On the motion of a sphere with arbitrary slip in a viscous incompressible fluid

An expression for the force on a sphere moving with a time-dependent velocity through an incompressible fluid in nonstationary, nonhomogeneous flow is obtained for the case of arbitrary slip on the surface of the sphere.     

Behavior of nonlinear fluid viscous dampers for control of shock vibrations

Fluid viscous dampers have been widely used for suppression of high velocity shocks. While linear fluid viscous dampers have been used for a long time, nonlinear fluid viscous dampers show considerable promise due to their superior energy dissipation characteristics and significant reduction in the damper force compared to a linear fluid viscous damper for the same peak displacement. This paper presents results from experimental study to characterize fluid viscous dampers when subjected to half-cycle sine shock excitation. The mathematical formulation and a numerical study to evaluate the relative performance of structures with fluid viscous dampers subjected to short-duration shock (impulse) loading are also discussed. The influence of damper nonlinearity (α) and the supplemental damping ratio (ξ_sd) on response has been investigated. The supplemental damping ratio of nonlinear fluid viscous dampers when subjected to shock excitation is found by equivalent linearization using the concept of equal energy dissipation. The paper also presents some design charts, which can be used for preliminary decisions on parameters of nonlinear dampers to be used in design.     

On the thermophoretic motion of a heated spherical drop in a viscous liquid

Expressions for the force and velocity of the thermophoretic motion of a spherical drop in a viscous liquid are derived for arbitrary temperature differences between the surface of the drop and regions away from it. The temperature dependence of the viscosity is taken into account in the form of an exponential-power series.     

Generation of magnetic field during shearing motion of a conducting viscous medium

Magnetic field generation in shear flows of an incompressible viscous conducting medium across the flux lines of the initial field created in them is considered in the framework of the plane 1D problem of magnetohydrodynamics. The conditions of free slip and “sticking” are stipulated at the boundary between the flows. The variations of the magnetic field and velocity of shear flow occurring in the moving medium correspond to an Alfven wave “spreading” during its propagation due to dissipative processes in the medium associated with its viscosity and electrical resistance. It is shown that a high-rate shear of metals under explosive or impact loading may lead to generation of megagauss magnetic fields.     

The design of an optimal viscous damper for a bridge stay cable using energy-based approach

An energy-based method is developed in the present paper to evaluate the damping property of a stay cable when transversely attached to a viscous damper. The overall increase of the cable damping offered by the external damper is determined by examining the time history of the kinetic energy in the damped cable. The concept of kinetic energy decay ratio is introduced as a key index to evaluate the effectiveness of a damper design in suppressing cable vibration. Compared to earlier studies, the proposed energy-based approach has no restrictions on the damper location. In addition, the flexural rigidity and sag extensibility of the cable are included in the formulation. Numerical simulation of free vibration of a damped stay cable is conducted using ABAQUS. To assist the design process, a set of damping estimation curves, which directly relate a damper design with the corresponding equivalent structural damping in a damped cable are developed for the practical parameter ranges of bridge stay cables. A number of numerical examples are presented. The validity and accuracy of the proposed method and damping estimation curves are verified by comparing with other studies. Results show that the energy-based approach developed in the present study is effective and efficient in determining the overall damping property of a cable-damper system, particularly in the preliminary stage of a damper design. In addition, the flexible applications of the developed damping estimation curves to damper design are demonstrated through these examples.     

On the motion of a uniformly heated drop in a viscous liquid under gravity

The motion of a uniformly heated spherical drop under gravity is theoretically studied within the Stokes approximation. The Stokes and Hadamard-Rybchinsky formulas are generalized so that the temperature dependence of the viscosity can be found in a wide temperature range. Also, the drag force and the velocity of gravity fall are calculated for an arbitrary temperature difference between the surface of the drop and distant points.     

Three vortex motion in the slightly viscous flow

The dynamics of three vortices moving in an ideal fluid in a plane can be expressed in Hamiltonian form. However, when viscosity can not be ignored, the system of point vortices has not this delicious structure. This investigation focuses on the viscosity effect on the motion of three vortices. Since the viscous diffusion of vortices is simulated by Brownian motion, the equations of intervortical distances are obtained by Ito formula. These equations show that there exist two viscosity effects on intervortical distances: stable expansion and random impulse. Furthermore, via employing the asymptotic solution to these equations, these two viscous effects have been shown to destroy the self-similar process of collapse and make it into a new configuration, which is similar to the near collapse in the ideal case.     

Whirling of flexible shafts with intermediate supports

The present paper deals with an approximate solution of the title problem using the Rayleight-Schmidt procedure. It is shown that rotating shafts of non-uniform cross section can be analyzed in a straightforward manner. Experimental and analytical results are obtained for the case of uniform shafts with intermediate supports, and good engineering agreement is shown to exist.     

Effect of internal heat evolution on the motion of a solid particle in a viscous fluid

The problem of the effect of internal heat evolution on the motion of a heated solid spherical particle in a viscous fluid is analytically solved in the Stokes approximation at small Reynolds and Peclet numbers. The temperature drop between the surface of the particle and the area away from it is assumed to be arbitrary. In solving hydrodynamic equations, the thermal conductivity of the particle is set to be a power function of temperature and the viscosity of the fluid, an exponential-power function of temperature. The observability of this effect is discussed.     

Applications of a simple theory of the acoustic motion of fibrous networks in viscous media

The rupture of blood capillaries in the spinal chords of rats by pulsed ultrasound and the motion of fibrils in the corneal stroma are analysed in detail in terms of a simple theory of wave propagation in a fibrous network permeated by a viscous medium. The advantages of inelastic light scattering experiments in connection with studies of ultrasound are emphasized.     

Unsteady analysis of six-DOF motion of a 6:1 prolate spheroid in viscous fluid

Free-moving simulations of airplanes, submarines and other automobiles under extreme and emergency conditions are becoming increasingly important from operational and tactical perspectives. Such simulations are fairly challenging due to the extreme unsteady motions and high Re(Reynolds) numbers. The aim of this study is to perform a six-DOF motion simulation of a 6:1prolate spheroid that is falling in a fluid field. Prior to conducting the six-DOF simulation, some verification simulations were performed. First, a laminar flow past an inclined prolate spheroid at a Re number of 1000 and incidence angle of 45. with a tetrahedral mesh was simulated to verify the relevant targeted discrete method for an unstructured mesh. Second, to verify the LES(large eddy simulation) models and dependent parameters for the DDES(delayed detached eddy simulation), a turbulent flow past a sphere was performed at a subcritical Re number of 10000. Third, a steady maneuvering problem about a prolate spheroid pitching up from 0. to 30. incidence at a uniform angular velocity was established based on a dynamic tetrahedral mesh with changing topology and the ALE(arbitrary Lagrangian-Eulerian) method of fluid-structure coupling at a Re number of 4.2 × 10~6.Finally, two six-DOF motions of an inclined 6:1 prolate spheroid at an initial incidence of 45. were simulated at different Re numbers of 10000 and 4.2 × 10~6.     

Parametric instabilities of a viscous liquid layer covered by a thin elastic plate under vertical periodic motion

Parametric instabilities of a horizontal liquid layer with a finite depth covered by a thin elastic plate under a vertical periodic motion are investigated with account taken of the viscosity of the liquid layer. The primary regions and the secondary ones of dynamic instabilities are determined by using the equation of a thin elastic plate including the normal component of the viscous stress, but not the tangential component of it. The critical amplitude of the imposed oscillation, beyond which a parametric instability occurs (that is, the neutral stability curves) is found in the space of the frequency and amplitude of the imposed vertical oscillation. These results are confirmed by experimental ones for a liquid layer of glycerine covered with a thin rubber plate.     

Optimal design of passive viscous dampers for controlling the resonant response of orthotropic plates under high-speed moving loads

In this article, the resonant response of plates traversed by moving loads is addressed being its main application the dynamic performance of railway bridges under high-speed traffic. An innovative alternative to reduce the deck inadmissible oscillations that may appear in short simply supported structures in resonant conditions is proposed, based on artificially increasing the superstructure damping by retrofitting the deck with fluid viscous dampers. A particular auxiliary structure transforming the deck vertical deflection into relative movement within the devices is envisaged, being the main objectives of the study to optimise the retrofitting system parameters and to prove its efficiency under the action of railway vehicles. For these purposes, the retrofitted deck behaviour is first investigated using an orthotropic plate model under harmonic excitation. On the basis of an analytical approach, a dimensionless version of the equations of motion is presented, the governing parameters are extracted and an intensive sensitivity analysis of the plate response is performed. Finally, analytical closed-form expressions for the optimal dampers constants are derived and their adequacy is numerically evaluated. To this end, an existing bridge belonging to the Spanish Railway network is analysed using a three-dimensional finite element code specifically programmed by the authors for this application. In the end the controlling effect of the retrofitting system and the applicability of the optimal parameters analytical expressions are proven for a wide range of circulating velocities.     

Spherical particle Brownian motion in viscous medium as non-Markovian random process

The Brownian motion of a spherical particle in an infinite medium is described by the conventional methods and integral transforms considering the entrainment of surrounding particles of the medium by the Brownian particle. It is demonstrated that fluctuations of the Brownian particle velocity represent a non-Markovian random process. The features of Brownian motion in short time intervals and in small displacements are considered.     

Thickness of a boundary layer attributed to the wave motion on the charged free surface of a viscous liquid

It is shown that the analytical estimator for the boundary layer thickness that contains the wave frequency in the denominator and is proposed for approximate calculation of the wave motion on the free surface of a viscous liquid cannot be formally applied to the wave motion on the uniformly charged liquid surface. The fact is that, when the surface charge density attains a value critical in terms for the Tonks-Frenkel instability, the wave frequency tends to zero. From the analysis of liquid motions near the electric charge critical density, a technique is proposed for calculating the thickness of a boundary layer attributed to flows of various kinds. It is found that the thickness of the boundary layer due to aperiodic flows with amplitudes exponentially growing with time (such flows take place at the stage of instability against the surface charge) does not exceed a few tenths of the wavelength, whereas the thickness of the boundary layer due to exponentially decaying liquid flows is roughly equal to the wavelength.