Numerical simulation of characteristics of propagation of symmetric waves in microwave circular shielded waveguide with a radially inhomogeneous dielectric filling

The paper presents a numerical simulation of the propagation characteristics of symmetric E-type and H-type waves in microwave circular shielded waveguide with radially inhomogeneous dielectric filling. Using the modified Galerkin method, the calculation of a circular two-layer shielded waveguide was carried out, as a result of which the distribution of the electromagnetic field of the waveguide with linear and parabolic distribution of permeability was determined. The results obtained using the modified Galerkin method were compared with the results obtained using the classical partial domain method, which agree well enough.

On Eshelby’s inclusion problem in nonlinear anisotropic elasticity

In this paper, the recent literature of finite eignestrains in nonlinear elastic solids is reviewed, and Eshelby’s inclusion problem at finite strains is revisited. The subtleties of the analysis of combinations of finite eigenstrains for the example of combined finite radial, azimuthal, axial and twist eigenstrains in a finite circular cylindrical bar are discussed. The stress field of a spherical inclusion with uniform pure dilatational eigenstrain in a radially-inhomogeneous spherical ball made of arbitrary incompressible isotropic solids is analyzed. The same problem for a finite circular cylindrical bar is revisited. The stress and deformation fields of an orthotropic incompressible solid circular cylinder with distributed eigentwists are analyzed.

Time-Harmonic Response of an Elastic Pile in a Radially Inhomogeneous Poroelastic Medium

The time-harmonic response of an elastic pile embedded in a radially inhomogeneous poroelastic medium and subjected to a torsional loading is studied in the present article. In engineering practice, the surrounding soil may be weakened due to the disturbance effect caused by pile driving. To simulate the weakened surrounding soil, a boundary zone model with the complex shear modulus of the inner disturbed soil changing in a parabolic form along the radial direction is proposed. In view of the axis-symmetric deformation of the surrounding soil under torsional load, the equation of motion of the saturated soil is solved in the cylindrical coordinate system. The vibration displacement and shear stress solutions for the inner disturbed soil are gained by expanding the displacement as a power series, and those for the outer undisturbed soil are obtained by solving the partial differential equation. By virtue of continuity conditions at the interface between inner and outer soil regions, the torsional impedance of the radially inhomogeneous soil is solved. Then, via the boundary and continuity conditions of the pile-soil system, the twist angle and torque of the pile are obtained in the frequency domain. Finally, selected numerical results are conducted to investigate the influence of the material damping, softening degree, and softening range of the inner soil on the distribution of the twist angle and torque of the pile along the depth direction.

Exact Solution for the Torsional Vibration of an Elastic Pile in a Radially Inhomogeneous Saturated Soil

An exact solution is proposed to study the time-harmonic torsional vibration of an elastic pile embedded in a radially inhomogeneous saturated soil. The radially inhomogeneous saturated soil is composed of inner disturbed and outer semi-infinite undisturbed concentric annular regions, with the shear modulus of the inner region changing in an exponential form along the radial direction. The governing equation of each region of the saturated soil is solved through rigorous mathematical derivation and the soil torsional impedance is derived with an exact and explicit expression. Making use of the boundary and continuity conditions of the pile-soil system, the torsional complex stiffness at the pile top is obtained in an exact closed form in the frequency domain. Selected numerical results are presented to investigate the influence of the radial inhomogeneity of the surrounding soil on the vibration characteristics of the pile-soil system.