Laszlo Adler

Reflection and refraction of elastic waves on a plane interface between two generally anisotropic media

A unified approach to the study of reflection and refraction of elastic waves in general anisotropic media is presented. Christoffel equations and boundary conditions for both anisotropic media in coordinate systems formed by incident and interface planes, rather than in crystallographic coordinates, are considered. Consideration of wave propagation in an acoustic‐axis direction is included in the general algorithm, so results can be obtained both generally and for planes of symmetry, including planes of isotropy. General features of the numerical results are discussed. Energy conversion coefficients are shown to satisfy reciprocity relations which are formulated. It is much more natural to consider intensity–conversion ratios, rather than amplitude–conversion ratios, showing the important role of ray (rather than wave‐vector) directions in describing phenomena such as grazing angles. In particular, it is shown that the incident wave vector for grazing incidence may be greater or less than 90°: The domain...

Reflection and transmission of elastic waves from a fluid‐saturated porous solid boundary

Based on the classical work of Biot [J. Acoust. Soc. Am. 28, 168 (1956)] which predicts that three different kinds of bulk waves may propagate in the fluid‐saturated porous solid, the wave equation is solved to determine the energy reflection and transmission coefficients of plane elastic waves at oblique incidence on an interface between a fluid and a fluid‐saturated porous solid. For this purpose, the necessary formalism of the energy equation, the Poynting energy flux vector, and the sound intensity of elastic waves in fluid‐saturated porous media are presented. Two general cases of mode conversion have been investigated: (1) The initial wave is incident from the fluid to the interface and generates three transmitted bulk waves in the fluid‐saturated porous solid, and (2) the initial wave is incident from the fluid‐saturated porous solid to the interface and generates three reflected bulk waves in the same medium. Furthermore, the transmission of sound through a fluid‐saturated porous solid plate immer...

Interaction of ultrasonic waves incident at the Rayleigh angle onto a liquid‐solid interface

The behavior of a Gaussian ultrasonic beam incident on a liquid‐solid interface at the Rayleigh angle, the angle at which surface waves are excited on the interface, has been studied in some detail. The reflected beam is displaced in the manner predicted by Schoch; however, the ’’Schoch displacement’’ in general is too large. Good agreement is obtained between experimental results and the theory of Bertoni and Tamir, which assumes that the incident beam couples resonantly into a leaky surface wave at the Rayleigh angle and that the energy reradiated from this leaky surface wave interferes with specularly reflected energy. The propagation distance of the ultrasonic beam is explicitly included in describing the ultrasonic wave reflection at the Rayleigh angle.

Real‐time study of frequency dependence of attenuation and velocity of ultrasonic waves during the curing reaction of epoxy resin

The frequency dependence of the phase velocity and attenuation of ultrasonic waves were measured as a function of time during the polymerization (curing) reaction of epoxy resins. The phase velocity and attenuation were evaluated from the amplitude and phase spectra of ultrasonic signals transmitted through a layer of curing epoxy resin. The measurements were made in the frequency range of 2–20 MHz. From the experimental data follows an important conclusion: The attenuation coefficient increases linearly with frequency at all stages of the curing reaction from the viscous liquid to the solid state. The slope of the attenuation coefficient as a function of frequency is strongly dependent on the time of cure (degree of cure). The linear behavior of attenuation versus frequency suggests that the attenuation effect cannot be explained by classical viscothermal absorption or relaxation theory. This type of behavior (so‐called hysteresis behavior) is poorly understood on the molecular level and was found previo...

Nondestructive evaluation of adhesive joints by guided waves

Guided waves in an adhesive layer between two adherend half‐spaces are shown to be uniquely sensitive to most types of bond defects. A simple experimental technique based on ultrasonic transmission mesurement is introduced to detect leaky guided modes in the interface layer. Experimental results for these dispersive guided modes are shown to be in good quantitative agreement with theoretical predictions. The suggested technique might find numerous applications in nondestructive evaluation of different bonds of layered structure such as adhesive and brazed joints.

Slow wave propagation in air‐filled porous materials and natural rocks

Slow compressional waves in fluid‐saturated porous solids offer a unique acoustical means to study certain material properties, such as tortuosity and permeability. We present a novel experimental technique based on the transmission of airborne ultrasound through air‐filled porous samples. The suggested method can be used to measure the velocity and attenuation of the slow compressional wave in a wide frequency range from 30 to 500 kHz. More important, the technique is so sensitive that it provides irrefutable evidence of slow wave propagation in air‐saturated natural rocks and lends itself quite easily to tortuosity measurements in such materials, too.

Determination of the Nonlinearity Parameter B/A for Water and m‐Xylene

The rate at which harmonics are developed during the propagation of an initially sinusoidal ultrasonic wave of finite amplitude depends on the nonlinearity of the compressibility of the medium. Thus, determinations of the harmonics as a function of propagation distance may be used to determine the parameter B/A (describing nonlinearity). A method which circumvents the effects of absorption in the medium is developed and used to determine the parameter B/A for water and m‐xylene. This method utilizes optical determinations of the second harmonic component of a distorted 3.0 Mc ultrasonic wave at various distances and initial pressure amplitudes. The second harmonic was isolated by use of a calibrated acoustic filter plate. The values obtained for the nonlinearity parameter are B/A = 6.2±0.6 for water and B/A = 9.6±1 for m‐xylene.

Surface roughness induced attenuation of reflected and transmitted ultrasonic waves

The problem of ultrasonic transmission and reflection at a randomly rough interface is considered in connection with ultrasonic NDE of rough surface samples by immersion method. A simple first‐order phase perturbation technique is used to calculate both transmitted and reflected components for comparison with experimental results. The transmitted wave is shown to be attenuated in a similar way to the reflected one, and their attenuation ratio is found to be independent of frequency in the considered cases of slight surface roughness. For instance, the surface roughness induced attenuation of the wave reflected from a water–aluminum interface is about seven times higher than that of the transmitted component. Experimental results are presented to show good agreement with calculated predictions of the suggested simple technique.

Diffraction of ultrasonic waves from periodically rough liquid–solid surface

Theoretical and experimental results concerning diffraction of ultrasonic waves on periodic liquid–elastic solid interfaces are presented. A general system of linear equations is established and solved numerically for triangular surfaces. Theoretical results are in good agreement with measurements obtained by a broadband pulse‐echo system in the region where the wavelength is of the same order of magnitude as the period and much greater than the depth of the grating. In the spectrum of the reflection coefficient frequency minima are identified as the surface waves excited along the periodic surface.

Ultrasonic method to determine gas porosity in aluminum alloy castings: Theory and experiment

The characterization of porosity in solids using the frequency dependence of the ultrasonic attenuation is discussed both from the theoretical and experimental viewpoint. The major thrust of our work is the determination of the volume fraction and size of the voids for the case of dilute porosity (<6%) in structural materials. An aluminum alloy (A357) was chosen for study due to its economic importance in large‐scale casting and the particular suitability of aluminum for this type of study. Following recent papers the attenuation is described by an independent scatterer model for spherical voids. Numerical results are presented in a form suitable for use with a range of materials. A method for determining the volume fraction and pore size is given. Specific tabular results are given for stainless steel, IN‐100, Ti, Si3N4, as well as aluminum. Figures of merit which partially describe those situations in which the method is usable are also presented. In the experimental work a digitized spectrum analysis s...