Synchronous whirling of spinning homogeneous elastic cylinders: linear and weakly nonlinear analyses

Nonlinear Dynamics - Stationary whirling of slender and homogeneous (continuous) elastic shafts rotating around their axis, with pin–pin boundary condition at the ends, is revisited by...     

Acoustoelasticity in a weakly anisotropic monoclinic elastic material

The acoustoelasticity in a stressed monoclinic elastic material is analyzed theoretically. It is assumed that the material has weak anisotropy, such that the second-order elastic constants differ slightly from those of an isotropic material and the third-order elastic constants retain general monoclinic anisotropy. The propagation velocities, the polarization directions and the acoustoelastic effects for principal longitudinal and transverse waves are obtained and presented as functions of the elastic constants, principal stresses and directions of principal axes of stress. The coefficients appearing in the formulas are tabulated for Laue groups.     

Electroconvective stability of a weakly conducting liquid

In inhomogeneous electric fields, at sufficiently high field strengths, a weakly conducting liquid becomes unstable and is set in motion [1–4]. The cause of the loss of stability and the motion is the Coulomb force acting on the space charge formed by virtue of the inhomogeneity of the electrical conductivity of the liquid [4–13]. This inhomogeneity may be due to external heating [4–6], a local raising of the temperature by Joule heating [2, 7, 8], and nonlinearity of Ohm's law [9–13]. In the present paper, in the absence of a temperature gradient produced by an external source, a condition is found whose fulfillment ensures that the influence of Joule heating on the stability can be ignored. Under the assumption that this condition is satisfied, a criterion for stability of a weakly conducting liquid between spherical electrodes is obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–142, July–August, 1979.     

Eshelby tensor construction for a weakly anisotropic elastic medium

A method of constructing the interior Eshelby tensor for a weakly anisotropic elastic medium is proposed.     

Degenerate weakly non-linear elastic plane waves

Weakly non-linear plane waves are considered in hyperelastic crystals. Evolution equations are derived at a quadratically non-linear level for the amplitudes of quasi-longitudinal and quasi-transverse waves propagating in arbitrary anisotropic media. The form of the equations obtained depends upon the direction of propagation relative to the crystal axes. A single equation is found for all propagation directions for quasi-longitudinal waves, but a pair of coupled equations occurs for quasi-transverse waves propagating along directions of degeneracy, or acoustic axes. The coupled equations involve four material parameters but they simplify if the wave propagates along an axis of material symmetry. Thus, only two parameters arise for propagation along an axis of twofold symmetry, and one for a threefold axis. The transverse wave equations decouple if the axis is fourfold or higher. In the absence of a symmetry axis it is possible that the evolution equations of the quasi-transverse waves decouple if the third-order elastic moduli satisfy a certain identity. The theoretical results are illustrated with explicit examples.     

Dynamics of electroconvective structures in a weakly conducting liquid

The finite-amplitude evolution of electroconvective structures in a weakly conducting liquid with an electroconductive charge formation mechanism is examined. The liquid is in the electrostatic field of a horizontally placed capacitor and is heated from below, and the electric charge time constant is much shorter than the characteristic hydrodynamic time. The interaction between the electroconductive convection and thermogravitational convection is considered. The evolution of the supercritical structures is investigated by direct numerical simulation using the finite-difference method. The bifurcations leading to the formation of stationary and wave liquid flows are analyzed. Nonlinear modes of stationary convection and traveling waves with different space-time patterns are identified and investigated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 20–27, May–June, 2008.     

Friction-induced vibration of a slider on an elastic disc spinning at variable speeds

Nonlinear Dynamics - The friction-induced vibration of a mass–slider with in-plane and transverse springs and dampers in sliding contact with a spinning elastic disc in three different...     

Convective stability of a weakly conducting liquid in an electric field

In an inhomogeneously heated weakly conductive liquid (electrical conductivity 10^–12–1 cm^–1) located in a constant electric field a volume charge is induced because of thermal inhomogeneity of electrical conductivity and dielectric permittivity. The ponderomotive forces which develop set the liquid into intense motion [1–6]. However, under certain conditions equilibrium proves possible, and in that case the question of its stability may be considered. A theoretical analysis of liquid equilibrium stability in a planar horizontal condenser was performed in [2, 4]. Critical problem parameters were found for the case where Archimedean forces are absent [2]. Charge perturbation relaxation was considered instantaneous. It was shown that instability is of an oscillatory character. In [4] only heating from above was considered. Basic results were obtained in the limiting case of disappearingly small thermal diffusivity in the liquid (infinitely high Prandtl numbers). In the present study a more general formulation will be used to examine convective stability of equilibrium of a vertical liquid layer heated from above or below and located in an electric field. For the case of a layer with free thermally insulated boundaries, an exact solution is obtained. Values of critical Rayleigh number and neutral oscillation frequency for heating from above and below are found Neutral curves are constructed. It is demonstrated that with heating from below instability of both the oscillatory and monotonic types is possible, while with heating from above the instability has an oscillatory character. Values are found for the dimensionless field parameter at which the form of instability changes for heating from below and at which instability becomes possible for heating from above.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–23, September–October, 1976.In conclusion, the author thanks E. M. Zhukhovitskii for this interest in the study and valuable advice.     

Axisymmetric wetting of a liquid droplet on a stretched elastic membrane

Wetting of a liquid droplet on another liquid substrate is governed by the well-known Neumann equations. The present work aims to develop an explicit modified version of the Neumann equations for axisymmetric wetting of a liquid droplet on a highly stretched elastic membrane of non-zero bending rigidity. An explicit modified form of the Neumann equations is derived to determine the two contact angles, which is reduced to Young’s equation for a liquid droplet on a rigid membrane or to the Neumann...     

Stability of plane poiseuille flow of a highly elastic liquid

The stability of fully developed pressure driven plane laminar flow of a Maxwell fluid has been studied using linear hydrodynamic stability theory. Elasticity is destabilizing in the inertial regime, but the flow is found to be stable to infinitesimal disturbances at low Reynolds numbers. This result contradicts previous calculations, which predicted a low Reynolds number flow instability at a critical recoverable shear of order unity. The previous calculations were carried out using less accurate numerical methods; the eigenvalue problem which must be solved is a delicate one, requiring sophisticated umerical techniques in order to avoid the calculation of spurious unstable modes.This work has direct bearing on the question of the mechanism of a low Reynolds number extrusion instability known as “melt fracture”. It is observed that the intensity of melt fracture increases with increasing die length for high density polyethylene, and it is therfore believed by some experimentalists that fully-developed die flow is unstable for this polymer above a critical recoverable shear. The analysis appears to be at variance with this interpretation of the experimental results.     

Impact of blunted bodies on a liquid or elastic medium

The impact interaction between a solid body and a liquid or elastic half-space and between two elastic bodies is analyzed. The main approaches and representative numerical results are set out.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 3–44, November 2004.This revised version was published online in April 2005 with a corrected cover date.     

Unsteady weakly perturbed motion of a body of revolution in a liquid with jet separation

The unsteady weakly perturbed motion of a body in a liquid with jet separation has been investigated on various occasions in the twodimensional formulation [1–3]. The present paper gives a generalization of the formulation of this two-dimensional problem to the threedimensional case of flow past a body of revolution in accordance with Kirchhoff's scheme. A method is proposed for solving the obtained boundary-value problem using a Green's function. This function is constructed in a special system of curvilinear coordinates. To obtain an effective solution, a Laplace transformation is used. Expressions are given for the Laplace transforms of the vectors of the force and torque acting on the body in the unsteady motion.     

Instability of a thermally inhomogeneous layer of weakly conducting liquid in an electric field

We give the results of a theoretical investigation of the hydrostatic stability of a plane horizontal layer of weakly conducting liquid for different constant temperatures and potentials on the thermally and electrically conducting capacitor plates bounding the layer. We found that the onset of electrothermal convection is of an oscillatory nature. The critical conditions for loss of stability were found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 133–138, November–December, 1974.     

Motion analysis of a spinning satellite system with off-centre tanks partially filled with liquid

The sloshing problem for, a spherical tank partially filled with liquid is analysed in this paper. The study is based on the goveming, equations of fluid dynamics and the Euler's equations of systems with the influences of tank off-centering, fluid vortices and the Coriolis' acceleration on the motion states of the systems taken into consideration. In the study, we adopt the concept of uniform vortex motion of fluid generalized by Pfeiffer and apply the boundary element method (BEM) to the calculation of the natural frequence and the velocity field of the liquid sloshing. The motion characteristics of the flow-solid spinning system is then analysed. The project is supported by the National Natural Science Foundation of China and Ministry of Astronautics.