Abstract-
In this paper, the method of wave function expansion is adopted to study the scattering of a plane harmonic acoustic wave incident upon an arbitrarily thick-walled, functionally graded cylindrical shell submerged in and filled with compressible ideal fluids. A laminate approximate model and the so-called state space formulation in conjunction with the classical transfer matrix (T-matrix) approach, are employed to present an analytical solution based on the three-dimensional exact equations of elasticity. Three models, representing the elastic properties of FGM interlayer are considered. In all models, the mechanical properties of the graded shell are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials across the thickness of the shell. In the first two models, the rule of mixture governs. The main difference between them is the set of elastic constants (e.g., Lame’s constants in model I and Young’s modulus and Poisson’s ratio in Model II) which are governed by the rule of mixtures. In the third model, an elegant self-consistent micromechanical model which assumes an interconnected skeletal microstructure in the graded region is employed. Particular attention is paid to backscattered acoustic response of these models in a wide range of frequency and for different shell wall-thicknesses. The results reveal a technical comparison between these models. In addition, by examining various cases (i.e., different shell wall-thicknesses, various profiles of variations and different volume concentration of constituents), the impact of the overall volume concentration of constituents and also the profile of variations, on the resonant response of the graded shell is investigated. Limiting cases are considered and good agreement with the solutions available in the literature is obtained.Abstract-
A body insonified by a sound field is known to experience a steady force that is called the acoustic radiation force. In this paper, the method of wave function expansion is adopted to study the scattering and the radiation force function caused by a plane normal harmonic acoustic wave incident upon an arbitrarily thick-walled functionally graded cylindrical shell submerged in and filled with compressible ideal fluids. A laminate approximate model and the so-called state space formulation in conjunction with the classical transfer matrix (T-matrix) approach are employed to present an analytical solution based on the two-dimensional exact equations of elasticity. Two typical models, representing the elastic properties of FGM interlayer, are considered. In both models, the mechanical properties of the graded shell are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials across the thickness of the shell. In the first model, the simple rule of mixture governs. In the second, an elegant self-consistent micromechanical model which assumes an interconnected skeletal microstructure in the graded region is employed. Particular attention is paid on dynamical response of these models in a wide range of frequency and for different shell wall-thicknesses. In continue, by focusing on the second model, the normalized radiation force function and the form function amplitude are calculated and compared for different shell wall thicknesses and various profile of variations. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.
Abstract-Ultrasonic tests were performed in the main directions at 300 kHz in poplar and spruce reaction wood and normal wood. The experiments were conducted on 2x2x10 cm3 specimens selected from the pith to the bark. The same phase velocity values were measured in poplar tension wood and normal wood. In compression wood, the phase velocity was lower in the longitudinal direction and higher in the transverse direction. The group velocity measured in the longitudinal direction in tension wood was greater than in normal wood, but lower values were obtained in compression wood in comparison to those obtained in normal wood. The results showed that wave attenuation cannot be significantly affected by the structural properties of reaction wood. A better wave energy transfer pathway (RMS voltage) was found in poplar and spruce reaction wood than in normal wood. Acoustic radiation in reaction wood of both species was lower than levels obtained in normal wood in all anisotropic directions. The results obtained when comparing reaction wood and normal wood of both species indicated that sound velocity decreased as moisture content increase, but the attenuation coefficients increased slightly.
Abstract-Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675–682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka ≤ 0:1. The incidence angle αc at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka ≤ 0:1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.
Abstract-In recent years, much attention has been paid to the use of Lamb waves for structural health monitoring. This choice is prompted by the high speed of Lamb wave inspection, although their dispersive nature can complicate the interpretation of results, especially when dealing with closely-spaced reflectors. In this paper, the objective is to improve the time resolution and signal-to-noise ratio of signals obtained from inspection of plates by the S0 Lamb mode. The signal processing scheme used is based on deconvolution of the measured signal by Wiener filtering, followed by autoregressive spectral extrapolation. The deconvolution technique is applied to signals obtained from finite element models and also to experimentally measured signals; both sets of data are based on plates with various types of notch discontinuities. Using this technique, the separation distance between adjacent notches was estimated with high accuracy in both simulated and experimental ultrasonic signals.
Abstract
-The study of the interaction of acoustic waves with cylindrical structures has numerous applications including the ultrasonic nondestructive testing of materials. In this paper, using a new mathematical model presented for the scattering of obliquely incident plane acoustic waves from a grating of immersed cylindrical shells, a detailed study of the resonant interaction of A-wave resonances originating from the shells is conducted. The nature of A-wave resonances and the effect of center-to-center distance of the shells on these resonances are examined. It is observed that this resonant interaction not only results in the splitting of A-wave resonances, but also causes an increase in resonance amplitudes. This interaction phenomenon is not seen in Rayleigh, whispering gallery and guided wave resonances. It is also shown that increasing the angle of wave incidence to the grating weakens the A-wave resonant interactions. The numerical results obtained from the mathematical model are compared to experimental results available in the literature for gratings composed of two and three aluminum shells. The numerical results are in very good agreement with their experimental counterparts.Abstract
-Ultrasonic testing of austenitic welds prepared by two different welding processes is studied in this paper. The two welding processes considered are shielded metal arc welding (SMAW) and gas tungsten arc welding (GTAW) and the ultrasonic testing technique used is time-of-flight diffraction (ToFD). Identical artificial flaws were implanted in both welds during the welding process. Austenitic characteristics consisting of grain orientation distribution and anisotropy show that the GTAW specimen is more isotropic than the SMAW due to the orientation of its grains. Moreover, comparison of echo amplitudes shows higher attenuation for the weld prepared by the GTAW process. The specimens were examined by the ultrasonic ToFD technique under identical conditions. B-scan images obtained from ToFD measurements of the two welds indicate that inspection of the specimen prepared by the SMAW process is easier than the one made by the GTAW process due to higher scattering of waves in the latter. The measurements also showed that the probe positioning is very important in the detection of diffracted echoes when using the ToFD technique.
Abstract-A signal processing technique is presented for significantly sharpening the resolution of ultrasonic images, similar to those acquired in the nondestructive evaluation of girth welds in oil/gas pipelines. This enhancement allows a much improved estimate of the exact size of any detected anomaly in the weld, such that fracture mechanics can be used to gauge the probability of weld failure. The algorithm is based on the synthetic aperture focusing technique (SAFT), combined with a variation of Wiener filtering and autoregressive spectral extrapolation. An analytical model of the transducer is used to construct an appropriate reference spectrum for the deconvolution operation, and accounts for the dependence of a beam’s frequency spectrum on the position of a flaw relative to the transmitter. Experimental results are used to provide an estimate of the improvement in flaw sizing accuracy.
Abstract-This paper considers the scattering of an infinite plane acoustic wave from a long immersed, solid, transversely isotropic cylinder. The mathematical model which has already been developed for this problem does not work in the case of a normally incident wave. Modifications to the mathematical model are proposed in order to make it applicable to all incidence angles, including α = 0. Numerical results are used to demonstrate the correctness of the modified equations. Moreover, using a mathematical discussion, it is shown that at normal incidence, the whole displacement field is constrained within the isotropic plane of the cylinder (cylinder cross section) and only the two elastic constants characterizing this plane appear in the remaining equations. A perturbation study on the five elastic constants of the transversely isotropic cylinder confirms this result.
Abstract-This paper discusses the use of pulse-echo ultrasonic testing for nondestructive evaluation of adhesive bonds of thin metal sheets (less than 1 mm) in which the thicknesses of the adhesive layer and the metal sheets as well as the acoustical properties of the adhesive are unknown. The aims of ultrasonic inspection of adhesive joints are to assess the integrity of the front (interface close to the interrogating transducer) and rear adherent/adhesive interfaces. To achieve these goals, accurate estimation of the reflectivity is required. In this study, a model-based approach was applied to signals obtained from adhesively bonded joints in order to estimate their reflectivity. The transducer wavelet was modeled by Gaussian echoes and the reflectivity, i.e. the desired system response, was estimated by using the expectation maximization (EM) algorithm. The decay rate of reverberations in the front metal sheet calculated from the estimated amplitudes of the sequence was used as a basis for detection of disbond and anomalies such as presence of grease or water in the front interface. By applying the proposed method, we were able to detect void-disbond and presence of wrong materials such as grease and water in the front interface of a joint made by 0.5 mm thick aluminum plates. Disbond in rear interface of this joint was also detected by examining the phase inversion of the echo reflected from the rear interface.
Abstract-Ultrasonic measurements have been used to characterise the solutionising phenomenon in Rene 80, a Ni based superalloy. Starting material was solutionised at 1204°C for 30–120 min on identical samples. The microstructures of these samples were evaluated by ultrasonic immersion technique, X-ray diffraction and scanning electron microscopy. It was observed that the area fractions and, consequently, the γ' volume fractions were decreased by increasing the solutionising time. A direct correlation was observed between ultrasonic wave velocity and solutionising time at 1204°C. The ultrasonic compression wave velocity followed a descending pattern similar to that of γ' area fraction with the increase in solutionising time. The observed variation in ultrasonic velocity has been attributed to the effect of the γ' dissolution on the elastic constants of the material
Abstract-In this paper, an elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson’s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler’s equation and the dynamic solution is derived by utilizing the separation of variables method and the orthogonal expansion technique. Radial displacement and stress distributions are plotted for various FGM hollow cylinders under different dynamic loads and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of FGM hollow cylinders of arbitrary thickness and arbitrary initial conditions which are subjected to arbitrary form of dynamic pressures distributed uniformly on their boundary surfaces.
Abstract-Various destructive and non-destructive testing techniques have been used for testing the joint quality in adhesive bonding. Ultrasonic testing has proven to be one the most efficient methods for this purpose. Among the many different ultrasonic testing techniques, C-scan imaging seems to be the most efficient for testing adhesive joints. In this paper, new testing schemes are proposed for extraction of the required information from the ultrasonic signals acquired in a C-scan imaging process. Three different indices, which are based on the amplitudes of the ultrasonic radio frequency signals, are introduced. Compared to the gating and peak detection approach used in conventional ultrasonic C-scan imaging, these indices provide much more information about the quality of the bonding in an adhesive joint. Moreover, while only one side of the adhesive layer can be tested in conventional C-scan imaging, the new technique makes the testing of both sides of the adhesive possible with scanning performed on one side of the specimen. Furthermore, in the case of very thin samples, where the returned echoes are not separable and, hence, no C-scan images can be generated, the new technique works quite well. The capability of the proposed approach in providing C-scan images from a number of samples, some of the which are considered not to be testable by conventional ultrasonic testing techniques, is demonstrated.
Abstract-This paper presents an approach for obtaining the exact frequency equations of axisymmetric and asymmetric free vibrations of transversely isotropic circular cylinders. The solution method is based on the three dimensional theory of linear elasticity and uses potential functions. Using this approach, the frequency spectra and vibration mode shapes are plotted for a number of transversely isotropic cylinders. The proposed approach introduces a number of merits compared to earlier approximate and exact solution methods. First, unlike numerically complicated series methods that provide approximate solutions, the proposed approach is exact. Second, combination of scalar functions employed for representing the displacement field is consistent with the physics of the problem. One scalar potential function has been considered for each component of the wave field inside the elastic cylinder. As a result, the solution is systematically divided into coupled and decoupled equations. In addition, by using this approach, there is no need to guess the final of the solution a priori. These merits make the proposed approach suitable for other vibration problems of anisotropic materials.
Abstract-Solving the frequency equation and plotting the dispersion curves in problems of wave propagation in cylinders and plates, particularly when the material is anisotropic, are complicated tasks. The traditional numerical methods are usually based on determination of the zeros of the frequency equation by using an iterative find-root algorithm. In this paper, an alternative method is proposed which extracts the solution of the frequency equation in the form of dispersion curves from the three-dimensional illustration of the frequency equation. For this purpose, a three-dimensional representation of the real roots of the frequency equation is first plotted. The dispersion curves, which are the numerical solutions of the frequency equation, are then obtained by a suitable cut in the velocity–frequency plane. The advantages of this method include simplicity, high speed, low possibility of numerical error, and presentation of the results in a graphical form that promotes ease of interpretation. This method is not directly applicable to problems which incorporate high damping or leaky waves. However, if the damping is not very high, it could be a good estimate of the true dispersion curves.
Abstract-An investigation on the dimensional properties of plain knitted fabric produced from cotton yarn and subjected to different relaxation treatments is presented in this paper. The main aim of this research is to characterize the internal energy of fabric by using yarn-pullout test method in ultrasonic relaxation state and compare it with other common mechanical relaxation treatments. A comprehensive experimental analysis showed that, by using ultrasonic waves, the area geometry constant value (ks) achieved was higher than the conventional relaxation methods. Then, we introduced residual-energy forming and loss-energy uniforming. The former appeared due to fabric shrinkage and the later one appeared due to release of fabric loops from extra forces which imposed during knitting process. The results also indicated that ultrasonic waves energy causes more uniformity on loop and consequently, the fabric reaches to a less internal energy than washing treatment.
Abstract-The ultrasonic nondestructive evaluation of composite cylinders requires a thorough under standing of the propagation of waves in these materials. In this paper, the propagation of flexural and longitudinal guided waves in fiber-reinforced composite (FRC) rods with transversely isotropic symmetry properties is studied .The frequency equations obtained for free cylinders and the effect of in creased fiber volume fraction (increased anisotropy) on the dispersion character is tics of the rod are explored. The numerical results reveal a number of previously un noticed characteristics of dispersion curves for composite cylinders. The mode shapes of longitudinal waves prop a gating in glass/epoxy cylinders are also plotted. These plots can be used to choose an appropriate strategy for inspecting composite cylinders by ultrasonic nondestructive evaluation techniques.
Abstract-Various approaches have been used for model1ing problems dealing with interaction of acoustic/elastic waves with transversely isotropic cylinders. The authors developed the first mathematical model for the scattering of acoustic waves from transversely isotropic cylinders [Honarvar, F., Sinclair, A.N., 1996. Acoustic wave scattering from transversely isotropic cylinders. Journal of the Acoustical Society of America 100, 57–63.]. In the current paper, this model is used for derivation of the frequency equations of longitudinal and flexural wave propagation in free transversely isotropic cylinders. Consistency of this model with the physics of the problem is demonstrated and a systematic solution to the corresponding equations is developed. Numerical results obtained for a number of transversely isotopic cylinders are used for verification of the mathematical model.
Abstract-Ultrasonic testing signals are sometimes hard to interpret because of low signal-to-noise ratio (SNR) or overlapping echoes. The combination of Wiener filtering and autoregressive spectral extrapolation has proven to be capable of improving the SNR and time resolution. However, these signal processing techniques are not sufficiently robust to be used in industrial non-destructive testing applications. This is mostly due to arbitrary manner of selection of the signal processing parameters associated with these techniques. In this paper, a new approach, which eliminates the need for arbitrary assignment of some of the parameters is described. This new approach is more robust and suitable for practical applications, and is demonstrated by considering both simulated and experimental signals.
Abstract-A resonance acoustic spectroscopy technique is assessed for nondestructive evaluation of explosively welded clad rods. Each rod is modeled as a two-layered cylinder with a spring-mass system to represent a thin interfacial layer containing the weld. A range of interfacial profiles is generated in a set of experimental samples by varying the speed of the explosion that drives the copper cladding into the aluminum core. Excellent agreement is achieved between measured and calculated values of the resonant frequencies of the system, through appropriate adjustment of the interfacial mass and spring constants used in the wave scattering calculations. Destructive analysis of the interface in the experimental specimens confirms that key features of the interfacial profile may be inferred from resonance acoustic spectroscopy analysis applied to ultrasonic measurements.
Abstract-A mathematical model for the scattering of acoustic waves from immersed transversely isotropic cylinders was developed by the authors [J. Acoust. Soc. Am. 100, 57 (1996)]. Ahmad and Rahman further elaborated on the mathematical aspects of this model and based on mathematical discussions showed that there exist two distinct types of transversely isotropic materials, which they named type I and type II [Int. J. Eng. Sci. 38, 325 (2000)]. They also described the expected behavior of the form functions of such materials. The purpose of this article is to distinguish the physical differences between these two types of transversely isotropic materials.
Abstract-When an immersed solid elastic cylinder is insonified by an obliquely incident plane acoustic wave, some of the resonance modes of the cylinder are excited. These modes are directly related to the incidence angle of the insonifying wave. In this paper, the circumferential resonance modes of such immersed elastic cylinders are studied over a large range of incidence angles and frequencies and physical explanations are presented for singular features of the frequency-incidence angle plots. These features include the pairing of one axially guided mode with each transverse whispering gallery mode, the appearance of an anomalous pseudo-Rayleigh in the cylinder at incidence angles greater than the Rayleigh angle, and distortional effects of the longitudinal whispering gallery modes on the entire resonance spectrum of the cylinder. The physical explanations are derived from Resonance Scattering Theory (RST), which is employed to determine the interior displacement field of the cylinder and its dependence on insonification angle.
Abstract-The principles of resonance acoustic spectroscopy (RAS) are applied to large-grained transversely isotropic copper rods, produced by the Ohno continuous casting process. It was determined that certain resonance frequencies and associated mode shapes are primarily dependent on cross sectional-averaged material properties, and are relatively independent of grain size below a critical value. However, for cases where the average grain cross sectional diameter is greater than 10% of the ultrasonic wavelength, it was found that the resonance spectrum is significantly distorted from its theoretical profile. This indicates that RAS could be applied in an on-line setting for non-destructive characterization of the grain structure. For smaller-grained samples produced at relatively high casting speeds, a series of resonance measurements can be used to determine four of the five independent elastic constants, with an estimated uncertainty of 1–2%.
Abstract-A mathematical model is developed to describe the scattering of a plane wave incident at an arbitrary angle on a transversely isotropic cylinder embedded in a solid elastic matrix. The model is based on the normal-mode expansion method, but is complicated by the coupling between the potential functions representing compressional and axially polarized shear waves. The solid matrix around the cylinder precludes the appearance of the leaky Rayleigh modes that dominate the spectrum of a cylinder immersed in a fluid. Instead, interfacial modes contribute to the scattered spectrum—these modes could be instrumental in the development of a nondestructive evaluation technique for the matrix-to-fiber bonds in a fiber-reinforced composite material. The presence of a solid matrix that supports shearing action leads to scattered compressional waves, and shear waves with polarization components in both the axial direction and r-u planes. The sensitivity of resonances in each of these scattered wave components to perturbations in the cylinder’s elastic constants is explored; results indicate that a judicious selection of resonance modes allows characterization of the cylinder’s elastic properties.
The authors comment on Rahman and Ahmad’s discussion on the representation of displacement fields by scalar potential functions.
Abstract-Examples of the applications of resonance acoustic spectroscopy (RAS) for the purposes of the non-destructive evaluation (NDE) and on-line monitoring of the properties of various cylindrical components are presented in this paper. The mathematical equations for the scattering of a plane acoustic wave from isotropic and transversely isotropic cylinders and isotropic clad rods are reviewed. A new technique called material characterization by resonance acoustic spectroscopy (MCRAS), for the evaluation of the elastic constant of isotropic rods and wires, is introduced. This new technique is compared to the traditional time-of-flight measurement technique. Possible applications of RAS in NDE and on-line monitoring of clad rods are demonstrated using practical examples. The possibility of using RAS for evaluation of axial and transverse properties of fiber-reinforced composite wires and rods, which are transversely isotropic in nature, is discussed. The results indicate that RAS can be used as a tool for NDE and on-line monitoring of various properties of cylindrically-shaped components.
Abstract-Statistical moment analysis has proven to be a very effective technique for diagnosis of rolling element bearings. The fourth normalized central statistical moment, kurtosis, has been the major parameter in this method. In this paper it will be shown that the third normalized statistical moment can be as effective as kurtosis if the data is initially rectified. The advantage of this moment over the traditional kurtosis value is its lesser susceptibility to spurious vibrations, which is considered to be one of the shortcomings of higher statistical moments including kurtosis. The sensitivity of this moment to changes of load and speed is also less than kurtosis. The proposed method can also be applied to higher odd statistical moments.
Abstract-The problem of scattering of an obliquely incident plane acoustic wave from an infinite solid elastic clad rod is formulated. Numerical calculations show the effects of the variations of the cladding thickness on both the backscattered pressure spectrum and individual normal modes. It is shown that various resonance frequencies have different levels of sensitivity to variations of the cladding thickness. Experimental measurements are also performed at both normal and oblique incident angles on a copper-clad aluminum rod; good agreement is observed between the calculated and the measured results. These results demonstrate the potential of acoustic resonance scattering procedures for application in nondestructive evaluation (NDE) of clad rods.
Abstract-Mathematical expressions are derived for the far-field backscattering amplitude spectrum resulting from oblique insonification of an infinite, transversely isotropic elastic cylinder by a plane acoustic wave. The normal-mode solution is based on decoupling of the scalar potential representing the horizontally polarized shear wave from those of the compressional and vertically polarized waves. The solution degenerates to the well-known simple model for isotropic cylinders in the case of very weak anisotropy. The solution is used to study the influence of each element of the stiffness matrix on the various resonant modes of vibration. Perturbations of the elements c33 and c44 , which characterize the cylinder along the axis, significantly affect resonant frequencies corresponding to axially guided waves. Perturbations of c11 and c12 , which characterize the material on the transverse plane, predominantly affect the Rayleigh and Whispering Gallery resonance frequencies. Perturbations of c13 affect all three types of resonances. These results are consistent with elasticity theory and the known modal shapes of these resonances.
Abstract-Failure of rolling element bearing plays a significant role in the breakdown of industrial machinery. However, the analysis of signals resulting from measurement taken from outer casing of equipment has proven to be an effective and powerful tool for the early detection of failure in bearing. Although a number of techniques have been developed over the years directed at warning of impending failure, in most cases these methods are only effective in the later stages of damage development. This paper looks at variations of the statistical moment analysis method that show potential for damage detection at a much earlier stage. This approach has several independent of load and speed. Data for the analysis is relatively easy to collect using an accelerometer mounted near the bearing of interest and can then be processed on a micro-computer using suitable software. An important part of the processing is separating out unwanted data from other energy sources within the machine. This is achieved by developing selective digital filtering within the software. In this paper data from damaged and undamaged bearings are compared on the basis of analysing both rectified and unrectified signals.