The Effect of the Walls of an Arbitrary Tank in the Problem of Separation–Free Impact on a Floating Body

An algorithm for constructing an asymptotic power series for large depths is proposed. It allows one to use the well–known solution of the problem of impact on a rigid body floating on the surface of a fluid half–space to obtain an approximate solution of the impact problem for the same body floating on the surface of a fluid in a bounded basin. The case where the domain occupied by the fluid has two perpendicular planes of symmetry is considered. Asymptotic expressions are given for the velocity potential on the wetted part of the body surface and for the added mass. Examples of solutions are considered.     

Topology optimization of a plate coupled with acoustic cavity

Optimization of the topology of a plate coupled with an acoustic cavity is presented in an attempt to minimize the fluid–structure interactions at different structural frequencies. A mathematical model is developed to simulate such fluid–structure interactions based on the theory of finite elements. The model is integrated with a topology optimization approach which utilizes the moving asymptotes method. The obtained results demonstrate the effectiveness of the proposed approach in simultaneously attenuating the structural vibration and the sound pressure inside the acoustic domain at several structural frequencies by proper redistribution of the plate material.Experimental verification is carried out by manufacturing topology optimized plates and monitoring their vibration and sound radiation into a rigid acoustic cavity. The measured sound pressure and plate vibration are found to be in good agreement with the predictions of the mathematical model.The presented theoretical and experimental techniques present valuable tools in the design of a wide variety of critical structures which must operate quietly when subjected to fluid loading.     

Impact of a strip of compressible liquid on a barrier

The exact solution of the plane problem of the impact of a finite liquid strip on a rigid barrier is obtained in the linearized formulation. The velocity components, the pressure and other elements of the flow are determined by means of a velocity potential that satisfies a two-dimensional wave equation. The final expressions for them are given in terms of elementary functions that clearly reflect the wave nature of the motion. The exact solution has been thoroughly analyzed in numerous particular cases. It is shown directly that in the limit the solution of the wave problem tends to the solution of the analogous problem of the impact of an incompressible strip obtained in [1]. A logarithmic singularity of the velocity parallel to the barrier in the corner of the strip is identified. A one-dimensional model of the motion, which describes the behavior of the compressible liquid in a thin layer on impact and makes it possible to obtain a simple solution averaging the exact wave solution, is proposed. Inefficient series solutions are refined and certain numerical data on the impact characteristics for a semi-infinite compressible liquid strip, previously considered in [2–4] in connection with the study of the earthquake resistance of a dam retaining water in a semi-infinite basin, are improved. The solution obtained can be used to estimate the forces involved in the collision of solids and liquids. It would appear to be useful for developing correct and reliable numerical methods of solving the nonlinear problems of fluid impact on solids often examined in the literature [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 138–145, November–December, 1990.The results were obtained by the author under the scientific supervision of B. M. Malyshev (deceased).     

Impact of a rectangular plate on a liquid half-space

The potential flow of an ideal incompressible fluid occupying a half-space resulting from the impact of a rectangular plate on its surface is considered. Outside the plate the surface of the fluid is free. An integral equation of the first kind is obtained for the impulsive pressure beneath a flexible plate. It is solved on a computer by the power series method for the particular case of a rigid nondeformable plate. The accuracy of the method is estimated. The theoretical dependence of the virtual mass and virtual moment of inertia coefficients of a rigid nondeformable plate on the plate geometry is constructed and compared with the experimental data and with empirical formulas [1-3] not directly related with the solution of the Laplace equation.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 120–126, September–October, 1992.     

The numerical solution of the transient two‐phase flow in rigid pipelines

Consideration is given in this paper to the numerical solution of the transient two‐phase flow in rigid pipelines. The governing equations for such flows are two coupled, non‐linear, hyperbolic, partial differential equations with pressure dependent coefficients. The fluid pressure and velocity are considered as two principle dependent variables. The fluid is a homogeneous gas–liquid mixture for which the density is defined by an expression averaging the two‐component densities where a polytropic process of the gaseous phase is admitted. Instead of the void fraction, which varies with the pressure, the gas–fluid mass ratio (or the quality) is assumed to be constant, and is used in the mathematical formulation. The problem has been solved by the method of non‐linear characteristics and the finite difference conservative scheme. To verify their validity, the computed results of the two numerical techniques are compared for different values of the quality, in the case where the liquid compressibility and the pipe wall elasticity are neglected. Copyright © 1999 John Wiley & Sons, Ltd.     

Impact of a surfacewave on an elastic hull

In order to model a ship hull’s response to the impact of surface waves, the two-dimensional problem of wave impact on an elastic beam whose ends are connected by springs with a rigid structure uniformly submerged in a fluid is considered. The fluid is assumed to be ideal and incompressible and its flow symmetric; the lateral bending of the beam is described by the Euler equation. The fluid flow and the size of the wetted region are determined simultaneously with the calculation of the the beam deflection within the framework of the Wagner approach which takes into account the reshaping of the free surface of the fluid on interacting with a body. The stresses and strains arising in the beam and at its ends during impact are found. The numerical algorithm developed makes it possible to analyze the elastic effects in fluid impacts on thin-walled structures of finite length. Moreover, as the stiffness of the connecting springs tends to zero, the solution of this problem describes the impact of an elastic beam with free ends on a weakly curved fluid surface.     

Effects of dynamic viscoelastic properties on acoustic diffraction by a solid sphere submerged in a viscous fluid

Summary  This study provides a general analysis for scattering of a planar monochromatic compressional sound wave by a homogeneous, isotropic, viscoelastic, solid sphere immersed in an unbounded viscous, heat-nonconducting, compressible fluid. The dynamic viscoelastic properties of the spherical scatterer and the viscosity of the surrounding fluid are rigorously taken into account in the solution of the acoustic-scattering problem. Havriliak–Negami model for viscoelastic material behaviour along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. Subsequently, the associated acoustic quantities such as the scattered far-field pressure directivity pattern, scattered intensity distribution, differential scattering cross section, and the acoustic radiation force are evaluated for given sets of viscoelastic material properties. Numerical results clearly indicate that, in addition to the traditional fluid viscosity-related mechanisms, the dynamic viscoelastic properties of the solid obstacle can be of major significance in sound scattering. Limiting cases are examined and fair agreements with well-known solutions are established. Received 15 January 2002; accepted for publication 2 July 2002 The authors wish to sincerely thank professors Daniel Levesque, Roderic Lakes, Yves Berthelot, S. Temkin, and Andrei Dukhin for valuable and productive consultations on dynamic theory of viscoelasticity and acoustics of (thermo)viscous media.     

Response of a solid infinite cylinder embedded in a poroelastic medium and subjected to a lateral load

This paper presents an analytical solution for the response of a poroelastic medium around a laterally loaded rigid cylinder using Biot’s consolidation theory. A plane-strain section of the cylinder-porous medium system is considered and the problem is formulated in polar coordinates. Expressions for the pore fluid pressure, stresses and displacements in the Laplace domain are derived analytically. The inverse of the Laplace transform is evaluated numerically using an efficient scheme. Curves showing decay of the pore fluid pressure with time, the corresponding change in mean effective stress and the variation of displacement, are plotted in non-dimensional form.     

Separation Impact on a Plate Floating on the Surface of an Ideal Incompressible Fluid in a Bounded Tank

The paper studies the planar problem of separation impact on a plate floating on the surface of an ideal incompressible fluid in a bounded tank. The problem is solved using an asymptotic method under the assumption that the immovable rigid walls of the tank are at a large distance from the plate. It is concluded that the tank walls of arbitrary shape have an ambiguous effect on the fluid particle separation zone formed on the plate surface is revealed. Examples of solutions are given.     

Exact solution for compressive flow of viscoplastic fluids under perfect slip wall boundary conditions

Based on the perfect slip condition between rigid walls and fluids, the compressive flow of Herschel-Bulkley fluids and biviscous fluids was studied. The explicit expressions of stresses and fluid velocity were given. To move the rigid walls for a Herschel-Bulkley fluid with the yield stress (τ₀), the mean pressure applied onto the rigid wall should be larger than 2τ₀/. No yield surface exists in the interior of the fluids when flow occurs. For a biviscous fluid, a critical load was given. The fluid behaves like the Bingham fluid when the external applied load onto the wall is larger than the critical load, otherwise the fluid is Newtonian. Received: 10 June 1997 Accepted: 22 September 1997     

THE DYNAMIC BUCKLING OF ELASTIC-PLASTIC COLUMN SUBJECTED TO AXIAL IMPACT BY A RIGID BODY

I. INTRODUCTIONSince the 1960s the investigation on the dynamic buckling of elastic-plastic structures under impactload has been a very active subject of study in solid mechanics. In this respect the research advanceswere summarized and reviewed from di?erent aspects by some famous scholars[1??4]. The column is themost important structural element in practical engineering. So the dynamic buckling of the column hasattracted much more attention of many researchers. Lindberg H.E. carried ou…     

A note on the periodic motion of a visco-elastic fluid in a radially non-symmetric constricted tube

An approximate solution for the problem of fluid flow through a rigid tube with a mild constriction is given. It is assumed that the fluid is visco-elastic (Maxwell fluid) and the constriction is non-symmetric with respect to the radial distance. A theoretical result is given for the wall shear stress and numerical solutions are shown graphically for different values of the relaxation time and the shape parameter of the constriction profile.     

DYNAMIC RESPONSE OF A RIGID,PERFECTLY PLASTIC FREE-FREE BEAM STRUCK BY A PROJECTILE ATANY CROSS-SECTION ALONG ITS SPAN

I. INTRODUCTION The dynamic plastic response of free-free beams subjected to intense dynamic loading is a subject ofinterest for aerospace engineering applications. For example, when a rocket is attacked by a missile, itslarge plastic deformation behav…     

The squeeze flow of a bi-viscosity fluid between two rigid spheres with wall slip

In this paper, the squeeze flow between two rigid spheres with a bi-viscosity fluid is examined. Based on lubrication theory, the squeeze force is calculated by deriving the pressure and velocity expressions. The results of the normal squeeze force are discussed, and fitting functions of the squeeze and correction coefficients are given. The squeeze force between the rigid spheres increases linearly or logarithmically with the velocity when most or part of the boundary fluid reaches the yield state, respectively. Furthermore, the slip correction coefficient decreases with the increase in the velocity. The investigation may contribute to the further study of bi-viscosity fluids between rigid spheres with wall slip.     

Convective heat transfer in a locally heated plane incompressible fluid layer

The problem of convection in a plane horizontal layer of incompressible fluid with rigid boundaries when the temperature is constant on the lower boundary and has a parabolic profile on the upper boundary can be reduced to solution of a system of time-dependent one-dimensional equations. An analytic solution of the problem is obtained directly at the extremum point. Together with the wellknown solutions which describe heat transfer for the linear temperature distribution on the boundaries, the results obtained make it possible to calculate the heat flux through a thin slit for an arbitrary given heating of a thin fluid layer between heat-conducting bodies.     

A mathematical model and numerical solution technique for a novel adjustable hydrodynamic bearing

An analysis model for a novel adjustable hydrodynamic fluid film bearing is described. The principles of hydrodynamic lubrication are outlined together with an expanded version of the governing pressure field equation as related to the novel bearing. Finite difference approximations are given for the pressure field equation and a temperature model, both related to the fluid film thickness. Relationships of viscosity with temperature and pressure are included. A finite element model and an iterative computational process are described, whereby full simultaneously converged field solutions for fluid film thickness, temperature, viscosity and pressure were obtained, together with oil film forces. The model and solution process were developed to apply to a variety of hydrodynamic bearings and an outline is given of its extensive use in the design and simulation of one version of the novel bearing. Observations are given on the operation, success rates and verifications of the computational process. Copyright © 1999 John Wiley & Sons, Ltd.     

Stokes flow in a cylindrical tube containing a line of spheroidal particles

Viscous flow in a circular cylindrical tube containing an infinite line of rigid spheroidal particles equally spaced along the axis of the tube is considered for (a) uniform axial translation of the spheroids (b) flow past a line of stationary spheriods and (c) flow of the suspending fluid and spheroids under an imposed pressure gradient. The fluid is assumed to be incompressible and Newtonian. The Reynolds number is assumed to be small and the equations of creeping flow are used. Two types of solutions are developed: (i) an exact solution in the form of an infinite series which is valid for ratios of the spheroid diameter to the tube diameter up to 0.80, (ii) an approximate solution using lubrication theory which is valid for spheroids which nearly fill the tube. The drag on each spheroid and the pressure drop are computed for all cases. Both prolate and oblate spheroids are considered. The results show that the drag and pressure drop depend on the spheroidal diameter perpendicular to the axis of tube primarily and the effects of the spheroidal thickness and spacing are secondary. The results are of interest in connection with mechanics of capillary blood flow, sedimentation, fluidized beds, and fluid-solid transport.     

Interaction between an acoustic wave and a disc

A numerical solution is obtained to the problem concerning a pressure measurement at the boundary between an ideal compressible fluid and a solid wall. It is assumedthat the fluid occupies a semiinfinite cylinder with a rigid bottom into which an elastic disc is inserted and heldfirmly around its edges. Motion is produced by a pressure wave originating at infinity. A finite-difference grid for this application is described and the results of actual calculations are shown.Deceased.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 84–91, January–February, 1972.The authors thank L. M. Flitman for reviewing the work.     

Analytical Solution for Isothermal Flow in a Shock Tube Containing Rigid Granular Material

Analytical solution of shock wave propagation in pure gas in a shock tube is usually addressed in gas dynamics. However, such a solution for granular media is complex due to the inclusion of parameters relating to particles configuration within the medium, which affect the balance equations. In this article, an analytical solution for isothermal shock wave propagation in an isotropic homogenous rigid granular material is presented, and a closed-form solution is obtained for the case of weak shock waves. Fluid mass and momentum equations are first written in wave and (mathematical) non-conservation forms. Afterwards by redefining the sound speed of the gas flowing inside the pores, an analytical solution is obtained using the classical method of characteristics, followed by Taylor’s series expansion based on the assumption of weak flow which finally led to explicit functions for velocity, density and pressure. The solution enables plotting gas velocity, density and pressure variations in the porous medium, which is of high interest in the design of granular shock isolators.     

A THEORETICAL ANALYSIS OF THE FLOW DISTURBANCE INDUCED BY A SPHERE OSCILLATING IN INCOMPRESSIBLE FLUID

为了改进基于不可压缩流场的声类比法的气动声数值预测方法,首先要明确扰动在可压缩和不可压缩流体媒介中的传播特性. 推导了震荡小球在不可压缩流体中产生的小扰动的理论解,分析其速度场与压力场的特点,并与可压缩情况的解进行比较. 结果显示,速度场中包含传播速度为无穷大和有限值的分量;而压力场只有传播速度为无穷大的分量. 当流体黏性趋于零或小球震荡频率趋于无穷大时,其流场与经典声学中震荡小球声辐射问题的近场声一致,这表明震荡小球产生的近场扰动为不可压缩流场,即伪声.