Numerical analysis of bulk conical waves in anisotropic cylinders; application to stiffness tensor measurement

A point source-point receiver technique, based on laser generation and laser detection of acoustic waves, allows determination of mechanical properties of an anisotropic cylinder. The nature of the material and the geometry of the sample give a dispersive behaviour to the diffracted waves and make the acoustic signature difficult to interpret. To overpass the intricacies, wave fronts (conical waves in the volume and helical waves on the surface) are synthesized from signals provided by scanning the primitive line of the cylinder with a laser point source. In order to distinguish between direct bulk conical waves and other contributions in the acoustic response, some considerations on line surface waves and on reflected bulk conical waves are supplied. The identification of the stiffness tensor components, based on the inversion of the bulk waves phase velocities, is applied to signals simulated for a composite material.     

Source bearing estimation in the Arctic Ocean using ice-mounted geophones

This paper investigates the use of geophones mounted on the surface of Arctic sea ice for estimating the bearing to acoustic sources in the water column. The approach is based on measuring ice seismic waves for which the direction of particle motion is oriented radially outward from the source. However, the analysis is complicated by the fact that sea ice supports several types of seismic waves, producing complex particle motion that includes significant nonradial components. To suppress seismic waves with transverse particle motion, seismic polarization filters are applied in conjunction with a straightforward rotational analysis (computation of particle-motion power as a function of angle). The polarization filters require three-dimensional (3D) measurements of particle motion, and apply theoretical phase relationships between vertical and horizontal components for the various waves types. In addition, the 180 degrees ambiguity inherent in the rotational analysis can be resolved with 3D measurements by considering particle motion in the vertical-radial plane. Arctic field trials were carried out involving two components. First, a hammer source was used to selectively excite the various ice seismic waves to investigate their propagation properties and relative importance in bearing estimation. Second, impulsive acoustic sources were deployed in the water column at a variety of bearings and ranges from 200-1000 m. For frequencies up to 250 Hz, source bearings are typically estimated to within an average absolute error of approximately 100.     

利用超声相干技术在室温和高压下研究几种不同性能的玻璃

 综合使用超声相干技术几种不同的测量方法，分别研究两类三种不同性能的玻璃材料，测量它们的声速和衰减在室温及高压条件下的变化规律。结果表明：两类玻璃的声速和衰减以及由此而得到的弹性常数存在较大差异。两种硅玻璃在高压下，声速随压力变化的规律相似，压力升高时，纵波速度随之单调增加，横波速度线性减少，纵波衰减也随压力升高呈增加趋势。不同的是：两种玻璃横波衰减随压力的变化规律完全相反，水白玻璃的衰减增加，窗口玻璃的减小。上述几种方法的测量结果基本一致，且在相应的压力范围内与布里渊散射的实验结果基本吻合。     

Processing an acoustic microscope’s spatiotemporal signal to determine the parameters of an isotropic layer

This paper presents a method for measuring the thickness and velocities of body waves and the density of an isotropic layer by a pulse scanning acoustic microscope. The method is based on recording the microscope signal as a function of the displacement magnitude of the focused ultrasonic transducer along its axis perpendicular to the sample surface and on the decomposition of the recorded 2D spatiotemporal signal into the spectrum of plane pulse waves. The velocities of the longitudinal and transverse waves and the layer’s thickness are calculated from the relative delays of the components of the spectrum of plane waves reflected from the surfaces of the layer and the density is computed by the amplitudes of these components. An experimental investigation of a test sample in the form of a glass plate carried out in the 50-MHz range shows that the error in measuring the thickness and velocities of body waves does not exceed 1% and the density measurement error does not exceed 10%.     

Investigation of the phase velocities of guided acoustic waves in soft porous layers

A new experimental method for measuring the phase velocities of guided acoustic waves in soft poroelastic or poroviscoelastic plates is proposed. The method is based on the generation of standing waves in the material and on the spatial Fourier transform of the displacement profile of the upper surface. The plate is glued on a rigid substrate so that it has a free upper surface and a nonmoving lower surface. The displacement is measured with a laser Doppler vibrometer along a line corresponding to the direction of propagation of plane surface waves. A continuous sine with varying frequencies was chosen as excitation signal to maximize the precision of the measurements. The spatial Fourier transform provides the wave numbers, and the phase velocities are obtained from the relationship between wave number and frequency. The phase velocities of several guided modes could be measured in a highly porous foam saturated by air. The modes were also studied theoretically and, from the theoretical results, the experimental results, and a fitting procedure, it was possible to determine the frequency behavior of the complex shear modulus and of the complex Poisson ratio from 200 Hz to 1.4 kHz, in a frequency range higher than the traditional methods.     

Unusual one-way edge state in acoustic gyroscopic continuum

Unusual one-way edge states have been observed in composite structures composed of periodic lattices loaded with gyroscopes.Here, we provide a continuum-mechanics understanding to the one-way edge state by formulating surface state equations of acoustic gyroscopic mediums with Hermite mass density tensor. We discover that the unidirectional edge effect arises from nontrivial off-diagonal components of Hermite densities, which causes the symmetric breaking of surface wave propagation towards forward and backward directions. Theoretical predictions on the velocity and decay length of surface waves coincide excellently with numerical simulations. The unidirectional edge state in a two-interface gyroscopic medium is also analyzed.Due to the rotational symmetry in geometry, the unidirectional edge state on one interface is able to prevent itself from the coupling to surface waves on the other interface regardless of the slab thickness. With these anomalous effects, surface waves residing on gyroscopic mediums can flow around the edge defects without back-scatterings, or can be split into two beams of equal energy magnitudes. Our findings may make a bridge that would help to reach the design of non-reciprocal composite materials via an effective medium approach.     

Combined spectral estimator for phase velocities of multimode Lamb waves in multilayer plates

A novel combined spectral estimate (CSE) method for differentiation and estimation the phase velocities of multimode Lamb waves whose wave numbers are much close or overlap one another in multiplayer plates is presented in this paper, which based on auto-regressive (AR) model and 2-D FFT. Simulated signals in brass plate were processed by 2-D FFT and CSE. And experiments are performed by using two conventional angle probes as emitter and receiver on the same surface of three-layered aluminum/xpoxy/aluminum plates, which include symmetrical and unsymmetrical plates. The multimode Lamb waves are excited in these laminates, and the received signal is processed by 2-D FFT and CSE, respectively. The results showed that the phase velocities of multimode signals whose wave numbers are much closed cannot be differentiated by 2-D FFT, but CSE has strong spatial resolution. Compared the measured phase velocities with the theoretical values, the error is smaller than 2% on the whole. It promises to be a useful method in experimental signals processing of multimode Lamb waves.     

Properties of surface waves in an elastic cylinder filled with a liquid

The properties of harmonic surface waves in an elastic cylinder filled with a liquid are studied. The case of elastic material for which the shear wave velocity is higher than the sound velocity in a liquid is considered. The wave motion is described based on the complete system of equations of the dynamic theory of elasticity and the equation of motion of an ideal compressible liquid. The asymptotic analysis of the dispersion equation in the region of large wave numbers and qualitative analysis of the dispersion spectrum showed that in such a waveguiding system there exist two surface waves, the Stoneley and the Rayleigh waves. The lowest normal wave forms the Stoneley wave on the internal surface of the cylinder. In this waveguide phase, velocities of all normal waves, except for the lowest one, have the velocity of sound in the liquid as their limit. Therefore, the Rayleigh wave on the external surface of the cylinder is formed by all normal waves in the range of frequencies and wave numbers in which phase velocities of normal waves of the composite waveguide and the lowest normal wave of the elastic hollow cylinder coincide.     

基于平移旋转的球面绝对检测技术仿真分析

基于平移旋转的球面绝对检测技术是一种实现高精度面形测量的有效手段。通过绕光轴多次等角度旋转被测球面测得被测面面形误差的旋转非对称部分,并由共心平移被测球面恢复出被测面面形误差的旋转对称部分,合成即可得到被测球面完整的面形信息。详细推导了平移旋转法的理论公式,并进行了仿真分析。仿真结果表明,基于上述方法获得的被测球面面形误差与初始面形误差残差图的均方根值为5.300 010-12 nm,其与初始面形误差均方根值的比值为1.164 110-12,理论误差极小,满足高精度面形检测要求。     

Two-tone ion-acoustic waves in degenerate quantum plasma

Ion-acoustic waves (IAWs) in a quantum electron-ion plasma with degenerate components are theoretically investigated using a system of quantum equations of gas dynamics that allow for the quantum-size character of the object (Bohm’s quantum force is included in the equation of motion) and the Pauli exclusion principle (equations of state for degenerate Fermi gases of electrons and ions are used). Linear analysis and numerical solution of equations yielded an identical qualitative result: periodic IAWs in a quantum electron-ion plasma are always a superposition of two waves with equal phase velocities but different wavelengths. The high-frequency component of the IAW is identified with free quantum oscillations of ions. A solution in the form of an ion-sound soliton with free quantum oscillations of ions superposed on its profile is also found.     

Pulsed Rayleigh wave scattered at a surface crack

This paper investigates Rayleigh wave interaction with machined slots on flat aluminium blocks to simulate surface breaking cracks. Using a finite element method, Rayleigh wave scattering by narrow slots of varied depth ranging from 0.5 mm to 20 mm is calculated. Pulsed wideband Rayleigh waves with a centre frequency of 590 kHz and -6 dB bandwidth of 520 kHz is considered. Reflection and transmission coefficients are calculated and compare well with the published literature. We and other workers have reported enhancement of the measured amplitude or particle velocity of an apparent Rayleigh wave close to a surface defect. In this paper, it is found that the predicted enhancement of in-plane components of particle velocities close to a crack is significantly higher than that of the out-of-plane components of particle velocities which appears to be mainly due to the mode-converted surface skimming longitudinal wave from the crack that has mainly in-plane components near the sample surface. The enhancement of the in-plane particle velocity will be observed regardless of the type of in-plane sensitive ultrasonic detector used. The explanation of the discrepancy of the reflection and transmission coefficients obtained by pulsed and narrow band or pseudo continuous Rayleigh waves is discussed. The later-arriving Rayleigh waves from reverberation along the inside of the crack surface are observed, as has been previously reported by other workers, and this may also be used to gauge slot depth.     

Analogy between linear sound scattering processes in a viscous liquid and in an isotropic elastic medium

Expressions for velocities and forces responsible for the monopole, dipole, quadrupole, and rotational oscillations of a spherical particle in an arbitrary sound field, as well as in fields of plane waves and waves scattered by other particles, are derived. The expressions are valid for both liquid and isotropic elastic media.     

Generation of electromagnetic waves by a rotating plasma

Generation of electromagnetic waves by an annular shell of plasma rotating in crossed radial electrostatic and axial magnetic fields in a cylindrical resonator is investigated theoretically. Dispersion relations are obtained describing the interaction of the waves with the plasma. It is shown that generation of waves by a narrow plasma shell is possible due to a cyclotron resonance, Čerenkov resonance, or plasma resonance. Here we consider a Čerenkov resonance, where the velocities of the plasma components and the phase velocities of the waves are perpendicular to the constant magnetic field. The frequencies and growth rates of the waves are found under conditions of the above-mentioned resonances in a uniform and in a nonuniform plasma shell. Advantages and disadvantages of wave generation under various conditions are noted. Zh. Tekh. Fiz. 69, 16–21 (February 1999)     

Effect of mechanical boundary conditions on the dynamic and static properties of a strongly anisotropic ferromagnet

The spectra of coupled magnetoelastic waves in a semi-infinite strongly anisotropic easy-plane ferromagnet with a rigidly fixed face are analyzed for two variants of fixation (in the basal plane and perpendicularly to it). The phase states of the system are determined. Differences in the phase diagrams and elementary excitation spectra depending on the choice of the sample fixation plane are considered. When rotational invariance is taken into account, the nonreciprocity effect for the velocities of sound in a crystal appears. It is shown that the velocity of sound in the sample considerably depends on the symmetry of the imposed mechanical boundary conditions. The phase diagrams of the system under investigation are presented.     

Vortex-antivortex wavefunction of a degenerate quantum gas

A mechanism of a pinning of the quantized matter wave vortices by optical vortices in a specially arranged optical dipole traps is discussed. The vortex-antivortex optical arrays of rectangular symmetry are shown to transfer angular orbital momentum and form the “antiferromagnet”-like matter waves. The separable Hamiltonian for matter waves in pancake trapping geometry is proposed and 3D-wavefunction is factorized in a product of wavefunctions of the 1D harmonic oscillator and 2D vortex-antivortex quantum state. The 2D wavefunction’s phase gradient field associated via Madelung transform with the field of classical velocities forms labyrinth-like structure. The macroscopic quantum state composed of periodically spaced counter-rotating BEC superfluid vortices has zero angular momentum and nonzero rotational energy.     

The effect of a surface impedance load on the properties of quasi-Rayleigh waves

The propagation of quasi-Rayleigh waves along an impedance-loaded plane boundary of an isotropic elastic half-space is studied theoretically. The dispersion equation of these waves is derived with allowance for the fact that an impedance load has both normal and tangential components. The conditions for the existence of such waves are analyzed depending on the magnitude and nature of each of these components. Specific examples of calculating the quasi-Rayleigh wave velocities are considered: for the models of surface and bulk cracked media, for a fluid layer in an elastic medium, and for a resonant load.     

Acoustic identification of the anisotropic nanocrystalline medium with non-dense packing of particles

A two-dimensional model of the anisotropic nanocrystalline (granular) medium being a rectangular lattice of elastically interacting elliptical particles with translational and rotational degrees of freedom was considered. In the long-wave approximation a system of linear equations in partial derivatives describing the propagation of the longitudinal, transverse, and rotational waves in such a system was obtained. The dependences of the wave velocities on the grain size and form were analyzed. It was shown how to determine the moduli of elasticity of the granular material from the change of the velocities of the acoustic waves propagating along different crystallographic directions.     

Sagnac effect in ring interferometers on “slow” waves

We consider the Sagnac effect in ring interferometers on magnetostatic and surface acoustic waves. It is shown that the Sagnac effect for waves of arbitrary type (including both magnetostatic and surface acoustic waves) propagating in an arbitrary medium cannot be calculated using Galilean transformations but is explained within the framework of the special relativity and is related to the difference between the phase velocities rather than group velocities of counter-propagating waves in the rotating reference frame. We also show that the phase difference of counterpropagating waves due to the Sagnac effect depends on neither the phase velocity of the wave in a medium at rest nor the dispersion of the medium; it depends only on the wave frequency and the angular velocity of interferometer rotation. The minimum angular velocity that can be measured in the ring interferometers using magnetostatic and surface acoustic waves is estimated. N. I. Labachevsky State University, Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 4, pp. 373–382, April 1999.     

Acoustic identification of nanocrystalline media

Two-dimensional (2D) models of nanocrystalline media with close proximity (a hexagonal lattice) and with non-dense packing (a square lattice) are considered in this paper. It is supposed that particles have a round shape and possess two translational and one rotational degrees of freedom. The differential equations describing the propagation of acoustic and rotational waves in such media have been derived. Analytical relationships between the macroelasticity constants of the medium and microstructure parameters have been found. These relationships appear to be different for nanocrystalline media with hexagonal and square lattices. It has been shown that identification of macroparameters of a nanocrystalline medium can be obtained by measurement of wave velocities and the form of dispersion dependences of acoustic and rotational waves.     

Acoustics of shells

We discuss the physical phenomena that arise in the scattering of acoustic waves from fluid-immersed elastic (metal) shells which may be either evacuated or filled with the same or with a different fluid. The phenomena occurring here include the formation of circumferential (peripheral, or “surface”) waves that circumnavigate the shells, propagating either as elastic waves in the shell material or as fluid-borne waves of the Scholte-Stoneley type in the external or the internal fluid. By phase matching along a closed circuit, these waves may lead to prominent resonances in the acoustic scattering amplitude, and we demonstrate how the set of observed resonance frequencies is related to the dispersive phase velocities of the surface waves, so that one can be determined from the other. In addition, we discuss how the dispersion curves (phase velocity plotted vs. frequency) of the various types of surface waves show repulsion phenomena due to their coupling through the boundary conditions. The cases of spherical and cylindrical shells are investigated here as typical examples, and as an introductory topic we additionally mention surface waves on plates where related phenomena also occur. Both the theoretical and the experimental aspects of the present subject will be considered, including the experimental visualization of the surface waves.