Circumferential waves in a composite circular cylinder

Circumferential waves propagating in a layered, circular cylinder are studied. The cylinder consists of an elastic circular core encased in a hollow, circular cylinder of distinctly different elastic properties. Both smooth and bonded contact are considered. The effect of curvature and layer thickness on the phase velocity of the lowest mode(s) is investigated for both an acoustically softer and an acoustically stiffer layer. When the outer radius of the composite cylinder is unbounded, Stoneley waves are a limiting case as the ratio of the radius of the core to the wavelength increases beyond bounds. When the outer radius is finite, waves in a layer and a half-space result for this limit. Some attention is also directed to the limiting case of small layer thickness to the wavelength ratio. In the limit as this ratio vanishes, the motion of the core reduces to that of Rayleigh waves on the curved surface. For smooth contact, the motion of the core becomes uncoupled from that of the layer for this limiting case, and two distinct modes are seen to exist.     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

弱界面压电覆层复合结构中的声导波

建立压电覆层复合结构中声导波传播模型,结合弱界面“弹簧”模型,推导了压电覆层复合结构存在刚性、滑移联接界面等几种不同界面条件下声导波的广义频散方程,数值计算钛锆酸铅基压电陶瓷覆层复合结构在不同界面条件下声导波的频散曲线,分析了界面特性对导波传播相速度的影响。数值计算和分析表明为了能够有效地评价界面的特性,选择合适的声波模式和声波频率是非常重要的。实验结果验证了界面假设的有效性,为进一步深入研究以多模式声导波参量为基础的压电覆层复合结构界面特性参数反演方法提供了理论基础。     

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.     

Shear waves guided by the imperfect interface of two magnetoelectric materials

In this paper, propagation of shear waves along a weak interface of two dissimilar magnetoelectric or magnetoelectroelastic materials is considered. Two exact dispersion relations are obtained for an imperfect electrode interface and an unelectroded interface, respectively. The existence condition of the interfacial waves is studied. Our results show that the interfacial imperfection strongly affects the velocity of the interfacial shear waves. In particular, for certain bi-magnetoelectric material, the interfacial shear waves may do not exist for a perfect interface and exist only for an imperfect interface. These findings are useful for the design of high-frequency wave devices.     

SH wave propagation in a piezoelectric/piezomagnetic plate with an imperfect magnetoelectroelastic interface

In this paper, we investigate the SH wave propagation in a layered piezoelectric (PE) and piezomagnetic (PM) plate with an imperfect magnetoelectroelastic interface. A linear magnetoelectroelastic spring model is used to describe the weakness of the imperfect interface. On the basis of this model, dispersion curves and mode shapes of the SH waves are computed. In particular, a PZT-5A/CoFe₂O₄ composite plate is considered in the numerical examples to calculate the dispersion curves and the mode shapes for different combinations of the magnetic, electrical and elastic spring constants. The effects of the layer thickness ratio and the electric-magnetic boundary conditions on the dispersion curves are discussed in details. Our results show that for a general weak bonding case, the high modes of the dispersion curves are not monotonous in the range of small wave numbers. With the layer thickness ratio increasing, the wave velocities of the SH waves increase. The electric boundary conditions mainly determine the dispersion curves of the SH waves in the case of a small layer thickness ratio, i.e. a large thickness of the PE layer. The present results have relevant applications in the nondestructive testing and evaluation of the layered PE/PM plate-like wave devices.     

Fringe waves on an impedance cylinder

Surface diffraction of the plane waves from an impedance cylinder was investigated by the method of physical theory of diffraction (PTD). Physical optics (PO) method was used to gain the uniform scattered fields which are produced by the induced surface currents. Nonuniform currents and scattered fields were obtained by the method of PTD with the assistance of the exact solutions.     

Nonlinear waves in a plasma cylinder

Nonlinear electron plasma waves in a cold plasma bounded by a cylindrical dielectric are investigated using the exact electron fluid equations. After the spatial wave structure is determined, a set of nonlinear equations governing the temporal behavior of the field quantities is solved. It is shown that finite amplitude waves and explosively unstable behavior can occur     

Damped waves in a cylinder shadow

The sound field in the region of a deep shadow behind an impedance cylinder is analyzed for the case of plane wave diffraction by the cylinder surface. The main part of the field is represented by a cylindrical wave that has a complex index determined from the boundary conditions and decays with the angular coordinate. An expression for the amplitude of this wave is determined by extracting it from the total field formed in the shadow region. It is demonstrated that this wave approximates more closely the total field behind the cylinder, as compared to the least damped wave in the field representation obtained on the basis of the Watson transform. A way to improve the sound barriers is indicated.     

Vibration and waves in a cylinder with screw anisotropy

On the basis of the three-dimensional theory of elasticity, we consider the features of propagation of harmonic waves in a hollow cylinder with screw anisotropy. The main attention is focused on studying axisymmetrical oscillations. To describe low-frequency long-wavelength longitudinal-torsional oscillations by perturbation theory methods, we construct an applied theory and evaluate the area of its applicability. To analyze high-frequency oscillations, a numerical method of determining the critical frequencies and dispersion curves is developed and implemented. It is shown that in the axisymmetrical case, screw anisotropy generates a relation between longitudinal and torsion oscillations, which is mathematically described by the amplitude coefficients of homogeneous waves.     

Influence of imperfect bonding on interface waves guided by piezoelectric/piezomagnetic composites

Interface waves, which can be guided by imperfectly bonded piezoelectric and piezomagnetic half-spaces, are studied. The cases of absorbent and permeable interfaces are discussed in detail. It is shown that imperfection of the interface bonding has significant impact on the existence of interface waves and on their velocities of propagation. Some interface waves present in the case of imperfect bonding vanish when the bonding becomes perfect. The waves that are guided by an imperfect interface are shown to be dispersive, although there is no explicit characteristic length in the structure model. The results obtained show that possible imperfections of interface bonding must be considered in the design and fabrication of piezoelectric/piezomagnetic composites.     

Generation of waves in an elastic plate by a torsional moment and a horizontal force

An approximate solution is determined for the motion of an infinite elastic plate, excited by a torsional moment (with the axis of the moment normal to the plate) and by a horizontal force (parallel to the plate). The driving moment and force are sinusoidal in time and applied to a small rigid indenter with a circular base, fixed to the plate. The solution is obtained from a three-dimensional approach but is evaluated only for low frequencies, where the wavelengths of the quasi-longitudinal, tranverse and bending waves are much larger than the thickness of the plate. For the case of excitation with a torsional moment, the solution contains two parts, one describing a travelling transverse wave and the other a local reaction. The local reaction is built up of two infinite sums of Love waves with imaginary wave numbers. The driving-point admittance due to the local reaction is larger than the admittance due to the tranverse wave when the diameter of the indenter is smaller than about twice the thickness of the plate. For the case of excitation with a horizontal force, the solution contains three parts that describe travelling waves (quasi-longitudinal, transverse and bending) and two parts that describe the local reaction (infinite sums of Lamb and Love waves). The admittances due to the three types of travelling waves are all of the same order of magnitude. The admittance due to the local reaction is of importance when the frequency is relatively high and the diameter of the identer much smaller than the thickness of the plate. For both cases of excitation, the admittance due to the local reaction increases with increasing thickness of the plate and tends to the value found for a semi-infinite medium.     

Nonlinear waves in a rotating plasma cylinder

Previous work on exact cylindrical surface waves in a nonneutral cold-electron plasma bounded by a dielectric is extended to include plasma rotation. A set of nonlinear rate equations describing the temporal behavior of the system is derived by first determining an appropriate spatial wave structure. Physically relevant periodic solutions are obtained     

Effects of the imperfect interface and piezoelectric/piezomagnetic stiffening on the SH wave in a multiferroic composite

Studied in the present work is the propagation of SH wave in a cylindrically multiferroic composite consisting of a piezoelectric layer and a piezomagnetic central cylinder. It is assumed that the interface in the composite is damaged mechanically, magnetically or electrically. The dispersion relations of SH wave are obtained for two kinds of electric-magnetic boundary conditions at the free surface, and then the phase velocity is calculated numerically. Parametric studies on the phase velocity yield three main conclusions. (a) The mechanical imperfection may remarkably reduce the phase velocity, depending on the combination of the values of the wavenumber and the thickness ratio. (b) The magneto-electrical imperfection has no obvious effect on the phase velocity in any cases. (c) The piezoelectric and piezomagnetic stiffening can increase the phase velocity.     

Effect of an imperfect interface on the SH wave propagating in a cylindrical piezoelectric sensor

Under harsh in situ conditions, the interface in piezoelectric sensors may be damaged mechanically and/or electrically. The damaged interface would in turn affect the electromechanical behaviors of the sensors. The purpose of the present work is to study the effect of the imperfect interface on SH wave propagating in a cylindrical piezoelectric sensor. The dispersion relations of SH wave are derived analytically and the phase velocity are obtained numerically. Parametric studies on the phase velocity indicate that the mechanical imperfection may reduce the phase velocity under certain circumstances; however, the electrical imperfection has no obvious effect on the phase velocity in any cases; with the thickness of the piezoelectric layer increasing, the phase velocity may increase, decrease or keep unchanged, depending on the combination of the values of the wave number and the mechanical imperfection parameter.     

Unusual spectral behavior of charge-density waves with imperfect nesting in a quasi-one-dimensional metal

Low-temperature electronic properties of the charge-density-wave system NbSe3 are reported from angle-resolved photoemission at 15 K. The effect of two instabilities q(1) and q(2) on the k-resolved spectral function is observed for the first time. With a pseudogap background, the gap spectra exhibit maxima at Delta*(1) approximately 110 meV and Delta*(2) approximately 45 meV. Imperfectly nested sections of the Fermi surface lack a Fermi-Dirac edge, and show the signature of a dispersion that is modified by self-energy effects. The energy scale is of the order of the effective gap 2 Delta*(2). The effect disappears above T2, suggesting a correlation with the charge-density-wave state.     

Dynamic stress around a cylindrical nano-inhomogeneity with an interface in a half-plane under anti-plane shear waves

Taking into account the size of the nanostructure, the effect of surface/interface stiffness on the dynamic stress around a cylindrical nano-inhomogeneity embedded in an elastic half-plane subjected to anti-plane shear waves is investigated. The boundary condition at the straight edge of the half-plane is traction free, which is satisfied by the image method. The analytical solutions of displacement fields are expressed by employing a wave function expansion method. The addition theorem for a cylindrical wave function is applied to accomplish the superposition of wave fields in the two half-planes. Analyses show that the effect of the interface properties on the dynamic stress is significantly related to the nano-scale distance between the straight edge and the center of the cylindrical nano-inhomogeneity. The frequency and incident angle of incident waves and the shear modulus ratio of the nano-inhomogeneity to matrix also show different effect on the dynamic stress distribution when the inhomogeneity shrinks to nano-scale. Comparison with the existing results is also given.