Numerical study of the influence of boundary conditions on the dynamic behavior of a cylindrical shell conveying a fluid

We consider a finite element algorithm intended to study the dynamic behavior of an elastic cylindrical shell filled with an immovable or flowing fluid. To describe the fluid, we use the perturbed velocity potential whose equations with the corresponding boundary conditions are solved by the Bubnov-Galerkin method. To describe the shell, we use the variation principle, which includes the linearized Bernoulli equation for calculating the hydrodynamic pressure acting on the shell on the side of the fluid. Solving the problem is reduced to calculating and analyzing the eigenvalues of the coupled system of equations obtained as a result of combining the equations for the perturbed velocity potential and the shell displacements. We consider several test problems in which, along with the comparison of the computational results with the earlier published experimental, analytic, and numerical data, we also study the dynamic behavior of the “shell-fluid” system for various boundary conditions for the perturbed velocity potential.     

Rheological properties of solutions and gels of combined systems hydrophobically modified polyacrylamides-new viscoelastic cationic surfactants

The rheological properties (viscosity and dynamic elasticity modulus) of solutions and gels of combined systems composed of hydrophobically modified polymers containing main-chain charged groups or lacking these groups and of newly synthesized viscoelastic cationic surfactants with different amounts of OH groups and long nonpolar saturated and trans monounsaturated radicals have been studied. It has been shown that the maximum viscosity of solutions of polymer-surfactant complexes corresponds to the very low concentration of the surfactant. Regions where homogeneous and heterogeneous combined solutions and gels exist are considered. An increase in the viscosity of the combined solutions with temperature is discovered and discussed. The synergistic effect of polymers and surfactants is demonstrated, and a more efficient role of surfactants in the case of uncharged polymers is revealed. The roles of the number of OH groups and the length of the nonpolar radical in a surfactant molecule and a difference in the properties of systems containing surfactants with saturated and unsaturated radicals are considered.     

Synthesis and properties of 4,4′-bis[5-alkyl(aryl)benzoxazol-2-yl]-2-hydroxy(alkoxy)biphenyls

Synthesis of 2-hydroxy(methoxy)-4,4′-biphenyldicarboxylic acids was developed. Based on their reactions with o-aminophenols we prepared for the first time 4,4′-bis[5-alkyl(aryl)benzoxazol-2-yl]-2-hydroxy-(alkoxy)biphenyls, which might be of interest as luminescent dyes. Hydroxy compounds in a salt form possess abnormally high Stokes shift.     

Optimization of geometry of elastic bodies in the vicinity of singular points on the example of an adhesive lap joint

The stress state in adhesive lap joints with various geometric shapes of spew fillet is studied. It is noted that the applied design models of the considered problem include singular points at which infinite stress values are possible if one uses the linear elasticity theory to calculate the stress state. Based on the conclusions of the solution of the geometry optimization problem in the vicinity of the singular points of elastic bodies, variants of the geometry of spew fillet, which provide the most significant decrease in the concentration of stresses in adhesive lap joints, are proposed.     

Stability analysis of stationary and rotating circular cylindrical shells conveying flowing and rotating fluid

The paper deals with numerical analysis of the stability of stationary and rotating cylindrical shells interacting witha fluid flowing and rotating inside them. It is shown that in the case of the fluid combined flow, the type of the loss of stability depends on the type of the boundary conditions. It is also shown that for different cases of boundary conditions and different geometric dimensions, the fluid rotation can result in an increase or a decrease in the critical velocity of the fluid axial flow.     

Finite-element simulation of myocardial electrical excitation

Based on a single-domain model of myocardial conduction, isotropic and anisotropic finite element models of the myocardium are developed allowing excitation wave propagation to be studied. The Aliev-Panfilov phenomenological equations were used as the relations between the transmembrane current and the transmembrane potential. Interaction of an additional source of initial excitation with an excitation wave that passed and the spread of the excitation wave are studied using heart tomograms. A numerical solution is obtained using a splitting algorithm that allows the nonlinear boundary-value problem to be reduced to a sequence of simpler problems: ordinary differential equations and linear boundary-value problems in partial derivatives.     

Hydroelastic stability of multi-plate structures interacting with flowing fluid

The paper is concerned with the finite-element analysis of natural vibrations and hydroelastic stability of two parallel plates interacting with liquid. The influence of the fluid layer thickness on the eigenfrequencies, vibration modes and hydroelastic stability boundary are estimated based on the results of numerical solution of some example problems. The numerical investigation substantiates the existence of various instability modes, the onset of which depends on the combinations of kinematic boundary conditions specified at the plate ends. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Definition of free hyperradial dynamics for the three-body pproblem

Following the analysis of [1,2], we define appropriate hyperradius-distorted free incoming and outgoing waves (HDFW) that incorporate unphysical long-range effects of the hyperradial-adiabatic (HA) treatment of the three-body scattering problem.