Boundedness of Solutions of Certain Volterra Systems in a Finite-Dimensional Space

We give conditions for the boundedness and periodicity of solutions of Volterra systems with matrix coefficients. The conditions are formulated in terms of the coefficients of these systems.     

Melnikov analysis for a ship with a general roll-damping model

In the framework of a general roll-damping model, we study the influence of different damping models on the nonlinear roll dynamics of ships through a detailed Melnikov analysis. We introduce the concept of the Melnikov equivalent damping and use phase-plane concepts to obtain simple expressions for what we call the Melnikov damping coefficients. We also study the sensitivity of these coefficients to parameter variations. As an application, we consider the equivalence of the linear-plus-cubic and linear-plus-quadratic damping models, and we derive a condition under which the two models yields the same Melnikov predictions. The free- and forced-oscillation behaviors of the models satisfying this condition are also compared.     

A Precise Computation of Drag Coefficients of a Sphere

We present a computational method for drag coefficients of axisymmetric bodies. It is a kind of consistent flux method but the introduction of a proper test function enables us to establish an error estimate under some assumption. Applying the method, we obtain drag coefficients of a sphere for Reynolds numbers between 10 and 200, which are found between numerical upper and lower bounds.     

The transmission coefficients of a random system

We study the reflection and transmission coefficients of a strip of parallel chains with random masses. We show that the transmission coefficients decay exponentially. For this we need the applicability of a theorem by Tutubalin, which is formulated as a conjecture.     

Hydrodynamics of a flexible cylinder under modulated vortex-induced vibrations

Both amplitude modulation and frequency modulation of Vortex-induced Vibration (VIV) are observed in a recent model test of a flexible cylinder under oscillatory flow, but its hydrodynamics has not yet been broached in detail. This paper employs the Forgetting Factor Least Squares (FF-LS) method for identification of time-varying hydrodynamics of a flexible cylinder under modulated VIV. The FF-LS method’s applicability to accurately identify time-varying hydrodynamic coefficients is demonstrated through an elastically mounted rigid cylinder under flow with a given modulated motion. Furthermore, we propose a framework to predict instantaneous amplitude (envelope) and frequency using time-varying hydrodynamic coefficients to establish their analytical relationship. This prediction method is further extended to a highly tensioned flexible cylinder through Fourier series expansion in the spatial domain. By performing the identification procedure for all sampled data of a flexible cylinder undergoing oscillatory flow, we obtain the corresponding time-varying hydrodynamics in the cross-flow direction considering the amplitude and frequency modulation. The results show that, under modulated VIV, hydrodynamic coefficients of the flexible cylinder also show time-varying characteristics. We further investigate differences between identified hydrodynamic coefficients and those obtained from the database of a cylinder with modulated motion under flow. Prediction results using these identified time-varying coefficients reveal that the time-varying excitation coefficients mainly influence the amplitude modulation, and the time-varying added-mass coefficients contain the major information of frequency modulation. These results further suggest including the temporal derivative of the instantaneous amplitude as one determining parameter in building databases to improve the prediction of modulated VIV.     

Equation of longitudinal vibrations of a beam with coefficients periodically depending on the coordinate

The equation of small longitudinal vibrations of a beam is considered for the case in which the coefficients are periodic and have “gaps” (sharp decreases in the value) at some point in the space inside the periodicity interval. We suggest to describe the process locally in the domain of minimum of the coefficients by an equation of the boundary layer approximation. Attention is mainly paid to the analysis of this equation. A time hierarchy of simplified models for describing this process is established.     

Slip and Macroparameter Jumps of a Polyatomic Gas with Rotational Degrees of Freedom on a Weakly Curved Spherical Surface

The problem of the slip of a temperature-inhomogeneous polyatomic gas along a spherical surface of small curvature is solved. The solution is obtained using the half-space moment method on the basis of a previously proposed model kinetic equation which takes into account the rotational degrees of freedom of the polyatomic gas. Both the first- and second-order (in the Knudsen number) slip coefficients and the polyatomic gas macroparameter jump coefficients on the phase interface are obtained. These coefficients are given as functions of the tangential momentum accommodation coefficients, the translational and rotational energy accommodation coefficients, and the Prandtl number. The kinetic coefficients are calculated for certain polyatomic gases.     

Interactions between a rectangular cylinder and a free-surface flow

The salient features of the interaction between a free-surface flow and a cylinder of rectangular cross-section are investigated and discussed. Laboratory-scale experiments are performed in a water channel under various flow conditions and elevations of the cylinder above the channel floor. The flow field is characterized on the basis of time-averaged and fluctuating local velocity measurements. Dynamic loadings on the cylinder are measured by two water-insulated dynamometers placed inside the cylinder structure. Starting from frequency and spectral analyses of the force signals, insights on the relationship between force dominant frequencies and the Strouhal number of the vortex shedding phenomenon are provided. Experimental results highlight the strong influence of the asymmetric configuration imposed by the two different boundary conditions (free surface and channel floor) on (i) the mean force coefficients and (ii) the vortex shedding frequencies. We provide an analysis of the nature of the dependence of average force coefficients on relevant dimensionless groups, i.e., the Reynolds number, normalized flow depth and cylinder submersion.     

Existence and stability of traveling waves in periodic media governed by a bistable nonlinearity

We prove the existence of multidimensional traveling wave solutions of the bistable reaction-diffusion equation with periodic coefficients under the condition that these coefficients are close to constants. In the case of one space dimension, we prove their asymptotic stability.     

Diffraction of a mode close to its cut-off by a transversal screen in a planar waveguide

The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced to a propagation problem on a branched surface and then is considered in the parabolic approximation. Using the embedding formula approach, the reflection and transmission coefficients are expressed through the directivities of the edge Green’s function of the propagation problem. The asymptotics of the directivities of the edge Green’s functions are constructed for the case of small gaps between the screen and the walls of the waveguide. As the result, the reflection and transmission coefficients are found. The validity of known asymptotics of these coefficients is studied.     

Torsion of an elastic rod whose cross-section is a parallelogram,trapezoid, or triangle,or has an arbitrary shape by the method of transformation to a rectangular domain

A coordinate transformation is used to take the domain of the rod cross-section to a rectangular domain for which the spectra of eigenfunctions and eigenvalues are known. The torsion function is represented as a generalized Fourier series to reduce the problem to solving a closed linear system of algebraic equations for the expansion coefficients. It is shown that these Fourier series converge absolutely, because the expansion coefficients decrease by a cubic law depending on the term number. We prove that the approximate solution in the form of a finite sum of the Fourier series converges to the exact solution. This theorem is generalized to the case of a rod cross-section of arbitrary shape.     

Stokes flow of a rotating sphere around the axis of a circular orifice or a circular disk

This paper presents an infinite series solution to the creeping flow equations for the axisymmetric motion of a sphere of arbitrary size rotating in a quiescent fluid around the axis of a circular orifice or a circular disk whose diameters are either larger or smaller than that of the sphere. Numerical tests of the convergence are passed and the comparison with the exact solution and other computational results shows an agreement to five significant figures for the torque coefficients in both cases. The torque coefficients are obtained for the sphere located up to a position tangent to the wall plane containing either the orifice or the disk. It is concluded that the torque coefficients of the sphere and the disk are monotonically increasing with the decrease of the distance from the disk or the orifice plane in both cases.     

The theory of dispersion of chemically active solutes in a rectilinear flow field

We report a procedure for the construction of the dispersion coefficients which define the dispersion approximation to the transverse average of the solution of the scalar convective diffusion equation; the procedure enjoys a generalization to the vector convective diffusion equation. We exhibit the full time dependence of the dispersion coefficients in any transverse average and identify a mathematically preferred transverse average for the dispersion of chemically active solute.     

Fluid-dynamic forces and wake frequencies on a tilted rectangular cylinder near a solid wall

We investigate the impact of different boundary conditions on the flow field developing around a tilted rectangular cylinder with two different values of the aspect ratio (l/s=3 and 4). We are mainly interested in analyzing the changes in force coefficients and in the vortex shedding Strouhal number when the cylinder is placed at various distances from a bottom wall and different values of attack angle. The angle of attack ranges between −30° and +30° and the cylinder elevation above the bottom wall is varied between almost zero and 5 times the thickness of the cylinder. A large body of experimental results is related to the small elevation conditions at different attack angles, where the presence of the wall has a non-negligible effect on the behavior of the force coefficients and Strouhal number of the vortex shedding.     

Homogenized Interface Model Describing Inhomogeneities Located on a Surface

We study the influence of heterogeneities located near a planar surface on the elastic response of a three-dimensional elastic medium. These heterogeneities can be either reinforcements, like steel reinforcements in concrete, or defects, like micro-cracks periodically distributed. We prove that their influence is of the second order from an energetic viewpoint. Then, we propose an ??up to second order effective model?? in which the influence of the heterogeneities is given by a surface energy contribution involving both the jump of displacement across the surface and the tangential strain components on the surface. The effective coefficients entering in the definition of the surface energy are obtained by solving ??elementary?? elastic problems formulated on an infinite representative cell containing the defects. We analyze this model, in particular the properties of the effective surface coefficients, and establish its coherence with limit models previously described in the literature for stiff or soft interfaces. This approach is finally applied to several kinds of heterogeneities.     

Heat and mass transfer characteristics of absorption of R134a into DMAC in a horizontal tube absorber

In this paper the heat and mass transfer characteristics of a horizontal tube absorber for the mixture R134a/DMAC in terms of experimentally gained heat and mass transfer coefficients are presented. The heat transfer coefficient is mainly dependent on the solution’s mass flow rate. The mass transfer coefficient is strongly related to the subcooling of the solution. The data are compared to experimental absorption characteristics of water into aqueous lithium bromide in an absorption chiller. The mass transfer coefficients are of similar size whereas the heat transfer coefficients are about one order of magnitude smaller for R134a-DMAC.     

Propagation of acoustic waves in porous media and their reflection and transmission at a pure-fluid/porous-medium permeable interface

We find a sufficient condition of hyperbolicity for a differential system governing the motion of a one-dimensional porous-medium, so ensuring the existence of a solution for the associated Cauchy problem. We study propagation of linear waves impacting at a pure-fluid/porous-medium interface and we deduce novel expressions for the reflection and transmission coefficients in terms of the spectral properties of the governing differential system. We show three-dimensional plots drawing reflection and transmission coefficients as functions of Biot’s parameters. In such a way we propose an indirect method for measuring Biot’s parameters when the measurement of the reflection and transmission coefficients associated to the traveling waves is possible.     

RESEARCH OF THE PERIODIC SOLUTION FOR A CLASS OF NONLINEAR DIFFERENTIAL EQUATIONS

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Drag of a rotating sphere

We consider the problem of steady incompressible viscous fluid flow about a rotating sphere, with the flow specified on a sphere of finite radius, which reduces to the solution of the complete Navier-Stokes equations.The dimensionless stream functions and circulai velocity are sought in the form of series in powers of the Reynolds numbers, which converge for small values of this number. Recurrence formulas are derived for determining the coefficients of these series. The pressure, rotational resistance torque, and drag are determined. It is established that the rotating sphere has higher drag than a stationary sphere. The leading term of the series in powers of the Reynolds number for the drag and resistive torque is calculated.