Saint-Venant torsion of orthotropic piezoelectric elliptical bar

The object of this paper is the Saint-Venant torsion of a solid elliptical cylinder made of orthotropic homogeneous piezoelectric material. We find the shape of the homogeneous orthotropic piezoelectric elliptical cross section which does not warp under the applied torque. The sizes of the orthotropic piezoelectric solid elliptical cross section, which has the maximum value of torsional rigidity for a given cross-sectional area, are also determined.

Equilibrium tilt of slippery elliptical rods in creeping simple shear

It is shown that shape anisotropy and intrinsic surface slip lead to equilibrium tilt of slippery particles in a creeping simple shear flow, even for nearly shape-isotropic particles with a cross-section that is close to circular provided the Navier-slip length is sufficiently large. We study a rigid particle with an elliptical cross-section, and of infinite extent in the vorticity direction, in simple shear. A Navier-slip boundary condition is imposed on its surface. When a Navier-slip length parameter $\lambda$ is infinite, an analytical solution is derived for the Stokes flow around a particle tilting in equilibrium at an angle $(1/2)\cos ^{-1}((1-k)/(1+k))$ to the flow direction where $0 \le k \le 1$ is the ratio of the semi-minor to semi-major axes of its elliptical cross-section. A regular perturbation analysis about this analytical solution is then performed for small values of $1/\lambda$ and a numerical continuation method implemented for larger values. It is found that an equilibrium continues to exist for any anisotropic particle $k < 1$ provided $\lambda \ge \lambda _{crit}(k)$ where $\lambda _{crit}(k)$ is a critical Navier-slip length parameter determined here. As the case $k \to 1$ of a circular cross-section is approached, it is found that $\lambda _{crit}(k) \to \infty$ , so the range of Navier-slip lengths allowing equilibrium tilt shrinks as shape anistropy is lost. Novel theoretical connections with equilibria for constant-pressure gas bubbles with surface tension are also pointed out.

Numerical simulation of a stabilizing Poiseuille-type polymer fluid flow in the channel with elliptical cross-section

This work is devoted to the numerical analysis of stabilization of the incompressible viscoelastic polymer fluid flow in the channel with elliptical cross-section. To describe the flow, mesoscopic rheological relations are used, and resolving non-stationary equations are derived. For solving them a special pseudo-spectral method is developed and implemented. As time increases, under certain conditions on the parameters of flow the solution to the non-stationary problem stabilizes and converges to the one of three branches of the solution to the corresponding stationary problem. It is shown that the variation of the parameters describing polymer microstructure leads to the switch of stabilized solution between these branches. The work provides the results of simulation of the flow stabilization and the analysis of the threshold values of parameters at which the switching occurs.

Analysis of Beam Bending with an Elliptical Cross-Section

This paper calculates the stress function constants to determine and analyse the stress field of a beam with an elliptical cross-section under transverse loading. This was performed using linear elasticity principles. The Beltrami-Michell compatibility equations were used to derive the formulas used to calculate these parameters in the beam with the elliptical cross-section. This paper uses dimensionless analysis to comprehend the effect of each variable in the problem. The loading was applied at the centre of the right-end face of the elliptical beam. This loading configuration is the same as an existing linear elasticity problem; however, that problem models a cylindrical beam instead of an elliptical one. Thus, the existing parameters from the cylindrical model were used to verify the formulas, calculated in this paper, for the elliptical beam.

Numerical Studies on the Stiffness of Arc Elliptical Cross-section Helical Spring Subjected to Circumference Force

Due to its excellent properties, elliptical cross-section helical spring has been widely used in automobile industry, such as valve spring, arc spring used in Dual Mass Flywheel and so on. Existing stiffness formulae of helical spring remain to be tested, and stiffness property of elliptical cross-section arc spring has been little studied. Hence, study on the stiffness of elliptical cross-section helical spring is significant in the development of elliptical cross-section helical spring. This paper proposes a method to study the stiffness property of elliptical cross-section helical spring that the experiment design method is adopted with finite element analysis. Firstly, the finite element analysis method was used to verify the cylindrical (circular cross-section and elliptical cross-section) springs. Then, the regression formula was designed and derived compared with the reference springs’ stiffness formulae by experimental design. Last, regression formula was verified with existing experiment data. The novelty in this paper is that simulation technology of arc spring was investigated and a stiffness regression equation of arc elliptical cross-section spring was obtained using orthogonal regression design, with significance in wide use of the arc elliptical cross-section helical spring promotion.

Elliptical plasma-filled waveguide as a new standard short-period undulator

Undulators as the sources of high-brilliance synchrotron radiation are of widespread interest in new generations of light sources and free-electron lasers. Microwave propagation in a plasma-filled elliptical waveguide can be studied as a standard short-period undulator. This structure as a lucrative insertion device can be installed in the storage ring of third- and fourth-generation light sources to produce high-energy and high-brilliance synchrotron radiation. In this article, the propagation of the transverse electric modes in a plasma-filled waveguide with an elliptical cross-section is investigated, and the field components, the cut-off frequencies and the electron beam trajectory are calculated. With due consideration of the electron beam dynamics and in order to achieve a standard short-period undulator, parameters such as the dimensions of the waveguide elliptical cross-section, the microwave frequency and the plasma density are calculated.