Two-dimensional acoustic wave propagation in elastic ducts

Integral transforms are employed in order to obtain a formal solution to the two-dimensional elastic-walled duct problem. The fluid inside the duct is stationary, inviscid and compressible, and is identical to the fluid outside the duct. A time-harmonic line source lies between the duct walls. With attention confined to the field inside the duct, an asymptotic analysis is implemented for high and low frequencies, yielding residues which are valid throughout the duct and branch-cut contributions which apply only in the far field.     

Ultrasonic wave propagation in a solid with frozen-in magnetization

Ultrasonic wave propagation is studied in the framework of the continual model of a nonconducting perfect solid with frozen-in magnetization. The theoretical results are found to agree well with the experimental data.     

Two-dimensional modeling of wave propagation in materials with hysteretic nonlinearity

A multiscale model for the two-dimensional nonlinear wave propagation in a locally microdamaged medium is presented, and numerical simulations are analyzed in view of nondestructive testing applications. The multiscale model uses a statistical distribution of hysterons and upscales their microscopic stress-strain relations to a mesoscopic level. Macroscopic observations are then predicted by finite integration techniques. The influence of a small region with hysteretic nonlinearity on the generation of harmonics is investigated, and numerical results for different amplitudes of the input signal and different analysis techniques of the response signal are presented. Second, a study is conducted on the interaction of a Rayleigh wave with a microdamaged zone with hysteretic nonlinearity at the surface of an otherwise linear body, and the influence of the microdamaged zone on the surface wave velocity and on the generation of harmonics is examined. It is found that the effect of hysteresis on the Rayleigh wave propagation can be barely seen in the surface wave velocity measurement, but shows up nicely in the wave spectrum. The potential of a nonlinearity based depth profiling technique is explored by evaluating the nonlinear responses at different frequencies for a vertically stratified medium with spatially varying hysteresis properties.     

Elastic wave propagation in a randomly stratified solid medium

The mean-field method is used to analyse longitudinal and transverse (both SV- and SH-type) wave propagation in an unbounded randomly stratified solid medium. It is assumed that elastic moduli of the medium are constant while a density is a random function of the cartesian coordinate z. For a case of small density fluctuations, expressions are obtained for z-components of effective propagation vectors of P-, SV- and SH-waves for arbitrary relations between wavelengths and a correlation length of the random inhomogeneities. It is shown, that when the correlation length is small in comparison with the wavelengths, the mean-field attenuation coefficients are proportional to the frequency squared. In this case P- and SV-waves convert into each other. When the correlation length is large in comparison with the wavelengths, the mean-field attenuation coefficients are also proportional to the frequency squared, but in this case P- and SV-waves propagate independently.     

Elastic wave propagation in a randomly stratified solid medium

Abstract

The mean-field method is used to analyse longitudinal and transverse (both SV- and SH-type) wave propagation in an unbounded randomly stratified solid medium. It is assumed that elastic moduli of the medium are constant while a density is a random function of the cartesian coordinate z. For a case of small density fluctuations, expressions are obtained for z-components of effective propagation vectors of P-, SV- and SH-waves for arbitrary relations between wavelengths and a correlation length of the random inhomogeneities. It is shown, that when the correlation length is small in comparison with the wavelengths, the mean-field attenuation coefficients are proportional to the frequency squared. In this case P- and SV-waves convert into each other. When the correlation length is large in comparison with the wavelengths, the mean-field attenuation coefficients are also proportional to the frequency squared, but in this case P- and SV-waves propagate independently.     

Acoustic wave propagation in fluid metamaterial with solid inclusions

Acoustic wave propagation in a composite of water with embedded double-layered silicone resin/silver rods is considered. Approximate values of effective dynamical constitutive parameters are obtained. Frequency ranges of simultaneous negative constitutive parameters are found. Localized surface states on the interface between metamaterial and “normal” material are found. The Doppler effect in metamaterial is considered. The presence of anomalous modes is shown.     

Modeling elastic wave propagation in kidney stones with application to shock wave lithotripsy

A time-domain finite-difference solution to the equations of linear elasticity was used to model the propagation of lithotripsy waves in kidney stones. The model was used to determine the loading on the stone (principal stresses and strains and maximum shear stresses and strains) due to the impact of lithotripsy shock waves. The simulations show that the peak loading induced in kidney stones is generated by constructive interference from shear waves launched from the outer edge of the stone with other waves in the stone. Notably the shear wave induced loads were significantly larger than the loads generated by the classic Hopkinson or spall effect. For simulations where the diameter of the focal spot of the lithotripter was smaller than that of the stone the loading decreased by more than 50%. The constructive interference was also sensitive to shock rise time and it was found that the peak tensile stress reduced by 30% as rise time increased from 25 to 150 ns. These results demonstrate that shear waves likely play a critical role in stone comminution and that lithotripters with large focal widths and short rise times should be effective at generating high stresses inside kidney stones.     

Bending wave propagation along a symmetric groove in an elastic plate

Normal bending waves propagating along a symmetric groove in an infinite elastic plate are considered. The characteristic equations in wave numbers of these modes are obtained for symmetric and antisymmetric modes of vibration. Critical frequencies and eigenfunctions of the problem are determined. Results of numerical calculations for the wave numbers, critical frequencies, and modes of vibration are presented.     

Bending wave propagation of carbon nanotubes in a bi-parameter elastic matrix

This article studies transverse waves propagating in carbon nanotubes (CNTs) embedded in a surrounding medium. The CNTs are modeled as a nonlocal elastic beam, whereas the surrounding medium is modeled as a bi-parameter elastic medium. When taking into account the effect of rotary inertia of cross-section, a governing equation is acquired. A comparison of wave speeds using the Rayleigh and Euler-Bernoulli theories of beams with the results of molecular dynamics simulation indicates that the nonlocal Rayleigh beam model is more adequate to describe flexural waves in CNTs than the nonlocal Euler-Bernoulli model. The influences of the surrounding medium and rotary inertia on the phase speed for single-walled and double-walled CNTs are analyzed. Obtained results turn out that the surrounding medium plays a dominant role for lower wave numbers, while rotary inertia strongly affects the phase speed for higher wave numbers.     

Propulsion with a rotating elastic nanorod

The dynamics of a rotating elastic filament is investigated using Stokesian simulations. The filament, straight and tilted with respect to its rotation axis for small driving torques, undergoes at a critical torque a strongly discontinuous shape bifurcation to a helical state. It induces a substantial forward propulsion whatever the sense of rotation: a nanomechanical force-rectification device is established.     

The limits of the rotating wave approximation in electromagnetic field propagation in a cavity

We consider three two-level atoms inside a one-dimensional cavity, interacting with the electromagnetic field in the rotating wave approximation (RWA). One of the three atoms is initially excited, and the other two are in their ground state. We numerically calculate the propagation of the field emitted by the excited atom and scattered by the second atom, as well as the excitation probability of the second and third atom. Our numerical results clearly show the limits of the RWA in subtle problems such as relativistic causality in the atom–field interaction.     

Modeling three-dimensional elastic wave propagation in circular cylindrical structures using a finite-difference approach

Wave propagation along circular cylindrical structures is important for nondestructive-testing applications and shocks in tubes. To simulate elastic wave propagation phenomena in such structures the governing equations in cylindrical coordinates are solved numerically. To reduce the required amount of computer memory and the computational time, the stress components are eliminated in the equilibrium equations. In the resulting coupled partial differential equations, in which only the three displacement components are involved, the derivatives with respect to spatial coordinates and time are approximated using second order central differences. This leads to the present new approach, which is both accurate and efficient. In order to obtain a stable scheme the displacements must be allocated on a staggered grid. The von Neumann stability analysis is performed and the result is compared with an existing empirical criterion. Mechanical energies are observed in order to validate the finite-difference code. Since no material damping or energy dissipation is taken into account in the equations of motion, the total energy must remain constant over time. Only negligible variations are observed during long-term simulations. Dispersion relations are used to check the physical behavior of the waves calculated with the proposed finite-difference method: Theoretically calculated curves are compared with values obtained by a spectrum estimation method, applied to the results of a simulation.     

A mathematical model for wave propagation in elastic tubes with inhomogeneities: Application to blood waves propagation

We study the propagation of waves in an elastic tube filled with an inviscid fluid. We consider the case of inhomogeneity whose mechanical and geometrical properties vary in space. We deduce a system of equations of the Boussinesq type as describing the wave propagation in the tube. Numerical simulations of these equations show that inhomogeneities prevent separation of right-going from left-going waves.Then reflected and transmitted coefficients are obtained in the case of localized constriction and localized rigidity. Next we focus on wavetrains incident on various types of anomalous regions. We show that the existence of anomalous regions modifies the wavetrain patterns.     

Harmonic wave propagation in an infinite viscoelastic medium with a periodic array of cylindrical elastic fibers

The work involves the propagation of plane harmonic waves in an infinite isotropic medium in which a doubly periodic array of cylindrical fibers is embedded. The direction of propagation is perpendicular to the fibers and the matrix material is taken to be viscoelastic in shear, modeled through hereditary integrals. A finite element method based on Galerkin's technique is employed, which leads to a non-linear eigenvalue problem. An iterative scheme is used to obtain two modes of dispersion, for both real and imaginary wave numbers, for a specific composite.     

Two-dimensional theory of elf electromagnetic wave propagation in the earth-ionosphere waveguide channel

We present a surface theory of the 2-D telegraph equation and describe the methods for obtaining parameters L and C of this theory from the electromagnetic field of the dominant normal wave and its propagation constant together with the first two azimuthal derivatives. To excite the waveguide by vertical and horizontal electric dipoles, we determine the external sources of the 2-D telegraph equation, which are the 2-D point external voltage and the oriented point external specific voltage, respectively. The relation between the effective and physical sources is practically independent of the ionospheric conditions. The effective source of the horizontal dipole is proportional to the earth 's surface impedance at the source location.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 9, pp. 1103–1113, September, 1996.This work was supported by grant 01.067 of the Competition Center at St. Petersburg State University.     

Two-dimensional numerical simulation of acoustic wave phase conjugation in magnetostrictive elastic media

The effect of parametric wave phase conjugation (WPC) in application to ultrasound or acoustic waves in magnetostrictive solids has been addressed numerically by Ben Khelil et al. [J. Acoust. Soc. Am. 109, 75-83 (2001)] using 1-D unsteady formulation. Here the numerical method presented by Voinovich et al. [Shock waves 13(3), 221-230 (2003)] extends the analysis to the 2-D effects. The employed model describes universally elastic solids and liquids. A source term similar to Ben Khelil et al.'s accounts for the coupling between deformation and magnetostriction due to external periodic magnetic field. The compatibility between the isotropic constitutive law of the medium and the model of magnetostriction has been considered. Supplementary to the 1-D simulations, the present model involves longitudinal/transversal mode conversion at the sample boundaries and separate magnetic field coupling with dilatation and shear stress. The influence of those factors in a 2-D geometry on the potential output of a magneto-elastic wave phase conjugator is analyzed in this paper. The process under study includes propagation of a wave burst of a given frequency from a point source in a liquid into the active solid, amplification of the waves due to parametric resonance, and formation of time-reversed waves, their radiation into liquid, and focusing. The considered subject is particularly important for ultrasonic applications in acoustic imaging, nondestructive testing, or medical diagnostics and therapy.     

Study of Love-type wave propagation in an isotropic tri layers elastic medium overlying a semi-infinite elastic medium structure

This paper deals with the propagation of Love-type wave in a composite isotropic structure embraced of tri layers elastic medium overlying a semi-infinite elastic medium. The heterogeneity is caused due to the variation of linear, exponential, and quadratic with respect to the depth. Modified Bessel function with Debye Asymptotic Expansion approach is used to achieve closed form of dispersion equation analytically and found to be in well agreement to the classical Love wave equation. Numerical computation has been carried out to accomplish the graphical demonstration to unravel some important peculiarities of wave number associated in presence or absence of layers medium and effect of heterogeneities on phase velocity of Love-type wave.     

Characteristics of wave propagation and energy distributions in cylindrical elastic shells filled with fluid

The dispersion behaviour and energy distributions of free waves in thin walled cylindrical elastic shells filled with fluid are investigated. Dispersion curves are presented for a range of parameters and the behaviour of individual branches is explained. A non-dimensional equation which determines the distribution of vibrational energy between the shell wall and the contained fluid is derived and its variation with frequency and material parameters is studied.     

Characteristic features of elastic wave propagation in a one-dimensional model of an unconsolidated medium

The characteristic features of elastic wave propagation in a one-dimensional model of a discrete inhomogeneous unconsolidated medium are investigated. The model is represented by a linear chain of 80 uncoupled steel spheres with a diameter of 6.5 mm. Nonlinear effects that may arise in such systems are reviewed. The experimental setup is described. Results of studying the dispersion of elastic waves in the system and the dependence of the elastic wave velocity on the wave amplitude under increasing compression are presented. The results are analyzed using the Hertz contact theory.     

Probing the interior of a solid volume with time reversal and nonlinear elastic wave spectroscopy

A nonlinear scatterer is simulated in the body of a sample and demonstrates a technique to locate and define the elastic nature of the scatterer. Using the principle of time reversal, elastic wave energy is focused at the interface between blocks of optical grade glass and aluminum. Focusing of energy at the interface creates nonlinear wave scattering that can be detected on the sample perimeter with time-reversal mirror elements. The nonlinearly generated scattered signal is bandpass filtered about the nonlinearly generated components, time reversed and broadcast from the same mirror elements, and the signal is focused at the scattering location on the interface.