Elastic Resonance Research Articles

Force constant and effective mass of 90° domain walls in ferroelectric ceramics

Domain wall contributions to the dielectric, piezoelectric, and elastic properties of tetragonal ferroelectric ceramics, as discussed extensively in the past, are calculated. A simple model shows that the motion of 90° domain walls causes a shear deformation and an approximately homogeneous electric field in the grain. The elastic and electric field energies involved allow the calculation of the force constant for the domain wall displacement by external fields. The displacements agree with experimental results. In a moderate electric field the displacement is a small fraction of the lattice cell only. By averaging over the orientational distributions of all grains the contributions of the 90° domain walls to the material properties are calculated for unpolarized and for polarized ceramics and agree with experimental results. The effective mass, which has to be attributed to the domain walls is the mass of the whole grain reduced by the factor S0 (spontaneous deformation), is independent of the domain width. The resonance frequency of the domain walls therefore is lower than the elastic resonance frequency of the grain.

Directionally Coupled Vibration of a Two-Dimensional Actuator for CD Players.

Directionally coupled vibration, referred to as "cross action" was analyzed to improve positioning accuracy in CD and CD-ROM optical pick-up systems having two-dimensional motion, i. e., autofocus and tracking directions. Cross action is defined as the secondary movement of the pick-up in the tracking direction when actuated to move in the autofocus direction. The main cause of cross action is found to be elastic resonance of the thin plate in the pick-up support. Assembly error is also found to amplify cross action. Optimum values for the support configuration were obtained by FEM and lumped mass vibration analyses.

Complex resonance frequencies in acoustic wave scattering from impenetrable spheres and elongated objects

Complex resonance frequencies of impenetrable (rigid or soft) elongated objects, namely, spheroids and cylinders with hemispherical endcaps, including the spherical limit of the latter, are studied. Complex resonance frequencies are obtained from the principle of phase matching of surface waves. Substantial differences are found between the two mentioned objects, and are explained physically. For the case where the surface waves are generated by plane acoustic waves at broadside incidence, the simultaneous presence of cylindrical circumferential‐wave resonances and of the resonances of meridionally propagating surface waves is discussed; this effect is also known from the observation of elastic surface wave resonances on hemispherically endcapped elastic cylinders (G. Maze and J. Ripoche).

Influence of nuclear reactions on electron transfer in energetic ion-atom collisions.

The influence of inelastic nuclear scattering on atomic charge transfer in asymmetric ion-atom collisions is described within a new theory, combining a two-channel model for the nuclear reaction with the impulse approximation for electron capture by the projectile. Test calculations of the capture probability during the reaction {sup 18}O({ital p},{alpha}){sup 15}N indicate that inelastic nuclear reactions are a more transparent probe for the atomic transition amplitudes than elastic resonances.

Explanation of resonance broadening of the [formula omitted] reaction for He ion channeling in oxides

The scattering cross section of the elastic resonance of 3.045 MeV 4He with 16O displays an increased half-width under channeling conditions. We explain this effect and demonstrate its correct application for the measurement of the difference in stopping for channeled and randomly incident He ions, as they are used for Rutherford backscattering spectroscopy (RBS) for LiNbO 3 and KNbO 3 single crystals.

Acoustic Resonance Scattering by Submerged Elastic Shells

We review a number of instances in which classical acoustic wave scattering from submerged elastic shells can be analyzed in the resonance region of their spectra. We recently reviewed (Refs 42, 43, 12) the cases dealing with acoustic resonance scattering from solid elastic bodies, or with elastic resonance scattering from fluid or solid inclusions in elastic media. It only remains for us to address the works dealing with submerged shells, which we analyze here. We study scattering by bare or viscoelastically coated spherical and cylindrical shells in water, by means of (exact) normal-mode solutions, and by spheroidal shells by numerical approaches, particularly via the T-matrix method. We consider the shell responses mostly in unbounded media and when the interrogating waves are plane and c.w., although some recent findings valid for pulsed incidences and in the vicinity of environmental boundaries are also included. We use the methodology of the resonance scattering theory (RST) as much as possible, emphasizing its post-1981 results. High-frequency findings, obtained by asymptotic methods, are extrapolated to lower frequencies, to confirm RST predictions for the intermediate spectral regions in which the most important structural resonances are known to reside. A large number of bibliographical entries are collected and discussed in connection with our approach.

Elastic and Acoustic Resonance Wave Scattering

The present article addresses classical elastic and/or acoustic wave-scattering problems for situations in which the pertinent targets are penetrable. In contrast to impenetrable scatterers, penetrable bodies admit interior fields coupled to the external fields through suitable (sets of) boundary conditions. When the wavelength of the incident radiation is either very long or very short, the scattered echoes returned to an interrogating active sensor can be described in a relatively simple way. This is not the case in the resonance region of the scattering cross section of any penetrable body. This region is sandwiched in between the long-wavelength (Rayleigh) region and the short-wavelength (geometrical) spectral regime. For penetrable (viz, acoustic, elastic, viscoelastic) structures, the resonance region becomes very broad, and results within it are quite difficult to describe analytically, to compute numerically, or to confirm experimentally. Resonance scattering (by definition) implies that the situation at hand occurs within that most troublesome of spectral regimes. We describe a technique particularly useful to simplify and interpret predictions and measurements in the resonance region. This technique exploits the presence of certain “features” clearly observable in the echoes returned by the targets that scatter them. It is by means of these (resonance) features that, for example, different submerged structures can be remotely distinguished from one another. The natural resonances of the structure, not in vacuum, but accounting for its fluid-loaded condition, are communicated to its returned echo in a unique fashion that unambiguously characterizes it as a “fingerprint.” It is always these echoes that we investigate for their “resonance” contents, either in the frequency or time domains. The resonance technique described here, often called the resonance scattering technique (RST), is a linear approximation that makes the understanding of resonance signatures from scatterers not only easier, but possible at all. Results obtainable from strictly classical approaches are so cluttered with information that it is difficult to use them. One simply “cannot see the forest for the trees.” The applications of the RST to various separable and nonseparable configurations are shown. Validating experiments are described, and a bibliography emphasizing the recent target-identification and target-camouflaging aspects of the technique is provided.

Evidence for vacancy-driven phase transitions inBaMnF4at elevated temperatures

Abstract Anomalies near 370 K and/or 400 K in dielectric constant, diffuse x-ray scattering, C11 elastic coefficient, electrical conductivity, and piezoelectric resonance have been reported for BaMnF 4. Particularly curious is the dielectric constant along the ac-diagonal, which rises from 15 at 300 K to a sharp peak of 73 at 400 K. These anomalies are discussed in terms of 2D ionic conduction mechanisms (fluorine vacancy hopping), and the disappearance of short-range antiferroelectric order at temperatures above 400 K. At 650 K the crystals lose all piezoelectricity, which is interpreted as a 3D vacancy-driven C2v – D2h, transition.

Harmonic generation and anisochronism in magnetostrictive materials

The present work uses the nonlinear, rotationally invariant equations of the magnetoelasticity of anisotropic magnetostrictive materials to provide the basic elements of nonlinear bulk wave propagation in these materials. In particular, near- and far-field solutions (the latter being uniformly valid on long spatial intervals) from a harmonic source within the framework of the monomode hypothesis are given using either a straightforward expansion of the magnetoacoustic solution in small parameters or a more refined multiple-scale technique. A bias magnetic field is necessarily present and harmonics are generated through all nonlinear features with a special attention to magnetostrictive couplings. A closed-form expression is deduced for the far-field solution at the first order in the small parameters. In the case of an elastic resonator tuned on the first partial mode and placed in a bias magnetic field, the expansion method provides the anisochronism due to magnetostrictive couplings at the second order. Anisochronism caused by the nonlinear purely clastic behavior requires solving the hierarchy of approximate boundary-value problems to higher order. In all the work presents all the prerequisites for a forthcoming study of nonlinear surface magnetoelastic waves and a more complete study of nonlinear vibrations of magnetoelastic resonators.

Nonlinear phenomena in magnetostrictive elastic resonators

The work considers the nonlinear vibrations in magnetostrictive resonators. To that purpose the Galerkin method, which is frequently employed to solve nonlinear wave propagation problems in finite regions (e.g. resonators), is used jointly with a multiple-time scale technique. One obtains thus the displacement at the first partial mode, placed in a bias magnetic field, as altered both in amplitude and velocity. Moreover, the change of velocity in the first partial mode provides the anisochronism due to magnetostrictive couplings at the second order. The problem is investigated on the basis of previously given, rotationally invariant nonlinear equations.

Low‐frequency elastic excitations of large aspect ratio, solid elastic targets and their couplings to the acoustic field

There is currently a controversy concerning the nature of the elastic resonances of large aspect ratio solids and the couplings of these resonances to the acoustic field. Previously [Williams et al., J. Acoust. Soc. Am. Suppl. 1 82, S50 (1987)], both theoretical and experimental evidence was presented to support our contention that the elastic wave underlying the low‐frequency resonances is essentially a “bar wave” with a phase velocity almost twice that of the shear speed. At this meeting, further evidence to this effect is presented and is carefully examined by the couplings of the elastic and acoustic fields. It is concluded that the excitation of the low‐frequency axisymmetric resonances of these targets is not due to phase matching, but that the coupling can be best described in terms of “impulse excitations.” Also established is the relationship of the prominent, off‐axis radiation lobes of these resonances to the surface displacements of the bar wave and it will be demonstrated that these lobes are not consistent with the Rayleigh surface wave interpretation.

K-shell ionization probability across a narrow nuclear elastics-wave resonance at 3388 keV in58Ni

TheK-shell ionization probabilityP K was measured at a scattering angle of 95° across the Γ = 2.4 keV nuclear elastic proton resonance in58Ni near 3388 keV. The results are in fair agreement with the theory of Blair and Anholt, especially the splitting of the resonance for the large valueU K /Γ = 3.5 in the coincident channel has been shown. A comparison with recently calculated ionization amplitudes was performed. A remeasurement of the Γ=5.6 keV resonance in58Ni near 3151 keV, originally measured by Blair et al., was found to be in reasonable agreement with the most detailed calculations.

Nuclear resonance effect in atomic electron capture by protons.

We have investigated electron capture accompanied by nuclear scattering by studying the probability for electron capture from $^{22}\mathrm{Ne}$ in the vicinity of the 1.510-MeV elastic nuclear resonance $^{22}\mathrm{Ne}$(p,p${)}^{22}$Ne. We have found a large nuclear resonance effect in the probability for electron capture. The data are in some disagreement with theoretical calculations by Jakubassa-Amundsen and Amundsen, based on the strong-potential Born approximation for electron capture.

Classification of resonances in the scattering from submerged spheroidal shells insonified at arbitrary angles of incidence

A numerical study is presented for plane-wave scattering from thin steel spheroidal shells in the frequency region corresponding to the onset of resonances. Arbitrary incidence angles are allowed for, in order to analyze the possible aspect-angle dependence of resonances. Both monostatic angular distributions and backscattered echoes are examined as a function of the nondimensionalized quantity kL/2, where the wavenumber k is 2π/λ and L is the length of the spheroid. Shell thickness is chosen to be very thin so that the physical mechanisms involved in the process can be isolated. In the analysis and in the absence of a resonance, only ‘‘background’’ effects associated with soft-body scattering are observed (due to the very small thickness of the shell), while a characteristic coherent effect is observed in the resonance region. Analysis of the exact theoretical predictions leads to the conclusion that elastic resonances for these objects correspond to modal, vibrational, surface standing waves at discrete frequencies with a relatively fixed phase velocity. Moreover, the surface standing-wave interpretation leads to simple semiphenomenological expressions that can reliably predict the resonance locations. Furthermore, the study leads to the conclusion that only two modes of vibration are allowed, namely those along the axis of symmetry and those perpendicular to it. Thus only two classes (or modes) of resonances exist, corresponding to surface standing waves along and perpendicular to the spheroid’s axis of symmetry. This property can be exploited to elicit geometrical (and to some extent material) characteristics of the object from its echo, in particular, its length-to-diameter or aspect ratio L/D.

Static and dynamic bifurcations in magnetoelastic ribbons (abstract)

The ΔE effect in certain field annealed amorphous ribbon is now about 10, i.e., Young’s modulus E, can be reversibly changed by a factor of 9 with the application of a field of less than 1 Oe. We have reported the field-induced buckling of a vertically oriented ribbon. The ribbon buckles under its own weight due to the reduction of E with field H. Critical buckling values of H were found to be in good agreement with the eigenvalues of the linearized version of the operator describing the process. Here we present: (a) holographic data where the gradient in the fringe spacing obtained from the hologram of the straight and buckled states is a measure of the curvature; and (b) a rigorous mathematical formalism for extracting from experiment the nonlinear constitutive relation between the curvature θ′(s) and the bending couple m(s) where s is the distance along the ribbon. This process must be carried out (with H as a parameter) from H=0, to values of H somewhat above the anisotropy field, to effect a complete description of the magnetoelastic behavior. In dynamic experiments where the ribbon is driven by H=H0+h sin ωt we observe a subharmonic bifurcation (parametric resonance) when ω is about twice the half-wavelength elastic resonance frequency and h exceeds a threshold value governed by the magnitude of ∂E/∂H. Other, more complicated bifurcations are seen as h is increased further. We show the nonlinear equation of motion with damping to explain the bifurcation structure.

The interplay between nuclear and atomic physics: Electron capture in the presence of a nuclear resonance

The total probability, P(E lab, θ lab), for electron capture from 12C, 14N, and 20Ne by protons of energy E lab between 1.510 MeV and from 22Ne by protons of energy E lab between 1.500 and 1.525 MeV has been measured at scattering angles θ lab of 30° and 150°. Experimental evidence for the dynamic interference effect between atomic electrons and nuclear reactions is clearly seen in P( E lab, θ lab) in the presence of the elastic s-wave nuclear resonance 22Ne(p, p) 22Ne at 1.510 MeV. The data is co with theoretical calculations by Amundsen and Jakubassa-Amundsen using the strong-potential Bom Approximation.

Resonance spectra of elongated elastic objects

The eigenfrequencies at which smooth convex objects resonate under the incidence of an acoustic wave correspond to the real parts of those complex frequency values at which circumferential waves generated by the incident signal phase-match after repeated circumnavigations around the object [H. Überall, L. R. Dragonette, and L. Flax, J. Acoust. Soc. Am. 61, 711 (1977)]. A resonance condition based on this principle is formulated, and applied to the case of elastic prolate spheroids and cylinders with hemispherical endcaps. Using then the known phase velocities of surface waves on elastic spheres, with a radius equal to the local radius of curvature along the surface path, the elastic resonance frequencies of these objects can be predicted. This was done for the Rayleigh wave on a prolate spheroid, where comparison with resonances in the scattering amplitude as obtained by a T-matrix calculation led to good agreement.

X-Ray-Generated Ultrasonic Signals: Characteristics and Imaging Applications

Experiments dealing with the characterization of X-ray- generated ultrasonic signals in materials and their application to the imaging of material inhomogeneities are described. A linear relation- ship is established between the X-ray photon power and the generated ultrasonic signals. The directivity of the X-raylacoustic source was found to resemble that of other thermoelastic sources. A new double- modulation measurement technique is described in which the magni- tude and phase of the modulated acoustic signals are measured. Use of the technique is explored with various materials, incident beam sizes, and inclusions. The results of preliminary imaging experiments are de- scribed which were carried out with direct and double-modulated X- ray/acoustic signals. The measured images exhibit features dominated by the effects of the transducer and elastic wave resonances in the spec- imens. It is shown from these results that using the images generated at two modulation frequencies, identification of the spatial inhomo- geneities in a specimen is possible.

Bistatic echoes from elastic bodies in the resonance scattering regime

The experimental technique that we described earlier [C. Y. Tsui et al., J. Acoust. Soc. Am. Suppl. 1 77, S79 (1985)] which extracts the active resonance spectrum of any scatterer from the echo it returns, was applied to solid elastic cylinders and to cylindrical shells of various thicknesses immersed in water. This technique consists in sampling the tailend of the returned pings, which contain the elastic (whispering gallery) resonances of the bodies, in order to isolate them from the (rigid) backgrounds they are usually mixed with. We now study various experimentally obtained differential scattering (bistatic) cross sections for the above mentioned objects. It is found that at certain resonance frequencies, the background‐suppressed, bistatic cross section, which is a measure of the free‐vibration target reradiation, ideally consists of a symmetric rosetta pattern, having twice the number of lobes as the modal order n of the body resonance being excited. Using theoretically computed plots of the actual ...

Resonance spectra of elongated elastic objects

It is well known [H. Überall, L. R. Dragonette, and L. Flax, J. Acoust. Soc. Am. 61, 711 (1977)] that the complex eigenfrequencies at which smooth convex objects resonate under the incidence of an acoustic wave are those at which circumferential waves generated by the incident signal phase match over a closed orbit. This principle was verified by us, by analytically obtaining the resonance frequencies of elastic cylinders and spheres [E. D. Breitenbach et al., J. Acoust. Soc. Am. 74, 1267 (1983)] and deriving phase and group velocities of the surface waves from this. In the present study, this approach is inverted, and applied to elastic prolate spheroids and to cylinders with hemispherical endcaps. From the known phase velocities and trajectories (geodesics) of the surface waves, we were able to predict the elastic resonance frequencies of these bodies. [Work supported by the David W. Taylor Naval Ship R & D Center, the Naval Research Laboratory, and the Office of Naval Research.]