Circumferential waves for a cylindrical shell in smooth contact with a continuum

Dispersion relations are determined for circumferential waves propagating in a layered, circular cylinder by using shell equations to approximate the behavior of the outer layer. These equations include the effects of transverse shear deformation and rotatory inertia. The cylinder consists of an elastic core in smooth contact with a hollow, circular cylinder of distinctly different elastic properties. Two distinct modes exist as the shell thickness reduces to zero. One mode is recognized to be surface waves on the convex cylindrical surface of the core; the second mode is associated with long longitudinal waves in the shell. The approximate dispersion curves for these modes are compared with curves obtained by employing elasticity equations for the layer. As the curvature increases, the agreement of the two theories becomes progressively poorer whether or not any disagreement exists for the case of no curvature. The agreement of the two theories is better when the layer is relatively stiff than when the layer is relatively soft. The shell equations simplify the calculations necessary to produce the dispersion curves.     

Scattering of antiplane shear waves by layered circular elastic cylinder

An exact analytical solution for the scattering of antiplane elastic waves by a layered elastic circular cylinder is obtained. The solution and its degenerate cases are compared with other simpler models of circular cylindrical scatterers. The effects of the geometrical and physical properties of the interphase are studied. Numerical results confirm the existence of a resonance mode in which the scatterer's core undergoes a rigid-body motion when the outer layer of the scatterer is very compliant. This resonance mode has been attributed [Liu et al., Science 289, 1734 (2000)] to a new mechanism for the band gap formed in the extremely low frequency range for phononic crystals made of layered spherical scatterers. Numerical results also show the existence of a similar resonance mode when the outer layer of the scatterer has very high mass density.     

Axially symmetric vibrations of fluid-filled poroelastic circular cylindrical shells

Employing Biot's theory of wave propagation in liquid saturated porous media, axially symmetric vibrations of fluid-filled and empty poroelastic circular cylindrical shells of infinite extent are investigated for different wall-thicknesses. Let the poroelastic cylindrical shells are homogeneous and isotropic. The frequency equation of axially symmetric vibrations each for a pervious and an impervious surface is derived. Particular cases when the fluid is absent are considered both for pervious and impervious surfaces. The frequency equation of axially symmetric vibrations propagating in a fluid-filled and an empty poroelastic bore, each for a pervious and an impervious surface is derived as a limiting case when ratio of thickness to inner radius tends to infinity as the outer radius tends to infinity. Cut-off frequencies when the wavenumber is zero are obtained for fluid-filled and empty poroelastic cylindrical shells both for pervious and impervious surfaces. When the wavenumber is zero, the frequency equation of axially symmetric shear vibrations is independent of nature of surface, i.e., pervious or impervious and also it is independent of presence of fluid in the poroelastic cylindrical shell. Non-dimensional phase velocity for propagating modes is computed as a function of ratio of thickness to wavelength in absence of dissipation. These results are presented graphically for two types of poroelastic materials and then discussed. In general, the phase velocity of an empty poroelastic cylindrical shell is higher than that of a fluid-filled poroelastic cylindrical shell.The phase velocity of a fluid-filled bore is higher than that of an empty poroelastic bore. Previous results are shown as a special case of present investigation. Results of purely elastic solid are obtained.     

Scroll waves in spherical shell geometries

The evolution of scroll waves in excitable media with spherical shell geometries is studied as a function of shell thickness and outer radius. The motion of scroll wave filaments that are the locii of phaseless points in the medium and organize the wave pattern is investigated. When the inner radius is sufficiently large the filaments remain attached to both the inner and outer surfaces. The minimum size of the sphere that supports spiral waves and the maximum number of spiral waves that can be sustained on a sphere of given size are determined for both regular and random initial distributions. When the inner radius is too small to support spiral waves the filaments detach from the inner surface and form a curved filament connecting the two spiral tips in the surface. In certain parameter domains the filament is an arc of a circle that shrinks with constant shape. For parameter values close to the meandering border, the filament grows and collisions with the sphere walls lead to turbulent filament dynamics. (c) 2001 American Institute of Physics.     

Free vibration of circular cylinders of variable thickness

Flexural vibrations of finite length circular cylinders with shear diaphragm ends and symmetric circumferential wall thickness variations are described by using the Rayleigh-Ritz method. Both symmetric and asymmetric solutions are presented. Only circumferential variations in the wall radial dimension are considered; the method is amenable, however, to consideration of longitudinal variations in wall thickness as well. The cylinder wall thickness variation is described as a Fourier series and the vibration is described as a series of modes of a uniform cylinder with the same mean radius. The theory has been applied to a cylinder whose inner bore is circular but is non-concentric with the circular outer surface. The mode shapes have been investigated experimentally by using time-averaged holograms of the vibrating cylinder and the results compare well with the predictions of the theory. The frequencies of the modes agree with the theoretical predictions to within 2%.     

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.     

Active control of normal particle velocity at a boundary between two media

A spatially one-dimensional model of a plane active double layer between two homogeneous elastic half-spaces is studied analytically. The layer synthesizes a preset smooth trajectory of the controlled boundary between the media without any mechanical support. The outer layer of the coating is a piezoelectric, and the inner layer is a polymer that is transparent for low-frequency sound and opaque for high-frequency sound because of dissipation. An algorithm for controlling the piezoelectric elements of the layer on the basis of signals from surface particle-velocity sensors is proposed, and a method for measuring the particle velocity is developed. Conditions of stability and efficiency of the synthesis are formulated. It is shown that the active layer thickness can be much smaller than the wavelength corresponding to the minimal time scale of the boundary trajectory to be formed. The accuracy of the trajectory synthesis depends on the accuracy of measuring, computing, and actuating elements of the system but does not depend on the vibroacoustic characteristics of the half-spaces separated by the active layer or on the presence of smooth waves in these half-spaces. For the synthesis to be efficient, the operating frequency band and the dynamic range of sensors and actuators should be many times greater than the frequency band and the dynamic range of the trajectory to be formed.     

Absorption of electromagnetic radiation by an inhomogeneous spherical particle

The cross section of absorption of electromagnetic radiation by an inhomogeneous spherical particle is calculated. The general case of an arbitrary value of the ratio of the particle radius to the radius of the dielectric core is considered. The condition of diffuse reflection of electrons from the inner and outer surfaces of the metal layer of the particle is taken as the boundary condition of the problem. The limiting cases are considered and the results obtained are discussed.     

Laser-induced circumferential waves on hollow cylinder and their interaction with defects by finite element method

A three dimensional (3-D) finite element model for simulating laser induced circumferential wave on a hollow cylinder is developed based on the thermoelastical mechanism, which can take any laser source into account and simulate the interactions between circumferential wave and defects in the hollow cylinder. The model is verified by a control calculation. The results show that the waveforms of circumferential wave are in very good agreement with those available in literature, not only on the arrival time and shape but also on the amplitudes of A ₀, S ₀ and A₁ modes. Using the model, circumferential waves on the surfaces of two series hollow cylinders are simulated, one with same thickness but different outer radius, and the other with the same outer radius but different thickness. The results show that a new mode appears in circumferential wave, compared with Lamb wave in plate. With increase of thickness or radius, the amplitude of the new mode reduces. Another conclusion is that with increase of the thickness of the hollow cylinder, the circumferential wave evolves gradually to the cylindrical Rayleigh waveform, which results from the attenuation of the coupling effect between the outer and inner surface. Moreover, the circumferential waves generated on a hollow cylinder with a surface defect are also simulated, and the results indicate that in the circumferential waves obtained at the point beyond the defect, the amplitude of A ₀ mode decreases and its dispersion enhances. More importantly, a new bipolar waveform corresponding to the interaction of S ₀ mode with the defect appears, its amplitude is larger than three times of that of S ₀ mode. As a result, we consider that the new bipolar waveform will be the optimal feature to nondestructively detect the surface defect on the hollow cylinder.     

Wave propagation in axially polarized piezoelectric hollow cylinders of sector cross section

In this paper, the problem of electroelastic waves propagating in piezoelectric hollow cylinders of sector cross section is studied for the case when the boundary surfaces of sector cut are covered by non-extensible membranes. The three-dimensional linear equations of motion for the piezoelectric cylinder are analytically integrated and different boundary conditions on the cylindrical surfaces yield frequency equations, which relate the frequencies of elastic waves to their wavenumbers. Numerical results for waveguides with various boundary conditions are presented to illustrate the approach. Analysis of the dispersion spectra is carried out, and cutoff frequencies are obtained and characterized; mode asymptotic behavior and amplitude distributions of wave characteristics are analyzed. The main effects of their transformation by variation of the angular measure and the ratio of inner and outer radii are discussed. The results obtained are in good agreement with the results for the special case of a hollow semicircular cylinder.     

Sound wave propagation in ducts whose walls are lined with a porous layer backed by cellular cavities

This paper concerns propagation and attenuation of sound waves through acoustically lined ducts. For a cylindrical duct whose liner consists of a point-reacting porous material layer backed by cellular cavities, the admittance formula derived by taking into account a wave motion within the liner is applied to an analysis of waves propagating downstream. For the point-reacting liner of fixed porous material properties, influences of the porous layer thickness, cellular cavity depth, mean flow profile, and three dimensionality of the duct (i.e., cylindrical or plane) on the attenuation are examined. The results show a significant role of the porous layer thickness. For the cylindrical duct, attenuation spectra evaluated from this analysis are compared with those given by the widely used semi-empirical formula.     

Dynamic compliance of multilayer coatings

The algorithm for calculation of dynamic compliance of multilayer coatings was developed. The compliance modulus and phase lag of coating surface motion vs. the current pressure depend on viscoelastic properties of materials, ratio of wavelength to layer thickness λ/H, and ratio of wave velocity to propagation velocity of shear vibrations in the base layer V / C _t,2 ⁰ Dynamic compliance of the two-layer coating consisting of a thick base layer and thin durable outer layer was calculated. The elasticity modulus of the outer layer ranged up to eight values of elastic modulus of the inner layer; the density of the outer layer either remained equal to the density of the inner layer or increased proportionally to the elastic modulus. Depending on V / C _t,2 ⁰ two scenarios of compliant coating interaction with the turbulent flow were distinguished: resonant and broadband ones. It is shown that the vibration properties of two-layer coatings can be significantly better than the properties of the monolayer coatings. This makes it possible either to increase the coating strength or to work efficiently at lower velocities.     

Homogenization of two-dimensional clusters of rigid rods in air

The scattering of sound waves by circular-shaped clusters consisting of two-dimensional distributions of rigid cylinders in air is studied in the low-frequency limit (homogenization) both theoretically and experimentally. Analytical formulas for the effective density and sound speed are obtained in the framework of multiple scattering. Here, an experimental demonstration is reported in which a cluster of wooden rods acoustically behaves as a cylinder of argon gas. Moreover, evidence is presented indicating the validity of the homogenization in this cluster at frequencies lower than 3 kHz, which corresponds to a wavelength that is only 4 times the parameter of the embedded lattice and is a quarter of the cluster's diameter.     

Accurate free vibration analysis of thick laminated circular plates with attached rigid core

This paper deals with the free vibration behavior of laminated transversely isotropic circular plates with axisymmetric rigid core attached at the center. The governing equations of motion are obtained based on Mindlin's first-order shear deformation plate theory. Two possible categories of vibration modes related to up-down translation of the core and wobbly rotation of the core about a diameter are studied. Accurate natural frequencies hitherto not reported in the literature are presented for a wide range of thickness-to-radius ratio, inner-to-outer radius ratio, mass and moment of inertia ratios of the core and various boundary conditions at the outer edge of the plate. Numerical results are compared with those of a three-dimensional finite element method (3-D FEM) to demonstrate the high accuracy and reliability of the current analysis.     

中等半径比反向旋转圆Couette系统流动稳定性的实验和数值研究

圆Couette系统已成为研究从层流转捩为湍流以及有限几何尺寸对图案选择影响的范例.本文以实验和计算机模拟方法研究中等半径比圆Couette系统的稳定性.考察同轴独立旋转圆筒之间的粘性不可压缩流体运动，推广了经典的Rayleigh离心不稳定性理论，导出稳定性判据，用来定量地确定稳定界限.实验采用了流动显示和激光散射技术.仪器有半径比η=0.699，形状比Γ=18.流动状态相图中的显著特征是新的首次失稳态：当外筒静止或反向旋转时，首次失稳出现具有非零方位角波数的螺旋涡流，在轴向和方位角方向为行进波，而并非与时间无关的Taylor涡.初步实验所得的转捩Reynolds数与数值计算结果一致.实验室和数值实验显示出半径比对图案形成和转捩序列的影响. 关键词：     

Backscattering enhancements from Rayleigh waves on the flat face of a tilted solid cylinder in water

When the face of a finite solid elastic cylinder is ensonified by an acoustic wave, a variety of backscattering contributions associated with acoustic wave coupling into elastic waves are observed. A significant backscattering enhancement is observed for tilts such that the acoustic wave is incident on the face of the cylinder in the vicinity of the coupling angle for launching Rayleigh waves across the face. The observed backscattering indicates that the Rayleigh waves are reflected at the edge of the face and subsequently radiate acoustic waves in the backscattering direction. The measured backscattering is compared to an approximate theoretical prediction. Approximating the focusing of the Rayleigh wave after reflection at the (circular) edge by a Gaussian beam pressure distribution on the cylinder's face yields simple expressions for the amplitude which are consistent with the measurements. In the vicinity of end-on incidence, other backscattering contributions due to the reflection of waves traveling down the length of the cylinder are observed. There is also evidence of a face-traversing longitudinal wave for slightly tilted cylinders.     

Calculation of curvature dependent surface plasmon resonance in gold nanospheroid and nanoshell

In this paper, theoretical calculations based on dipole-limit are performed to investigate the effects of curvature on the surface plasmon resonance (SPR) properties of nanometer size gold spheroid and shell. By comparing the aspect ratio with the shell thickness, we demonstrated that the curvature radius is a common better factor that can be used to predict the SPR wavelength and shift fashion. For nanospheroid, increasing the ratio of curvature radius corresponding to the climaxes leads to an increase in the ratio of SPR wavelength, whereas increasing the ratio of curvature radius of outer and inner surface in nanoshell leads to an decrease in the ratio of SPR wavelength. As a morphologic factor, curvature radius plays an important role in affecting the distribution of electron density, and consequently controlling the SPR frequency.     

Formation of a deep scattering layer in a stratified flow behind a two-dimensional obstacle

A stratified stationary flow around a circular cylinder is accompanied by the formation of a thin, acoustically contrasting layer extending along the horizontal axis of the flow. The theoretical and experimental studies show that the pressure differential and the backscattering coefficient of the layer can be quantitatively estimated in the framework of the problem on a stratified ideal incompressible liquid flow around a cylinder.     

Kink instability of a highly deformable elastic cylinder

When a soft elastic cylinder is bent beyond a critical radius of curvature, a sharp fold in the form of a kink appears catastrophically at its compressed side while the tensile side remains smooth. The critical radius increases linearly with the diameter of the cylinder but remains independent of its material properties such as modulus; the maximum deflection at the location of the kink depends on both the material and geometric properties of the cylinder. The catastrophic dynamics of evolution of the kink depicts propagation of a shear wave from the location of the kink towards the edges signifying that kinking is an elastic response of the material which results in extreme localization of curvature. We have rationalized this phenomenon in the light of the classical Euler's buckling instability in slender elastic rods.     

Capacitance analysis of a circular disk on a dielectric layer

Using the Hankel transform, the mixed boundary value problem of a conducting, circular disk on a dielectric layer in an electric field was reduced to the solution of dual integral equations. Analytical expressions of the capacitance of the electrical system to the second approximation were derived for the ratio of the layer thickness to the disk radius being larger than one and the ratio being less than one, respectively. Both expressions yield numerical results in accord with those reported in literature. The capacitance of a circular disk on a semi-infinite dielectric can be used for a ratio larger than or equal to 4. Using the results, the thickness effect on electrowetting of a disk-like conducting film on a dielectric substrate was discussed. There exists an upper bound of the electric voltage applied to the film above which the saturation of contact angle or local instability will occur.