Harmonic vibrations and waves in a cylindrical helically anisotropic shell

A Kirchhoff-Love type applied theory is used to study the specific characteristics of harmonic waves and vibrations of a helically anisotropic shell. Special attention is paid to axisymmetric and bending vibrations. In both cases, the dispersion equations are constructed and a qualitative and numerical analysis of their roots and the corresponding elementary solutions is performed. It is shown that the skew anisotropy in the axisymmetric case generates a relation between the longitudinal and torsional vibrations which is mathematically described by the amplitude coefficients of homogeneous waves. In the case of a shell with rigidly fixed end surfaces, the dependence of the first two natural frequencies on the shell length and the helical line slope α, i.e., the geometric parameter of helical anisotropy, is studied. A boundary value problem in which longitudinal vibrations are generated on one of the end surfaces and the other end is free of forces and moments is considered to analyze the degree of transformation of longitudinal vibrations into longitudinally torsional vibrations. In the case of bending vibrations, two problems for a half-infinite shell are studied as well. In the first problem, the waves are excited kinematically by generating harmonic vibrations of the shell end surface in the plane of the axial cross-section, and it is shown that the axis generally moves in some closed trajectories far from the end surface. In the second problem, the reflection of a homogeneous wave incident on the shell end is examined. It is shown that the “boundary resonance” phenomenon can arise in some cases.     

Saint-Venant problem for solids with helical anisotropy

We discuss the solution of Saint-Venant’s problem for solids with helical anisotropy. Here the governing relations of the theory of elasticity in terms of displacements were presented using the helical coordinate system. We proposed an approach to construct elementary Saint-Venant solutions using integration of ordinary differential equations with variable coefficients in the case of a circular cylinder with helical anisotropy. Elementary solutions correspond to problems of extension, of torsion, of pure bending and of bending of shear force. The solution of the problem is obtained using small parameter method for small values of twist angle and numerically for arbitrary values. Numeric results correspond to problems of extension–torsion. Dependencies of the stiffness matrix (in dimensionless form) on angle between the tangent to the helical coil and the axis of the cylinder corresponding to stiffness on stretching and torsion are illustrated graphically for different values of material and geometrical parameters.     

On surface elasticity theory for plane interfaces

A closed system of surface elasticity equations was derived in terms of surface quantities defined as integrals of respective excess bulk quantities normal to the interface. The equations were consistently linearized for the case of small strains. It is shown that these equations are more general than the Shuttleworth equations. Equations of this type were also derived for the particular case of an interface formed by a thin layer with constant properties. The derived equations were used to consider bending of a plate under pressure applied to both sides.     

Hysteresis-free spin valves with a noncollinear configuration of magnetic anisotropy

A noncollinear configuration of magnetic anisotropy in spin valves with strong and weak interlayer couplings has been formed by annealing and cooling in a magnetic field. The dependence of the low-field magnetoresistance hysteresis loop width on the angle between the applied magnetic field and the principal axes of the magnetic anisotropy in a spin valve has been investigated. It has been found that, only in the case of a strong ferromagnetic interlayer coupling, the formation of a noncollinear configuration of the magnetic anisotropy provides a hysteresis-free character of the magnetization reversal of the free layer with retaining the maximum magnetoresistance and magnetoresistive sensitivity.     

Spin resonance associated with itinerant electrons affected by the injected spin current

The effect of spin injection on the spin resonance associated with itinerant electrons in a nonmagnetic semi-conductor has been studied within the phenomenological approach. The power absorbed under the resonance conditions has been analyzed as a function of the frequency, effective g-factor, and magnetic field direction. It is shown that the power absorbed by the spin-polarized charge carriers under the resonance conditions can provide a tool for studying the spin injection.     

Tollmien-Schlichting wave generation by flow turbulence

The problem of freestream-turbulence-generated instability waves in the flat-plate boundary layer is solved on the basis of a nonlinear turbulence model admitting the deviation of the speed of propagation of vortex disturbances from the flow velocity. The solution obtained well describes the experimental dependence of the laminar-turbulent transition Reynolds number on the freestream turbulence degree.     

Taking into account van der Waals interaction in some problems of elasticity

We obtain the correction due to van der Waals forces to the flexural rigidity of a layer. The cases of a monolayer and a film consisting of several monolayers are considered. The correction due to van der Waals interaction to the force acting on an indentor is obtained. Two versions of determining the elastic forces at the microlevel are considered. Numerical estimates of the parameter values for which the correction is essential are given.     

Monolithic white LEDs: Approaches, technology, design

The results of investigations of monolithic white InGaAlN LEDs with an active region containing several thin InGaN layers, emitting in the range from blue to yellow-green, and separated by short-period InGaN/GaN superlattices, are presented. The influence of the growth conditions and layer sequence in the active region on the optical properties of monolithic white LEDs was studied with the aim of controlling their color parameters.     

Effect of inhomogeneity on magnetic, magnetocaloric, and magnetotransport properties of La0.6Pr0.1Ca0.3MnO3 single crystal

The effect of magnetic inhomogeneity on magnetic, magnetocaloric, and transport properties of the colossal magnetoresistance manganites with first order ferromagnetic-to-paramagnetic phase transition is studied. The experiments were performed on the single-crystalline samples of La_0.6Pr_0.1Ca_0.3MnO₃. The inhomogeneity is described by the Curie temperature distribution function, which is found from the magnetization data. The temperature dependence of the magnetic field induced change in the entropy is shown to be determined by the distribution function and the shift of the transition temperature in a magnetic field. Similarly, magnetoresistance in the transition region is determined by the resistivity at H=0 and the shift of the transition temperature. The maximum entropy change as well as maximum magnetoresistance can be achieved in the magnetic field of order δT_C/B_M where δT_C is the transition width and B_M is the rate of change of the Curie temperature with magnetic field.Our approach to analysis of the effects of inhomogeneity is general and therefore can be used for all compounds with the first order magnetic phase transition.     

Computation of the energy of an inhomogeneity: Asymptotics and their scope

By passing to the limit in the general solution, we obtain several exact asymptotic formulas for the energy of an inhomogeneity in a body located in an external stress field. The parameters determining the type of the asymptotic behavior are the inclusion semiaxis ratio and the inclusion-matrix elastic modulus ratio. In the case of a large simultaneous deviation of the parameters from unity, we distinguish seven regions corresponding to various successive passages to the limit as these parameters approach zero (or infinity).