The propagation in metal tubing of ultrasonic wave modes equivalent to Lamb waves
TL;DR: In this article, it is shown that the L(0, 1) mode, which is comparable to the A0 Lamb wave mode in flat plate, can be generated with acceptable efficiency.
About: This article is published in Ultrasonics.The article was published on 1979-01-01. It has received 309 citations till now. The article focuses on the topics: Lamb waves & Ultrasonic sensor.
Citations
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TL;DR: The results indicate that Lamb waves may be used to find notches when the wavelength to notch depth ratio is on the order of 40, and the 2-D Fourier transform method is used to quantify Lamb wave interactions with defects.
Abstract: The interaction of individual Lamb waves with a variety of defects simulated by notches is investigated using finite-element analysis, and the results are checked experimentally. Excellent agreement is obtained. It is shown that a 2-D Fourier transform method may be used to quantify Lamb wave interactions with defects. The sensitivity of individual Lamb waves to particular notches is dependent on the frequency-thickness product, the mode type and order, and the geometry of the notch. The sensitivity of the Lamb modes a/sub 1/, alpha /sub 0/, and s/sub 0/ to simulated defects in different frequency-thickness regions is predicted as a function of the defect depth to plate thickness ratio and the results indicate that Lamb waves may be used to find notches when the wavelength to notch depth ratio is on the order of 40. Transmission ratios of Lamb waves across defects are highly frequency dependent. >
912 citations
TL;DR: In this article, the authors provide a vision of ultrasonic guided wave inspection potential as we move forward into the new millennium and provide a brief description of the sensor and software technology that will make ultrasonic guidance wave inspection commonplace in the next century.
Abstract: Ultrasonic guided wave inspection is expanding rapidly to many different areas of manufacturing and in-service inspection. The purpose of this paper is to provide a vision of ultrasonic guided wave inspection potential aswe move forward into the new millennium. An increased understanding of the basic physics and wave mechanics associated with guided wave inspection has led to an increase in practical nondestructive evaluation and inspection problems. Some fundamental concepts and a number of different applications that are currently being considered will be presented in the paper along with a brief description of the sensor and software technology that will make ultrasonic guided wave inspection commonplace in the next century.
623 citations
TL;DR: In this paper, the authors present a review of the studies of the propagation of the waves and their sensitivity to defects which have been conducted in order to provide a sound scientific basis for the method.
581 citations
TL;DR: In this article, the authors discuss the selection of the appropriate mode and frequency range for different inspection requirements and review the possible methods of excitation, response measurement and signal processing, and show that the presence of defects can be detected reliably from changes in the shape of the received waveform.
Abstract: Lamb waves can propagate over long distances which means that they are attractive for the quick, long range inspection of large structures, and they can also be useful for localized inspection, particularly in thin structures. This paper discusses the selection of the appropriate mode and frequency range for different inspection requirements and reviews the possible methods of excitation, response measurement and signal processing. It is usually desirable to transmit a single, non-dispersive mode, and excitation methods to achieve this are discussed. A variety of signal processing techniques from simple time domain to relatively complex two-dimensional Fourier analysis are available. Time domain processing can often be applied satisfactorily in low frequency-thickness regions where only two modes can propagate, but tends to be unreliable above the cut-off frequency of the a 1 mode. As an example of the design of a Lamb wave testing regime, a set of tests on a butt-welded steel plate with simulated weld defects of different depths is described. It is shown that by operating below the a 1 cut-off frequency with judicious selection of testing technique, the presence of defects can be detected reliably from changes in the shape of the received waveform.
371 citations
TL;DR: In this article, the reflection of the L(0, 2), axially symmetric guidea elastic wave from notches in pipes is examined, using laboratory experiments and finite element simulation.
Abstract: The reflection of the L(0, 2), axially symmetric guidea elastic wave from notches in pipes is examined, using laboratory experiments and finite element simulation The result show that the reflection coefficient of this mode is very close to a linear function of the circumferential extent of the notch, and is a stronger function of the through thickne depth of the notch. The motivation for the work was the development of a technique for inspecting chemical plant pipework, but the study addresses the nature of the reflection function and has general applicability.
292 citations
References
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TL;DR: In this article, the authors considered the problem of two-dimensional wave propagation in a solid bounded by parallel planes, and proposed a simple solution to the problem, which has no bearing on the questions referred to in this paper.
Abstract: The theory of waves in an infinitely long cylindrical rod was discussed by Pochhammer in 1876 in a well-known paper The somewhat simpler problem of two-dimensional waves in a solid bounded by parallel planes was considered by Lord Rayleigh and by the present writer‡ in 1889 The main object in these various investigations was to verify, or to ascertain small corrections to, the ordinary theory of the vibrations of thin rods or plates, and the wave-length was accordingly assumed in the end to be great in comparison with the thickness It occurred to me some time ago that a further examination of the two-dimensional problem was desirable for more than one reason In the first place, the number of cases in which the various types of vibration of a solid, none of whose dimensions is regarded as small, have been studied is so restricted that any addition to it would have some degree of interest, if merely as a contribution to elastic theory Again, modern seismology has suggested various questions relating to waves and vibrations in an elastic stratum imagined as resting on matter of a different elasticity and density These questions naturally present great mathematical difficulties, and it seemed unpromising to attempt any further discussion of them unless the comparatively simple problem which forms the subject of this paper should be found to admit of a practical solution In itself it has, of course, no bearing on the questions referred to
1,413 citations
TL;DR: In this paper, the propagation of free harmonic waves along a hollow circular cylinder of infinite extent is discussed within the framework of the linear theory of elasticity, and a characteristic equation appropriate to the circular hollow cylinder is obtained by use of the Helmholtz potentials for arbitrary values of the physical parameters involved.
Abstract: The propagation of free harmonic waves along a hollow circular cylinder of infinite extent is discussed within the framework of the linear theory of elasticity. A characteristic equation appropriate to the circular hollow cylinder is obtained by use of the Helmholtz potentials for arbitrary values of the physical parameters involved. Axially symmetric waves, the limiting modes of infinite wavelength, and a special family of equivoluminal modes are derived and discussed as degenerate cases of the general equations.
702 citations
TL;DR: In this article, the results of a numerical evaluation of a characteristic equation derived in Part I, appropriate to free harmonic waves propagated along a hollow cylinder of infinite extent, were given for some representative cylinders covering the entire range from thin shells to solid cylinders.
Abstract: The results are given of a numerical evaluation of a characteristic equation derived in Part I, appropriate to free harmonic waves propagated along a hollow cylinder of infinite extent. This equation is evaluated for some representative cylinders covering the entire range from thin shells to solid cylinders, and the results are compared with the corresponding results of a shell theory. Observations are made regarding the variation of the frequency spectrum with the physical parameters, as well as the range of applicability of shell theories.
329 citations
TL;DR: In this paper, a high speed computer was used to investigate the problem of wave propagation in an isotropic elastic cylinder, and an approximate solution was found for the L(0,1) mode impinging on a traction-free interface.
Abstract: A high‐speed computer was used to investigate the problem of wave propagation in an isotropic elastic cylinder. Dispersion curves corresponding to real, imaginary, and complex propagation constants for the symmetric and the first four antisymmetric modes of propagation are given. The radial distributions of axial and radial displacements and of shear and normal stresses are given for the symmetric mode. By using a finite number of modes of propagation, an approximate solution is found for the problem of the L(0,1) mode impinging on a traction‐free interface. The reflection coefficient is determined in this way and the accompanying generation of higher order modes at the interface is shown to cause a high‐amplitude end resonance. Experimental results obtained by using the resonance method in conjunction with a long rod are presented to substantiate the calculated reflection coefficient and the frequency of end resonance. Phase velocities, based on measurements of the wavelength of standing waves and resonance frequencies, were obtained for the symmetric and first two antisymmetric modes. These measurements extend into the frequency range of more than one propagating mode. The rms deviation between theoretical and experimental results is in general less than 0.2% with the exception of the dispersion curve for the L(0,2) mode which deviates by 0.7%.
264 citations