Fundamentals and analysis of lamb waves springerlink. On waves propagated along the plane surface of an elastic solid. In such instances some parts of the dispersion curves may exhibit features that resemble lamb wave plate wave patterns and not rayleigh wave, free rayleigh waves. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus. I a viktorov, rayleigh and lamb waves, plenum press, new york, 1967. Measurements of coupled rayleigh wave propagation in an. Rayleigh and lamb waves physical theory and applications. The phenomenon of continuous mode conversion of lamb. Achenbach 8, giurgiutiu 9, graff 10 and viktorov 11 considered lamb waves, which exists in an elastic plate with traction free boundaries. For what thickness of plate, rayleigh wave will become. Rayleigh and lamb waves at liquidsolid boundaries sciencedirect.
The rayleigh wave equation is involved in the solution of many elastodynamic problems. A detailed discussion of rayleigh and lamb waves can be found in the treatise by viktorov 1. Both rayleigh and lamb waves are constrained by the elastic properties of the. On waves propagated along the plane surface of an elastic. A nonlinear rayleigh wave approach is presented for nondestructive evaluation of material damage in this paper. However, we observed a continuous mode conversion in a multilayer composite plate. Numerous and frequentlyupdated resource results are available from this search. Rayleighlamb wave propagation on a fractional order. V rayleigh and lamb wavesphysical theory and applications, plenum press, new york, 1967. Ultrasonic guided waves in piezoelectric layered composite with different interfacial properties authors. Lamb waves occur in multiple modes, which can transform into each other under special conditions.
Viktorov, rayleigh and lamb waves, plenum press, new. Rayleigh waves are experimentally generated and detected with wedge transducers, and the nonlinear parameters are measured at different stress levels for az31 magnesium alloy plate specimen. Rayleigh waves are a type of surface acoustic wave that travel along the surface of solids. Wave propagation in an elastic plate is well known from lamb 6 classical work. Dynamics research group department of mechanical engineering, university of. Pdf on analyzing of the elastic surface wave in solid media. Therein lies my problem as it seems to be one of the rarest books out there. The rayleigh distribution can be used to model the lifetime of an object or a service time. Rayleigh waves have horizontal displacement and the motion of a point in the medium is an ellipse. Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. It was lord rayleigh in 1889 who first explained wave propagation along a guided surface 1, and the waves are known as rayleigh waves today. Wright 242s batra and kim 1992 studied the initiation and growth of.
Viktorov, rayleigh and lamb waves plenum, new york, 1967, pp. The wedge method of generating guided waves in isotropic layers was analyzed both theoretically and experimentally by viktorov et. Rayleigh waves are part of the seismic waves that are produced on the earth by earthquakes. The term rayleighlamb waves embraces the rayleigh wave, a type of wave that propagates along a single surface. The antecedent work on lamb waves is not hard to identify. Lamb wave theory is fully documented in a number of textbooks viktorov, 1967. Likewise, rayleigh waves attenuate exponentially with depth as the oscillating particles or atoms depart away from the lowdamping air interface. Full derivation of the helmholtz potential approach to the. Leaky rayleigh and scholte waves at the fluidsolid. Laser generation and detection of lamb waves in graphite. Physical theory and applications ultrasonic technology softcover reprint of the original 1st ed. Rayleigh waves are distinct from other types of surface or guided acoustic waves such as love waves or lamb waves, both being types of guided waves supported by a layer, or longitudinal and shear waves, that travel in the bulk.
Rayleigh waves have a speed slightly less than shear waves by a factor dependent on the elastic constants of the material. Buy this book softcover 103,99 price for spain gross buy softcover isbn 9781489956835. The main parts of the work were later reproduced in viktorovs now famous book on rayleigh and lamb waves 2. By experimental way, it is observed that there is a direct correlation between the acoustic. Lambtype waves generated by a cylindrical bubble oscillating. Rayleigh and lamb waves have the advantage that they prop agate far. Rayleighlamb wave from eric weissteins world of physics. Laser generation and detection of ultrasound has the obvious advantage of requiring no mechanical contact with the materials under investigation. The use of reflected rayleigh waves to study rough contact interfaces eng s ooi and r s dwyerjoyce leonardo centre for tribology and surface technology, department of mechanical engineering, university of sheffield, sheffield, uk abstract.
In reading this paper one is struck by the fact that, except for minor changes in notation, the formulation established by rayleigh is still followed today in the theory of. The use of reflected rayleigh waves to study rough contact. In recent years, the lamb wave analysis by the multichannel analysis of surface waves masw for concrete structures has been an effective nondestructive evaluation, such as the condition assessment and dimension identification by the elastic wave velocities and their reflections from boundaries. Backscattering enhancements associated with subsonic rayleigh waves on polymer spheres in water. Typically mode conversion takes place at discrete positions inside a structure, e. Exact expressions for the roots of the secular equation for rayleigh waves m. It appears in the denominator of reflection and conversion coefficients of longitudinal and transverse elastic waves and also in the solution of lambs problem for. Typically, lambwave patterns can be observed when there is a high velocity stiff layer at the top of your section.
So these two lamb waves appear to be simultaneously present in the plate, though s. Generation and detection of lamb waves for the characterization of. Physical theory and applications ultrasonic technology on. Physical theory and applications german hardcover january 1, 1967 see all formats and editions hide other formats and editions. Appl phvs 2 1973 157 7 derived from general equation given in ref. That is, a rayleigh wave launched on one surface gradually transfers to the other and then back. Lamb waves with particle displacement in both the x and ydirection actually represents a group. It gives the velocity of the wave propagating on the free surface of an isotropic halfspace. A comprehensive study of rayleigh waves and leaky rayleigh waves has been given by viktorov 1967. Lamb waves are the counterparts of rayleigh waves in thin samples with two free surfaces. Rahman department of mechanical engineering and applied mechanics, university of michigan, ann arbor, mi 481092125. Backscattering enhancements associated with subsonic. Analysis of the wedge method of generating guided waves. Critical strain ranking of 12 materials in deformations involving adiabatic shear bands r.
This study proposes an effective lamb wave analysis by the practical application of masw to. Nondestructive evaluation of material damage using. Rayleigh and lamb waves, plenum press, new york 1967 6 bertoni, h. Achenbach 8 presented lamb wave in an isotropic elastic. It is now a century since lord rayleigh published his theoretical proof of the existence of elastic waves propagating along the plane surface of an elastic solid 1. Viktorov has published extensively on the use of rayleigh and lamb waves in nondestructive testing and monitoring applications, and his book viktorov 1970.
Viktorov immersion inspection investigation lamb and rayleigh lamb waves layer thickness leigh wave liquid longitudinal and transverse longitudinal waves material. Design considerations for efficient wedge transducers h l bertoni. On the directivity of lamb waves generated by 2 wedge pzt. Lamb waves generation using a transducer embedded in a composite plate emmanuel moulin 1. Viktorov, 9781489956835, available at book depository with free delivery worldwide. Viktorov, rayleigh and lamb waves, plenum press, new york, ny, usa, 1967. Rayleigh probability density function matlab raylpdf. The simple lamb wave analysis to characterize concrete.
Following rayleighs work, horace lamb, a british applied mathematician, reported the waves discovered in plates in one of his historic publications, on waves in an elastic plate, in. In this thesis ultrasonic lamb wave measurements are performed to detect material. Y raylpdfx,b computes the rayleigh pdf at each of the values in x using the corresponding scale parameter, b. Lamb waves are formed by interference of multiple reflections and mode conversion of longitudinal waves pwaves and shear waves swaves at the free surfaces of the plate viktorov, 1967. They can be produced in materials in many ways, such as by a localized impact or by piezoelectric transduction, and are frequently used in nondestructive testing for detecting defects. Third, while rayleigh waves are essentially guided waves, as they inherently follow are guided by the contour of the surface, they differ from all other guided waves in that they are nondispersive. An improved approximation for the rayleigh wave equation.
Pdf this paper discusses mathematically the behaviour of the elastic waves that. Swindlehurst, university of sussex acoustic emission amplitudes a. Ultrasonic reflectometry is commonly used in the field of tribology. Lamb waves with particle displacement in both the x and ydirection actually represents a group of wave types including the bending wave, the rayleigh wave, and the quasilongitudinal wave. Find all the books, read about the author, and more. Exact expressions for the roots of the secular equation. X and b can be vectors, matrices, or multidimensional arrays that all have the same size, which is also the size of y. In an elastically isotropic semiinfinite medium having a free surface with a weak harmonic corrugation, the interaction between the rayleigh wave guided along the free surface and the shear vertical and pressure bulk elastic waves propagating in the substrate is investigated for the propagation directions lying in a plane perpendicular to the average free surface and containing the grating vector. Lamb 1917 derived the dispersion equation that can handle the transitions between these types of waves. A scalar input for x or b is expanded to a constant array with the same dimensions as the other input the rayleigh pdf is. Of several detailed observations made in these investigations, one was that. The effect of mode conversion of lamb waves is a well known phenomenon. I have been told to get myself a copy of rayleigh and lamb waves. Articles from the journal of the acoustical society of america are provided here courtesy of acoustical society of america.
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