Leaky Rayleigh Wave Research Articles

Exact treatment of leaky Rayleigh waves in the presence of a layer

An exact theory, supported by experimental measurements, of bounded acoustic‐beam reflection near the Rayleigh angle from a fluid‐solid interface loaded by a solid layer is presented. We derive an analytical expression for the reflection coefficient by applying continuity conditions appropriate for the problem geometry to wave potentials in the three media. The reflected field, including leaky Rayleigh‐wave effects, is calculated by evaluating numerically the Fourier integral containing the incident beam transform and the reflection coefficient. The dispersion of the Rayleigh wave speed is deduced from the behavior of the reflection coefficient in the complex plane. We find excellent agreement with measurements of the wave speed over a wide range of frequency and layer thickness in stainless steel samples loaded with copper layers. The beam displacement parameter, which is also deduced from characteristics of the reflection coefficient, displays an unexpected minimum as a function of frequency. Experimental results are compared to theory for the acoustic amplitude distribution in the reflected field, both near and at the Rayleigh angle.

Fringe pattern around surface crack observed with scanning acoustic microscope

A surface crack of MgO single crystal was observed with a scanning acoustic microscope and a fringe pattern was found around the cracking line. A model was proposed in which a leaky Rayleigh wave reflected by the crack plays an essential role in the formation of the fringe pattern.

Restrictions on the Existence of Leaky Rayleigh Waves

Restrictions on the Existence of Leaky Rayleigh Waves

Generation of ultrasonic leaky waves at liquid-solid interfaces

Recent experimental investigations by M. A. Breazeale, L. Adler, and G. W. Scott [J. Appl. Phys. 48, 530–537 1977)] have verified the theory of Bertoni and Tamir [Appl. Phys. 2, 157–172 (1973)]. Excitation of leaky Rayleigh waves takes place at the liquid-solid interface when a Gaussian ultrasonic beam is incident at or near the Rayleigh angle to the interface. Now we should like to report two additional examples of leaky wave generation: (1) When a thin (less than a wavelength) ceramic layer is added to a metal surface, leaky waves are generated. The velocity and amplitude distribution of these waves will be discussed. (2) For interfaces such as water-Plexiglas no real solution of the leaky Rayleigh velocity exists since the sound velocity in the water is larger than the shear velocity in Plexiglas. By studying the reflection of an incident Gaussian beam from water-Plexiglas interfaces we have observed leaky waves near the longitudinal critical angle. Similar observations were made at water-sediment interfaces. [M. A. Breazeale and L. Bjørnø, Proc. Ultrasonics Int., 1977, pp. 440–444]. [Research supported in part by the Office of Naval Research.]

Ray interpretation of the material signature in the acoustic microscope

The output voltage of the reflection acoustic microscope depends on the location on the object surface in a way that is characteristic of its elastic properties. We present a ray model showing that this dependence is due to interference between a narrow bundle of axial rays and rays associated with the leaky Rayleigh wave excited on the surface.

Investigation of the conditions for the existence of a leaky Rayleigh wave

The Rayleigh wave, an inhomogeneous surface wave, exists for all isotropic elastic solids. When the free surface of the solid is bounded by a liquid, a leaky Rayleigh wave, or inhomogeneous damped interface wave, may exist. In the limit that the density of the liquid goes to zero, the leaky Rayleigh wave tends to the free Rayleigh wave. However, the leaky Rayleigh wave does not exist for all liquid/isotropic solid systems. A well‐known condition for the existence of the leaky Rayleigh wave is that the velocity of sound in the liquid must be less than that of the shear in the elastic solid. Upon investigation of the secular equation for the leaky Rayleigh wave velocity, other necessary conditions for existence become apparent. The conditions are influenced by the density ratio and the ratios of the various velocities in the liquid/solid system. [Work supported by ONR.]

Unified theory of Rayleigh-angle phenomena for acoustic beams at liquid-solid interfaces

Various phenomena have been observed when a bounded acoustic beam is incident from a liquid onto the surface of a solid at or near the Rayleigh angle. These phenomena include: a shift of the reflected beam from the position predicted by geometrical acoustics, a null or minimum of intensity within the reflected beam, a 180° phase reversal of the field on either side of the null, a weak trailing field on only one side of the reflected beam and a frequency of least reflection when the solid is lossy. By carefully examining the reflection coefficient for angles in the vicinity of the Rayleight angle, and by taking into account the angular spectrum of plane waves that comprise a bounded beam, a model of the reflection process is developed that explains all of the observed phenomena. This model shows that the various critical-reflection effects result from the interference between a geometrically reflected field and the field of a leaky Rayleigh wave, which is excited by the incident beam. Moreover, this model resolves the conflict between various explanations made for these phenomena in the past; in particular, it is found that Schoch's classical description of a laterally displaced reflected beam is valid only for beams having a large width.

Microwave Network Methods for Guided Elastic Waves

The possibility of obtaining true microminiaturization by the use of elastic wave circuitry on solids is hampered by the lack of knowledge regarding the behavior of the constituents of those circuits. Since boundary value problems involving elastic waves in solids are generally very intricate and difficult to solve, a direct frontal attack on those problems will in many cases lead to frustration. In this paper, a series of steps is outlined which avoids the frontal attack and lends itself to a systematic procedure for achieving the understanding sought. It involves the application of concepts and techniques of proven value in electromagnetic microwaves to corresponding categories of problems in elastic guided waves. To demonstrate the value of this approach, it is used to derive the properties of several well-known types of elastic wave on layered media, such as Rayleigh surface waves, leaky Rayleigh waves, Lamb waves, and Love waves. In the building-block approach employed, the results derived separately include transmission-line models for body waves in fluids and isotropic solids, with expressions for the characteristic impedances and the velocity and stress vector mode functions, and equivalent networks for several types of interface which are constituents of the layered media mentioned above. The propagation properties of the guided waves are then obtained by the use of the transverse resonance procedure in a systematic, simple, and direct fashion.