Application of type Timoshenko equations for shock action

The generalized Timoshenko type equations are obtained from the plane problem equations of the theory elasticity. They might be applied for quick acting forces or displacements problems as the transversal shock on a beam or quick displacement of beam ends. The quick and slow solutions components аге extracted. The quick ones describe the propagation of the shear wave due to the action of a concentrated force or an explosion; the slow solutions are generated by the common verification of the boundary conditions the slow and quick solutions

Linear stability of magnetohydrodynamic flow in a square duct with thin conducting walls

This study is concerned with numerical linear stability analysis of liquid metal flow in a square duct with thin electrically conducting walls subject to a uniform transverse magnetic field. We derive an asymptotic solution for the base flow which is valid not only for high but also moderate magnetic fields. This solution shows that for low wall conductance ratios $c\ll1,$ an extremely strong magnetic field with the Hartmann number $Ha\sim c^{-4}$ is required to attain the asymptotic flow regime considered in the previous studies. We use a vector stream function/vorticity formulation and a Chebyshev collocation method to solve the eigenvalue problem for three-dimensional small-amplitude perturbations in ducts with realistic wall conductance ratios $c=1,0.1,0.01$ and Hartmann numbers up to $10^{4}.$ As for similar flows, instability in a sufficiently strong magnetic field is found to occur in the side-wall jets with the characteristic thickness $\delta\sim Ha^{-1/2}.$ This results in the critical Reynolds number and wavenumber increasing asymptotically with the magnetic field as $Re_{c}\sim110Ha^{1/2}$ and $k_{c}\sim0.5Ha^{1/2}.$ The respective critical Reynolds number based on the total volume flux in a square duct with $c\ll1$ is $\bar{Re}_{c}\approx520.$ Although this value is somewhat larger than$\bar{Re}_{c}\approx313$ found by Ting et al. (1991) for the asymptotic side-wall jet profile, it still appears significantly lower than the Reynolds numbers at which turbulence is observed in experiments as well as in direct numerical simulations of this type of flows.Comment: 18 pages, 9 figures, final versio

Preparation of Ag/C Nanocomposites Based on Silver Maleate and Their Use for the Analysis of Iodine Ions

In recent decades, metal-containing nanocomposites have attracted considerable attention from researchers. In the present study, a detailed analysis of the preparation of Ag/C nanocomposites through the thermolysis of silver maleate was carried out. Thermolysis products are nanocomposites containing silver nanoparticles (NPs) uniformly distributed in a stabilizing carbon matrix. The composition, structure, and properties of the obtained nanocomposites were studied using IR-spectroscopy, X-ray diffraction (XRD), atomic force microscopy (AFM), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and energy dispersive X-ray spectroscopy (EDS). This article reports on the possibility of using Ag/C nanocomposites to create new indicator papers that are sensitive to iodide ions in the concentration range of 0.03–1.6 mg/L (0.24–12.6 μM). The developed papers are used in a technique based on the oxidation of iodides with the formation of molecular iodine, which is extracted in an air stream and transferred to a sensitive paper layer containing silver NPs. The interaction of silver NPs with iodine leads to optical changes that can be tracked using a conventional scanner