found to be affected differently by the internal defect as the frequency changes. Experimental observations are justified from the model predictions. The model takes into account the interaction between the T-ray of finite width and the tile containing the internal defect.

Mesh-free modeling of the interaction between a point-focused acoustic lens and a cavity

Interaction between a cavity or void in a liquid and a converging ultrasonic beam generated by a point-focused acoustic lens is investigated. A semi-analytical technique called the distributed point source method (DPSM) is adopted because no analytical solution is available for this problem involving cavities of different size and the finite element method is not very efficient for modeling high-frequency ultrasonic problems. The solution shows that if the cavity is placed very close to the focal point of the lens then it can be detected by the acoustic lens. The detectability of the cavity at the off-focus position depends on the distance of the cavity from the focal point. The variation of this distance as the cavity moves in horizontal and vertical directions from the focal point is also investigated.

Modeling of transient ultrasonic wave propagation using the distributed point

Transient ultrasonic waves in a fluid medium generated by a flat circular and a point-focused transducer of finite size are modeled by the distributed point source method (DPSM). DPSM is a Greens-function-based semi-analytical mesh-free technique which is modified here to incorporate the transient loading from a finite-sized acoustic transducer. Conventional DPSM solves acoustic problems in steady-state frequency domain. Here, DPSM is extended to the time domain without the fast Fourier transform (FFT) but using the Greens function in the time domain. This modified method is denoted t-DPSM. Harmonic point sources of DPSM are replaced by time-dependent point sources in t-DPSM. Generated t-DPSM results are compared with the finite element (FE) results for both focused and flat circular transducers. The developed method is used to solve the transient problem of wave scattering by an air bubble in a fluid as the bubble is moved horizontally or vertically from the focal point of the focused transducer. The received energy signal is compared for different eccentricities.

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.

Wave guiding and wave modulation using phononic crystal defects

In this article, we address the effect of regular and irregular distribution of phononic lattices on acoustic wave and investigate wave bending and refraction phenomena for some specific patterns of phononic crystals consisting of a square array of polyvinylchloride cylindrical rods in air matrix using finite element model. Bucay et al. have demonstrated that for a given configuration, the striking acoustic beam angle varying between 20° and 40° at 14.1 kHz central frequency shows positive, negative, and zero angle refraction inside phononic crystal and exhibits beam splitting after exiting the phononic crystal. These results are used as the benchmark in this article to validate the proposed model. Transmission spectrum in the phononic crystal has been studied for complete acoustic band gap as well as for positive and negative dispersion bands at frequencies ranging from 1 to 18 kHz. Using this established theory, in this article, the acoustic beam propagation through irregular phononic crystal structures and waveguides are investigated. It can be seen that small irregularity produces significant change in the acoustic field. It is shown that with a localized defect, resonating cavity waveguide is formed in the proposed acoustic metamaterials.

Scattering of focused ultrasonic beams by two spherical cavities in close proximity

Ultrasonic fields generated by one and two spherical cavities placed in front of a point-focused acoustic lens are modeled by the semi-analytical distributed point source method (DPSM). Results are generated by properly considering the interaction effect between two cavities placed in the focused ultrasonic field. The interaction effect between the two cavities prohibits the linear superposition of single cavity solutions to obtain the solution for two cavities placed in close proximity. Therefore, although some analytical and semi-analytical solutions are available for the single cavity in a focused ultrasonic field, those solutions cannot be simply superimposed for solving the two-cavity problem even for a linear elastic material. Solution of this problem is necessary to evaluate when two cavities placed in close proximity can be distinguished by an acoustic lens and when it is not possible. The comparison between the reflections of ultrasonic energy from two small cavities versus a single big cavity is also investigated.

Heat induced damage detection in composite materials by terahertz radiation

In recent years electromagnetic Terahertz (THz) radiation or T-ray has been increasingly used for nondestructive evaluation of various materials such as polymer composites and porous foam tiles in which ultrasonic waves cannot penetrate but T-ray can. Most of these investigations have been limited to mechanical damage detection like inclusions, cracks, delaminations etc. So far only a few investigations have been reported on heat induced damage detection. Unlike mechanical damage the heat induced damage does not have a clear interface between the damaged part and the surrounding intact material from which electromagnetic waves can be reflected back. Difficulties associated with the heat induced damage detection in composite materials using T-ray are discussed in detail in this paper. T-ray measurements are compared for different levels of heat exposure of composite specimens.

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.

Distributed point source method and its applications in solving acoustic wave scattering problems

A recently developed semi-analytical technique called distributed point source method (DPSM) is used for solving various wave scattering problems. Scattering of focused ultrasonic fields by air bubbles or cavities in solid media is investigated here. Results for both single and multiple cavity geometries are presented. It is investigated when two cavities in close proximity can be distinguished and when it is not possible. The interaction effect between two cavities prohibits simple linear superposition of single cavity solutions to obtain the solution for the two cavities placed in close proximity. Therefore, although some analytical and semi-analytical solutions are available for the single cavity in a focused ultrasonic field, those solutions cannot be simply superimposed for solving the two-cavity problem even in a linear elastic material. The comparison between the ultrasonic energies reflected from two small cavities versus a single big cavity is also investigated.