The Slow Wave in a Two-Layer Acoustic Waveguide Placed in an Elastic Medium

Kinematic characteristics of the slow wave propagating in an acoustic medium that consists of two layer (water-oil and gas-oil) and is located inside an elastic medium are considered. It is shown that the slow wave originates for arbitrary parameters of the model. Its velocity in the low-frequency approximation depends on the densities of the gas and liquid and does not depend on the velocities in them. Dispersion curves of the phase velocity of the wave are constructed for a wide range of frequencies. Bibliography: 6 titles.     

Torsion Waves on the Cylindrical Surface of a Semiinfinite Elastic Medium

Torsion waves on a cylindrical cavity in a semiinfinite elastic medium are investigated. The waves are generated by steady-state torsional vibrations of a flat, circular punch coupled with the half-space. A technique of contour transformation of the integrals involved in problems of this kind is described. An algorithm and numerical results are given for calculating the modulus of the complex amplitude of the displacement vector on the cylindrical surface as a function of the vertical coordinate in both the near and far fields.     

Scattering on a Small Inhomogeneity in an Elastic Medium

Problems on the diffraction of elastic plane waves (transverse and longitudinal) scattered on a cylinder are investigated. The radius a of the cylinder is small enough ( , where is the wave number). The waves of horizontal polarization (SH waves) are scattered similarly to the electromagnetic wave of the respective polarization. It is proved that a small inhomogeneity radiates as a point source, with its amplitude proportional to the difference of the Lamé parameters and and to the area of a cross section of the inhomogeneity. The scattering of a plane wave of vertical polarization is subject to a more complicated law of radiation, because of the vector nature of the problem, and the respective components of the displacement vector are represented in terms of the scalar and vector potentials. However, the scattering of the wave field on the small inhomogeneity has qualitatively the same asymptotic behavior as in the case of the SH wave. Bibliography: 4 titles.     

Variational Problem on Equilibrium of an Elastic Medium Located in Elastic Shell

The global solvability of the problem about equilibrium of an elastic medium located in an elastic shell is established by variational methods. In the case of one-parametric force field, the bifurcation problem is studied. As is shown, the standard necessary condition for bifurcation is also sufficient for the problem under consideration. Bibliography: 7 titles.     

Point Defect in a Nonlocal Elastic Medium

We investigate the stress field in the vicinity of a point defect in a nonlocal elastic solid. Unlike the classical solution, the stress field has no singularities. We estimate the values of the elastic energy of a defect and maximum stresses.     

Using Condensing Grids to Simulate an Electron-Beam Relativistic Amplifier in a Cylindrical Waveguide with a Plasma-Dielectric Filling

A simulation algorithm is considered for the amplification of electromagnetic waves in a cylindrical waveguide with a plasma-dielectric filling. The field part of the problem is described by a Schrödinger-type equation for the polarization potentials. Matching conditions with discontinuities of 1st and 2nd kind are specified on the interface. Correct resolution of the singularities is achieved with a step-doubling condensing grid. Prototype calculations are reported for the Bessel equation used to choose the condensing grid parameters. The field equations are solved numerically by five-point matrix sweeping with 2×2 matrices. Simulation results are reported for the process of amplification.     

Transformation of a Pressure Pulse in a Fluid-Filled Cylindrical Elastic Shell

The influence of a tubular elastic insert of finite length in a fluid-filled elastic shell on the propagation of a pressure pulse generated at a certain distance from the insert is investigated. The Laplace integral transform is used to solve the corresponding mathematical problem. Analytical solutions are first obtained in each separate domain of the hydroelastic system, subject to the coupling boundary conditions, and then the Laplace transforms are inverted numerically. The influence of the geometrical parameters of the insert and the shell on the pressure distribution in the fluid, the radial displacement, the bending moments, and the shearing forces are analyzed in detail both quantitatively and qualitatively. It is shown that the transmission of the pressure pulse in the junctions of the insert with the shell is accompanied by highly localized stress concentration there, which is several orders of magnitude greater than in the homogeneous shell.     

Transverse Oscillations of a Cylindrical Vessel with a Two-Layer Liquid Separated by an Elastic Membrane

A solution is given for the transverse oscillations, under elastic forces, of a cylindrical vessel containing an ideal two-layer liquid with elastic membranes at the free and inner surfaces of the stratified liquid. The following limiting cases for the elastic membrane are examined: it lies only at the free surface of a uniform and two-layer liquid; it separates a two-layer liquid; it exists at both the free and the inner surfaces of a two-layer liquid. The numerically calculated dependences of the first eigenfrequency on the tension of the membrane, liquid densities, and filling depth are analyzed.     

Pulse Propagation in a Cylindrical Elastic Shell Filled with a Viscous Fluid

The propagation of waves generated by pressure pulses in a cylindrical elastic shell filled with a viscous fluid is investigated. The problem models the propagation of a pulse pressure wave in a blood vessel and is solved by means of Laplace transforms. This approach permits analytical solutions to be constructed in transform space. The original functions are recovered by numerical inversion of the Laplace transform. The results are analyzed for various values of the parameters.     

弹性梁方程共振问题的几个多解存在定理

本研究弹性梁方程边值共振问题－d^4u/dx^4 πu g(x,u)=e(x)(0相似文献   

Multiobjective Optimization of a Composite Cylindrical Shell with an Elastic Core with Account of Reliability

Multiobjective optimization of the structure and geometry of a laminated anisotropic composite shell with an elastic core under thermal action is considered. The thermoelastic properties of the laminated composite are determined from the known properties of the monolayer and the given values of the variable structural and geometric parameters. The properties to be optimized - the critical load and thermal stresses - depend on two variable parameters, the stochastic properties of the composite, and the temperature. In the space of the properties being optimized, the domain of allowable solutions and the property scatter ellipses for the optimum compromise project are found. The reliability of the project is determined with regard for the correlation between the critical and thermal stresses.     

An Inner Source in a Transversely Isotropic Elastic Medium

For a homogeneous, transversely isotropic elastic medium excited by a point force acting on the isotropy plane, an exact displacement field is constructed. This field decomposes into P-SV waves and SH waves. For SH waves satisfying the Lamé equations, boundary conditions are established and rather simple expressions are derived. These expressions are compared with the first terms of the ray series. Bibliography: 9 titles.     

Wave Propagation in an Elastic Medium Intersected by Systems of Parallel Fractures

An elastic anisotropic medium intersected by systems of parallel fractures is investigated. Every fracture is considered as a plane boundary with jumps of displacements and stresses, and these jumps are linear functions of displacements and stresses averaged on the boundary. For this medium, an effective model is constructed by the method of matrix averaging. The equations of this model describe wave propagation in the given medium and are more complicated than the equations of elasticity theory. In particular cases, the equations obtained are converted to the equations of elastic media. On the basis of the equations of the effective model, expressions for the densities of the kinetic and potential energies are derived, and conditions of absoption in the medium are established. Bibliography: 15 titles.     

Scattering of Acoustoelectric Waves on a Cylindrical Inhomogeneity in a Transversely Isotropic Piezoelectric Medium

Scattering of acoustoelectric waves on a inhomogeneity is studied. The scatterer is a circular, continuous piezoelectric cylinder (fiber) embedded in a transversely isotropic piezoelectric medium. Expressions are found for the scattering amplitudes and total cross sections of three acoustoelectric waves propagating in the direction normal to the fiber axis. In the long-wave approximation, these expressions are obtained in an explicit form.     

Propagation of Electromagnetic Waves in an Open Planar Dielectric Waveguide Filled with a Nonlinear Medium II: TM Waves

Computational Mathematics and Mathematical Physics - A nonlinear eigenvalue problem on an interval is considered. The nonlinearity in the equation is specified by a nonnegative monotonically...