Effect of the non-homogenity on the composite infinite cylinder of orthotropic material

In this Letter, the solution of non-homogeneous orthotropic elastic cylinder for plane strain problems is developed. The dynamical problem of an orthotropic cylinder containing: (i) an isotropic core and (ii) a rigid core are considered. The elastic constants and density are taken as a power function of the radial coordinate. Analytical expressions for the component of the displacement and the components of the stresses in different cases are obtained. The numerical calculations are carried out for the component of displacement and the components of the stresses through the radial of the cylinder. The results indicate that the effect of inhomogeneity is very pronounced. Those cases have been illustrated and discussed by figures.     

A mixed 3D-Shell analytical model for the prediction of sound transmission through sandwich cylinders

The sound transmission through an infinite multilayer cylinder composed of orthotropic skins and an isotropic polymer core is calculated analytically. The motions of the two thin orthotropic skins are described with the first-order shear deformation theory while the isotropic core is modeled with the three-dimensional elasticity theory. The polymer core transfer matrix relating the displacements and the stresses at the two common interfaces between the core and the skins is first calculated. The coupling of the two skins is then made using the modal transfer matrix of the core, leading to the global dynamic equilibrium of the multilayer cylinder. The sound Transmission Loss (TL) of the cylinder excited by an acoustic plane wave is finally calculated. Our results are compared with results published recently in the literature. Excellent agreement is observed for thin cores where the three layers vibrate in phase in the radial direction. The usefulness of the three-dimensional model is demonstrated for a thick and soft core in the higher frequency domain where the skins are vibrating out of phase with a relative displacement in the radial direction. Finally, a parametric study is conducted to demonstrate the influence of the damping of each layer and some observations are made on the shear and compressional strain energies of each layer.     

The transient response of a transversely isotropic cylinder under a laser point source impact

The transient response of a transversely isotropic cylinder under a laser point source impact is solved theoretically. The radial displacement generated by the laser under the ablation regime is numerically calculated by introducing Fourier series expansion and two-dimensional Fourier transform. The validity of this theoretical solution is demonstrated on a fiber reinforced composite cylinder with a strong anisotropy. Experimental displacements are detected at the cylinder surface by the laser ultrasonic technique, and are analyzed by the ray trajectories. Corresponding theoretical displacements are calculated numerically and compared to the experimental signals. Good agreement is found. The diffraction effect caused by the cusp is observed in both theory and experiment.     

Analysis of Functionally Graded Piezoelectric Cylinders in a Hygrothermal Environment

This paper presents an analytical solution for the interaction of electric potentials, electric displacement, elastic deformations, and describes hygrothermal effect responses in hollow and solid cylinders, subjected to mechanical load and electric potential. Exact solutions for displacement, stresses and electric potentials in functionally graded piezoelectric material are determined using the infinitesimal theory. The material properties coefficients of the present cylinder are assumed to be graded in the radial direction by a power law distribution. Numerical examples display the significant of influence of material inhomogeneity. It is interesting to note that selecting a specific value of inhomogeneity parameter can optimize the piezoelectric hollow and solid cylinders responses, which will be of particular importance in modern engineering designs.     

Separation of 3-D displacement components in the white light speckle method

Measurement of in-plane and out-of-plane displacement components using the white light speckle method is considered for three different cases. The first is applicable when in-plane components are small and stresses are directly related to the second differential of the out-of-plane component. The other cases involve components of the same order of magnitude but require recording of either one or two specklegrams. Evidence of experimental demonstration of each case is given.     

Symmetry properties of three-dimensional magnetization distributions induced by focused circularly polarized lights

We analyze symmetry properties of the three-dimensional magnetization distribution in the optic-magneto film induced by focused circularly polarized lights. The magnetization distributions are derived and evaluated based on the vector diffraction theory and the inverse Faraday effect of the isotropic and nonmagnetically ordered material. It is shown that for any radial symmetrical amplitude, phase, or hybrid amplitude-phase pupil filter, the magnetization distribution of the axial component is circular symmetric but those of the radial and azimuthal components are annular symmetric with regard to the optical axis. All of the three components have a symmetric distribution with regard to the focal plane. The direction of both axial and radial components can be inversed with the helicity of incident circularly polarized light but the direction of azimuthal component is independent of helicity. The axial component has a decisive effect to all-optical magnetic recording, and within the effective axial range, the size of its magnetization domain hardly expands in the transverse direction.     

Stresses and displacements for some Rayleigh-type surface acoustic waves propagating on an anisotropic half space

Specific relations between mechanical displacements and stresses for Rayleigh-type surface acoustic waves propagating on an anisotropic half space are demonstrated. For 16 symmetry configurations belonging to the orthorhombic, tetragonal, hexagonal and cubic systems, involving only two displacement and stress components, it is shown that the ratio between the shear and normal stresses inside the propagation media is equal to the ratio between the normal and in-plane displacement components at the free surface. This result generalizes the previous one obtained in the case of an isotropic solid [W. Hassan and P. B. Nagy, J. Acoust. Soc. Am. 104, 3107-3110 (1998)].     

Line-integral solution for the stress and displacement fields of an arbitrary dislocation segment in isotropic bi-materials in 3D space

The solutions for the stress and displacement fields due to an arbitrary dislocation segment in an isotropic bi-material medium consisting of joined three-dimensional (3D) half spaces are derived and expressed in terms of line integrals, integrands of which are given in an exact analytical form that, in turn, can also be integrated to yield analytical expressions for the stress–displacement field. The solution is constructed by employing a general solution derived by Walpole [Int. J. Eng. Sci. 34 (1996) p.629] for any elastic singularity in joined isotropic half space, and combining it with Mura's integral formula for the displacement gradient of an arbitrary dislocation segment in homogeneous medium. The resulting new solution provides a framework for deriving analytical expressions for stress and displacement fields of dislocation curves of arbitrary shapes and orientations. The benefit of the method developed, as compared with other methods found in the literature, is that the new solution presented is naturally divided into two components, a homogenous component representing the field of a dislocation in an infinitely homogenous medium, and an image component. This makes it easy and straightforward to modify existing dislocation dynamics codes that already include the homogenous part. To illustrate the accuracy of the method, the stress field expressions of an edge dislocation with Burgers vector perpendicular to the bi-material interface are derived as a degenerate case of the general result. It is shown that our solution is identical to that found in the literature for this case.     

Solving dislocation equation for the dislocation with complex core

The solution of dislocation equation is explored by extracting the core component from the total displacement field. The core component, which describes the core structure of dislocation, can be given by a set of localized functions which are orthogonal each other. The displacement field with both the edge and screw components are studied simultaneously by introducing an intrinsic frame which is given by directions parallel and perpendicular to the Burger’s vector. From application to the dislocations in the materials YCu, it is found that the method is efficient in solving the dislocation equation in particular for the dislocation with a complex core.     

The Three-Dimensional Dirac Oscillator in the Presence of Aharonov-Bohm and Magnetic Monopole Potentials

No Heading We study the Dirac equation in 3+1 dimensions with non-minimal coupling to an isotropic radial three-vector potential and in the presence of a static electromagnetic potential. The space component of the electromagnetic potential has angular (non-central) dependence such that the Dirac equation separates completely in spherical coordinates. We obtain solutions for the case where the three-vector potential is linear in the radial coordinate (Dirac oscillator) and the time component of the electro-magnetic potential vanishes. The relativistic energy spectrum and spinor eigenfunctions are obtained.     

Study on the radial vibration and acoustic field of an isotropic circular ring radiator

Based on the exact analytical theory, the radial vibration of an isotropic circular ring is studied and its electro-mechanical equivalent circuit is obtained. By means of the equivalent circuit model, the resonance frequency equation is derived; the relationship between the radial resonance frequency, the radial displacement amplitude magnification and the geometrical dimensions, the material property is analyzed. For comparison, numerical method is used to simulate the radial vibration of isotropic circular rings. The resonance frequency and the radial vibrational displacement distribution are obtained, and the radial radiation acoustic field of the circular ring in radial vibration is simulated. It is illustrated that the radial resonance frequencies from the analytical method and the numerical method are in good agreement when the height is much less than the radius. When the height becomes large relative to the radius, the frequency deviation from the two methods becomes large. The reason is that the exact analytical theory is limited to thin circular ring whose height must be much less than its radius.     

The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium

This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.     

Screw dislocations in the field theory of elastoplasticity

A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress field of an infinitely long screw dislocation in a cylinder, a dipole of screw dislocations and a coaxial screw dislocation in a finite cylinder. The stress fields have no singularities in the dislocation core and they are modified in the core due to the presence of localized moment stress. Additionally, we calculated the elastoplastic energies for the screw dislocation in a cylinder and the coaxial screw dislocation. For the coaxial screw dislocation we find a modified formula for the so‐called Eshelby twist which depends on a specific intrinsic material length.     

Microwave scattering diagrams of three-layered SiC-metamaterial/gyrotropic ferrite-SiC cylinders

We present here for the first time the rigorous solution of the boundary diffraction problem of microwave scattering by a multilayered 2D cylinder. The cylinder layers may be made of isotropic, uniaxial anisotropic, electrically and (or) magnetically gyrotropic materials. The number and thickness of the layers may have arbitrary values in our solution. We calculated scattering diagrams (a radial component of real part of the Poynting vector) inside and outside of cylinder using the solution. Here we present scattering diagrams from a three-layered cylinder made of SiC and metamaterial or saturate magnetized ferrite. Diagrams were computed for wave incidence angles θ=π/2,π/3,π/6 inside of metamaterial/ferrite layer at a distance of 1 mm and outside of cylinder at a distance of 2.5 mm from the cylinder axis.     

Nonlinear sigma model and the origin of geometric frustration on curved manifolds

Classical Heisenberg spins considered on an elastic two-dimensional curved manifold in the continuum limit correspond to the nonlinear σ model. If the corresponding Euler-Lagrange (EL) equations support a soliton solution, a mismatch of length scales induces geometrical frustration in the region of the soliton which is relieved by a deformation of the manifold in the region of the soliton. We illustrate the origin of this elastic effect in four different cases: (i) A single soliton on a circular cylinder with anisotropic spin-spin coupling, (ii) a soliton lattice on a circular cylinder with isotropic spin-spin coupling, (iii) a single soliton on an elliptic cylinder, and (iv) a circular cylinder in an external axial magnetic field. For the first three cases the EL equation is the sine-Gordon equation while for the last case it is the double sine-Gordon equation. Geometrical frustration results whenever the solution of the EL equation does not satisfy the self-dual equations of Bogomol’nyi which are a necessary condition to reach the minimum energy configuration in each homotopy class.     

Surface waves propagating around the periphery of a piezoelectric cylinder of hexagonal symmetry with time dependent elastic stiffness

Acoustic surface waves propagating around the periphery of a piezoelectric cylinder of hexagonal symmetry are investigated. A co-axial structure with a piezoelectric insulator as the inner cylinder and electric conductor as the outer cylinder is considered. The dispersion equation is derived and solved under certain approximations assuming the elastic stiffness to be time dependent as in Voigt's model of viscoelasticity. The final expressions for the mechanical displacement component and electric potential are obtained. Ultimately some important parameters of such waves as group velocity, Poynting vector and power flow components have also been determined.I am grateful to Dr. A. K. Pal for his helpful suggestions in the preparation of the paper.     

Analytic solutions to Maxwell–London equations and levitation force for a general magnetic source in the presence of a long type-II superconducting cylinder

The interaction between a general magnetic source and a long type-II superconducting cylinder in the Meissner or mixed state is studied within the London theory. We first study the Meissner state and solve the Maxwell–London equations when the source is a magnetic monopole located at an arbitrary position. Then the field and supercurrent for a more complicated magnetic charge distribution can be obtained by superposition. A magnetic point dipole with arbitrary direction is studied in detail. It turns out that the levitation force on the dipole contains in general an angular as well as a radial component. By integration we obtain the field and supercurrent when the source is a two-dimensional monopole (a magnetically charged long thread along the axial direction), from which the results for a two-dimensional point dipole easily follow. In the latter case the levitation force points in the radial direction regardless of the orientation of the dipole. The case for a current carrying long straight wire parallel to the cylindrical axis is solved separately. The limit of ideal Meissner state is discussed in most cases. The case of mixed state is discussed briefly. It turns out that vortex lines along the axial direction and vortex rings concentric with the cylinder have no effect outside the cylinder and the levitation forces remain the same as in the case of the Meissner state.     

DISPERSION OF WAVES IN IMMERSED LAMINATED COMPOSITE HOLLOW CYLINDERS

A layer element method (LEM) is presented for analyzing frequency and group velocity dispersive behaviours of waves in a laminated composite cylinder surrounded by a fluid. The LEM applies finite elements to model the radial displacement of the cylinder and the radial pressure of the fluid, and complex exponentials to express the axial and circumferential displacements of the cylinder as well as the axial and tangential pressures of the fluid. The dispersive equation for the fluid-loaded cylinder follows from variational techniques. The frequency and group velocity dispersive relationships of the fluid-coupling cylinder are obtained by means of the Rayleigh quotient. Numerical results are given for hybrid laminated composite cylinders and cylindrical shells submerged in water. The addition of the fluid is proven to have considerable impact on the group velocity spectra of waves in laminated composite cylinders.     

A New Approach for Modeling of Industrial Adsorption Column

A theoretical analysis of the effect of velocity radial nonuniformity on nonstationary gas-solid adsorption processes in the column apparatuses is presented. The average concentration model, where the radial velocity component in the gas phase is equal to zero (in cases of a constant velocity radial nonuniformity along the column height), is used in the cases of an axial modification of the radial nonuniformity of the axial velocity components in the gas phase. The use of experimental data, for average concentrations in the gas phase at the column end, for a concrete process (physical or chemical adsorption), permits obtaining the gas phase model parameters related with the radial nonuniformity of the velocity. These parameter values allow using the average concentration model for modeling different adsorption processes.