The laser gain under nonhomogeneous boundary conditions

The method proposed by the authors for solving the Helmholtz equation with homogeneous boundary conditions was tested for an elliptic section. The method is generalized to the Helmholtz equation with inhomogeneous boundary conditions. The generalization is verified for circular and elliptical sections.

Torsion of anisotropic and non-uniform cylindrical rods with elliptical section

In work the limit state of cylindrical and prismatic rods from anisotropic ideal rigid-plastic material is investigated under torsion for arbitrary condition of plasticity, and the torsion of anisotropic and non-uniform rods with elliptic section under the condition of Mises-Hill plasticity is considered. The integrals determining the stressed state of an anisotropic rod under arbitrary condition of plasticity are obtained, the field of characteristics of the basic ratios for anisotropic and composite rods under the condition of Mises-Hill plasticity is constructed, the ratios along characteristics are obtained, the envelopes of the family of characteristics and lines of tension rupture are found.

Numerical Simulations of an Oscillating Flow Past an Elliptic Cylinder

This paper presents a numerical investigation of a two-dimensional (2D) oscillatory flow around a cylinder of different elliptic ratios, in order to study the effect of the elliptic form of the cylinder on the vorticity field and the hydrodynamic forces that act on it. The elliptic ratio ε was varied from 1 to 0.1, where the small axis is parallel to the flow direction, simulating cases ranging from a circular cylinder to the case of a cylinder with a profiled elliptic section. The investigations presented here are for Reynolds number Re = 100 and Keulegan number KC = 5. The numerical visualization of the flow for different elliptic ratios shows five different modes of vortex shedding (symmetric and asymmetric pairing of attached vortices, single-pair, double-pair, and chaotic), which depend on the range of the elliptic ratio. The results show that the longitudinal force increases with the reduction of the elliptic ratio. The transverse force appears from the elliptic ratio ε=0.75 and increases with the reduction of this ratio in the range of 0.75≥ε≥0.4, then decreases for ε<0.4. On the other hand, concerning the Morison coefficients the results show that the drag coefficient is sensitive to the swirling layout while the coefficient of inertia does not seem to be much affected by the geometry of the cylinder.