Dispersion relations of waves in a rod embedded in an elastic medium

The dispersion relations of waves propagating in a system consisting of an elastic rod of radius a embedded in a linear elastic medium are investigated, and phase speeds of waves of wavelength λ which propagate under steady state conditions are determined. The dispersive behaviour is found to be dependent on several non-dimensional parameters defined by the geometric ratio $\text{a}\text{λ}$, as well as on non-dimensional ratios of the rod-medium properties. It is shown that the resulting waves which can propagate under steady state conditions are surface waves which decay with the radial distance and which permit no radiation damping of energy. It is further shown that such waves can propagate freely only if the propagation speed of longitudinal waves in the corresponding free rod is less than that of shear waves propagating in the medium. Results are presented by means of dispersion curves and surfaces. From a study of the analytical results obtained, lower and upper bounds on the phase speeds are established.     

Dispersion of elastic waves in a triangular bar

It is shown that in a bar with an equilateral triangular cross-section longitudinal, torsional, and bending modes of wave propagation are possible. The first few branches of the dispersion curves for each of these modes have been calculated using the collocation method. The first branch of the longitudinal mode shows excellent agreement with experiment. The existence of an “end-resonance” is inferred from the experimental results.     

Dispersion of elastic waves in microinhomogeneous media and structures

Acoustical Physics - The propagation of elastic waves in periodic stratified media with arbitrary local anisotropy and in anisotropic plates and bars inhomogeneous in thickness is considered under...     

Modelling of shallow sea waves in non-linear transmission lines

Summary We have modelled gravity waves in shallow water by means of non-linear transmission lines working in the radiofrequency range. The analogy between a one-dimensional shallow-water medium and a transmission line is demonstrated by the similarities of both their non-linear and dispersive properties. We discuss the results of our experiments on specially constructed radiofrequency models, and compare them with the observations of other authors on shallow-water sea swell. The formation of the shallow-water swell spectrum may be explained, in a whole variety of cases, by the non-linear mixing of the spectral components of waves approaching the shore. This is accompanied by both up- and down-conversion of the wave energy.     

Dispersion properties of helical waves in radially inhomogeneous elastic media

In this paper, a method describing dispersion curve calculation for waves propagating in radially layered, inhomogeneous isotropic elastic waveguides is developed. Particular emphasis is placed on the helical waves with noninteger azimuthal wavenumbers, which can be potentially applied in such fields as nondestructive evaluation, acoustic tomography, etc., stipulating their practical importance. To solve the problem under consideration, the matrix Riccati equation is formulated for an impedance matrix. The use of the latter yields a simple form of the dispersion equation. Numerical computation of dispersion curves can encounter difficulties, which are due to potential singularities of the impedance matrix and the necessity to separate roots of the dispersion equation. These difficulties are overcome by employing the Cayley transform and invoking the parametric continuation method. The method developed by the authors is demonstrated by calculating dispersion diagrams in support of helical waves for several models of practical interest. Such computations for an inhomogeneous layer and its approximation by a set of homogeneous layers using a transfer matrix and Riccati equation methods revealed higher computational accuracy of the latter. Dispersion curves calculated for layers with different types of inhomogeneity demonstrated significant discrepancies at low frequencies.     

Dispersion and angular analysis of acoustic modes in a shallow sea

An experiment that allowed constructing a pattern of mode signals radiated by a point source at the distances of 7 and 10 km has been staged in the Barents Sea. The image of mode signals focused by time reversal is obtained in the mode number-group delay coordinates. The used algorithm is based on the coincidence of frequency characteristics of modes of a real waveguide and an ideal waveguide in a shallow sea. A mechanism of the phenomenon that explains the observed results is proposed.     

Sound fluctuations caused by internal waves in a shallow sea

Estimates are presented for the fluctuations of the parameters of low-frequency sound fields in shallow-water regions of the Barents Sea, in the presence of seasonal internal gravity waves. The objective of the experiments is to reveal the main mechanisms that govern the sound fluctuations and their statistical parameters on paths of moderate lengths (50–60 to 100–120 km). Another objective is to determine the features of the sound interaction with internal waves for the sound speed profile of the summer—autumn type for which the water stratification is most pronounced. As the probing signals, continuous tonal ones produced by bottommoored sources at the frequencies about 100 and 300 Hz are used along with the 1/3-octave noise signals with the central frequency 1000 Hz, which are generated by a source deployed from a vessel. For the signal reception, both fixed bottom-moored hydrophones and a vertical chain of hydrophones are used, the chain also being deployed from the vessel. The water temperature, the salinity, and the thermocline displacements are monitored with standard hydrographic sensors. The following main results are presented: the estimate of the degree of correlation between the sound fluctuations and the parameters of the water layer, the comparison of the fluctuations in the signal amplitude envelope with the data obtained in other regions, and the estimate of the statistical parameters of the signal amplitude fluctuations, including their dependence on the path length. One more result consists in the proof of the wave nature of the interaction of sound and internal waves, which manifests itself in a strong dependence of the sound interaction with internal waves of discrete frequencies on the frequency of the probing signal and on the angle at which these wave beams intersect. An attempt is made to explain the observed phenomena by the synchronism in the interacting sound and gravity waves. The data obtained can be used to analyze and compare the fluctuations of the sound fields in the ocean, especially in shallow-water regions.     

Dispersion of waves in a plane acoustic layer with flexible elastic walls

A plane acoustic layer bounded by elastic membranes is considered. Dispersion relations for symmetric and antisymmetric waves are derived. The limit behavior of dispersion curves is investigated for wave numbers tending to zero and to infinity. With the use of the resulting asymptotic expansions, the two-point Pade approximations are constructed. The orthogonality relations for eigenmodes are presented.     

三维浅海环境下孤立子内波对低频声能流的传播影响

针对三维浅海环境下孤立子内波对低频声信号传播特性的影响问题,基于Oxyz坐标系下的三维浅海低频声场有限元计算方法,以声能流为研究对象,仿真分析了内波存在对低频声信号传播特性的影响规律。研究结果表明:受内波影响,在xOz平面,声能流垂直分量的传播偏转角度呈现周期性的起伏规律;随着声源深度的增加,内波对声能流偏转角度的影响深度也随之增加。对xOy平面,当声源位于温跃层以上时,随着接收深度的增加,各深度平面上声能流水平分量的偏转角越大;随着声源深度的增加,内波对各深度平面上声能流的影响逐渐减弱。     

On-site observations of seismoacoustic waves under the conditions of an ice-covered water medium

Patterns of wave disturbance propagation in nonuniform media, including the layered Earth, a liquid waveguide, and a covering ice layer are studied. The velocities of different modes are estimated based on the cross-correlation function for signals set in two spatially spanned points. Experimental data are compared to numerical modeling results.     

Dispersion curves of bulk acoustic waves in an elastic body with a two-dimensional periodic structure of circular holes

The dispersion curves of bulk acoustic waves in systems of circular holes made in an isotropic elastic material are calculated by the finite-element method for the cases of the square and hexagonal symmetries of the hole arrangement. The presence of total band gaps for acoustic waves is demonstrated, and the presence of inverse quasi-transverse first-order modes is revealed. For the hexagonally symmetric system of holes, total band gaps are found in the region of higher-order modes. For waves with a purely shear polarization, the imaginary part of the wave number in the first band gap is calculated.     

Stagnant waves in an elastic wedge-shaped plate

Stagnant antisymmetric waves in an elastic wedge-shaped plate were studied theoretically and experimentally. The solution to the nonuniform problem was obtained in the approximation of a small and smooth field nonuniformity. The vibration amplitudes in a standing wave were calculated and measured for a small wedge angle. Experimental measurements were performed on an original setup.     

Drilling and operational sounds from an oil production island in the ice-covered Beaufort sea

Recordings of sounds underwater and in air, and of iceborne vibrations, were obtained at Northstar Island, an artificial gravel island in the Beaufort Sea near Prudhoe Bay (Alaska). The aim was to document the levels, characteristics, and range dependence of sounds and vibrations produced by drilling and oil production during the winter, when the island was surrounded by shore-fast ice. Drilling produced the highest underwater broadband (10-10,000 Hz) levels (maximum= 124 dB re: 1 microPa at 1 km), and mainly affected 700-1400 Hz frequencies. In contrast, drilling did not increase broadband levels in air or ice relative to levels during other island activities. Production did not increase broadband levels for any of the sensors. In all media, broadband levels decreased by approximately 20 dB/tenfold change in distance. Background levels underwater were reached by 9.4 km during drilling and 3-4 km without. In the air and ice, background levels were reached 5-10 km and 2-10 km from Northstar, respectively, depending on the wind but irrespective of drilling. A comparison of the recorded sounds with harbor and ringed seal audiograms showed that Northstar sounds were probably audible to seals, at least intermittently, out to approximately 1.5 km in water and approximately 5 km in air.     

浅海孤子内波对水平纵向相关性的影响*

基于理论和模型仿真对孤子内波存在下的水平纵向相关系数的变化进行了研究。理论上推导出浅海孤子内波存在情况下的声场水平纵向相关系数随时间的变化规律,并且运用二维抛物方程模型（Ram）验证理论推导结果。结果表明,孤子内波会导致水声纵向相关系数的变化,并且水平纵向相关系数的变化是由于简正波的干涉所导致。我们给出特定环境下的水平纵向相关系数随时间变化的结果,当环境中第一、二号简正波占主导地位时,水平纵向相关系数会呈现出周期变化的结果。     

Helical waves of an elastic cylindrical shell

Properties of helical waves of a cylindrical shell described by Kirchhoff-Love equations are considered. The problem is reduced to the case of the propagation of plane waves in an equivalent plate. On the basis of the corresponding dispersion equation and its solution, a conclusion is made about the anisotropy of the shell properties. Dispersion curves are plotted for different angles of propagation of helical waves with respect to the shell axis. Displacements of the shell along and across the direction of wave propagation are calculated.     

Surface acoustic waves in an elastic wedge media

We consider surface acoustic waves in an elastic wedge media. It is established that the investigated waves substantially differ from known ones. For example, the movement of surface Rayleigh wave in the direction to the edge leads to a change of its structure, accompanied by the splitting of the initial wave to two separate modes and radiation of shift and longitudinal waves. Along the edge of the wedge the surface wave is strongly localized in the transverse direction. Are discussed the properties of the wedge antisymmetric normal waves, propagating parallel to the edge of the wedge.     

Scattering of time-harmonic elastic waves by an elastic inclusion with quadratic nonlinearity

This paper considers the scattering of a plane, time-harmonic wave by an inclusion with heterogeneous nonlinear elastic properties embedded in an otherwise homogeneous linear elastic solid. When the inclusion and the surrounding matrix are both isotropic, the scattered second harmonic fields are obtained in terms of the Green's function of the surrounding medium. It is found that the second harmonic fields depend on two independent acoustic nonlinearity parameters related to the third order elastic constants. Solutions are also obtained when these two acoustic nonlinearity parameters are given as spatially random functions. An inverse procedure is developed to obtain the statistics of these two random functions from the measured forward and backscattered second harmonic fields.     

Dispersion of laser generated surface waves in an epoxy-bonded layered medium

In this paper, the dispersion of laser generated surface wave in an epoxy bonded copper-aluminum layered specimen is studied. A laser ultrasonic experiment based on the point-source/point-receiver (PS/PR) technique was conducted to measure the surface wave signals in the layered specimen. The received wave signals were then processed in the frequency domain to obtain the dispersion relation of the fundamental surface wave mode. Theoretical calculations of the dispersion relations of the fundamental surface wave modes in two-layered and three-layered specimens were conducted to explore the influence of the bonding layer thickness on the dispersion relation. The experimental dispersion relation for the epoxy bonded copper-aluminum layered specimen is in good agreement with the calculated dispersion relation. The influence of the bonding layer thickness on the dispersion relation is studied and the potential application of the present results to the NDE of bonded layered media based on laser ultrasonics is also addressed.