ANALYSIS OF OSCILLATORY FLOW IN CONSIDERATION OF A PLASMA LAYER IN ARTERIAL STENOSES

ＡＮＡＬＹＳＩＳ　ＯＦ　ＯＳＣＩＬＬＡＴＯＲＹ　ＦＬＯＷ　ＩＮ　ＣＯＮＳＩＤＥＲＡＴＩＯＮ　ＯＦ　Ａ　ＰＬＡＳＭＡ　ＬＡＹＥＲ　ＩＮ　ＡＲＴＥＲＩＡＬ　ＳＴＥＮＯＳＥＳＷａｎｇ．Ｃｈａｎｇｂｉｎ（王长斌）；ＬｉｕＺｈａｏｒｏｎｇ（柳兆荣）（Ｒｅｃｅｉ...     

METHOD OF MOMENT EXCITATION IN TESTING OF STRUCTURES

The method of the moment excitation in the studies of the structure-borne sound using a moment actuator is introduced.Some design considerations for themoment actuator are presented.A standard mechanical system is established to calibratethe performance of the moment actuator.The frequency and mechanical powerperformances of the actuator are discussed.     

APPLICATION OF ONE-PARAMETER GROUPS OF TRANSFORMATION IN MECHANICS

In this paper,including some partial differential equations with a number ofindependent variables,which can be reduced by the.infinitesimal form of the group,weobtain the theory of similarity transformation and its application of the second ordernonlinear partial differential equations which have two independent variables and twodependent variables in mechanics.     

CLASSIFICATION OF VARIATIONAL PRINCIPLES IN ELASTICITY

In this paper, variational principels in elasticity are classified according to the differences in the constraints used in these principles. It is shown in a previous paper that the stress-strain relations are the constraint conditions in all these variational principles, and cannot be removed by the method of linear Lagrange multiplier. The other possible constraints are four of them: (1) equations of equilibrium,(2) strain-displacement relations, (3) boundary conditions of given external forces and (4) boundary conditions of given boundary displacements. In variational principles of elasticity, some of. them have only one kind of such constraints, some have two kinds or three kinds of constraints and at the most four kinds of constraints. Thus, we have altogether 15 kinds of possible variational principles. However, for every possible variational principle, either the strain energy density or the complementary energy density may be used. Hence, there arealtogether 30 classes of functional of variation     

SYNTHESIS OF NICKEL NANOPOWDERS IN MICROEMULSION

IntroductionNanometer-scalecrystallitesofvariousmetalsandnonmetalshaveattractedagreatdealofattentionoverthepastdecade.Forsuchcrystallites,thephysicalandchemicalpropertiesareheavilydependentonparticlesizeandshape,and,asaresult,thesematerialshaveawiderangeofapplications(Ai&Kang,2003).Monodispersefinenickelparticlesarerequiredforhightechnologyapplicationsinalkalinerechargeablebatteries,magneticrecordingmediaandchemicalcatalysts,etc.,suchasconductingandmagneticinks,andferrofluids(Glicksman,1984).…     

CUSP CATASTROPHE MODEL OF INSTABILITY OF PILLAR IN ASYMMETRIC MINING

IntroductionSometimes, symmetric mining is not carried into execution by the geologic conditionrestriction, and the stability of rock is more important with extending of the mining depth,which affects mine safety and mining layout of ore body. Pillars sup…     

BIFURCATIONS OF AIRFOIL IN INCOMPRESSIBLE FLOW

Bifurcations of an airfoil with nonlinear pitching stiffness in incompressible flow are investigated. The pitching spring is regarded as a spring with cubic stiffness. The motion equations of the airfoil are written as the four dimensional one order differential equations. Taking air speed and the linear part of pitching stiffness as the parameters, the analytic solutions of the critical boundaries of pitchfork bifurcations and Hopf bifurcations are obtained in 2 dimensional parameter plane. The stabilities of the equilibrium points and the limit cycles in different regions of 2 dimensional parameter plane are analyzed. By means of harmonic balance method, the approximate critical boundaries of 2-multiple semi-stable limit cycle bifurcations are obtained, and the bifurcation points of supercritical or subcritical Hopf bifurcation are found. Some numerical simulation results are given.     

SIMPLIFICATION OF THE EXPANSIONS OF VISCOUS TERMS IN BASIC AERODYNAMIC EQUATIONS IN NON-ORTHOGONAL CURVILINEAR COORDINATE SYSTEM

The application of non-orthogonal curvilinear coordinate system to the calculation ofthe flow field inside the channel,with complex boundary geometry,can effectively simplifythe work of designing the calculation program and improve the accuracy of calculation.Therefore, it is obviously necessary to expand the viscous terms,i.e.viscous force,rate ofwork done by viscous stress and dissipation, in basic aerodynamic equations in the non-orthogonal curvilinear system. However, each of these expansions consistes of tens oreven hundrede of algebraic terms.The expansions of these three viscous terms discribed inthis paper are considerably simplified by analysing their order of magnitude.     

A STUDY OF CRACK CLOSURE IN ELECTRIC-FIELD-INDUCED FATIGUE IN FERROELECTRIC CERAMICS

Considering the influence of the domain switching near the tip of a crack and apply-ing the idea of multiscale singularity fields in piezoelectric fracture,we have obtained an empiricalcriterion for the crack closure.Based on the domain switching in the electric yield region,referringto Yang's results on the small scale yield model for the electrical fatigue crack,a model of thecrack closure during electric-field-induced fatigue is developed to analyze the crack growth.Interms of the model we have obtained the formula of the rate of the crack growth under cyclicelectric loading.Finally we compare the theoretical predictions with the results given by Cao andEvans experimentally.It should be pointed out that the model proposed is empirical and needsto be verified by more experimental results.     

THE PROBLEM OF INEQUALITY IN SOLID MECHANICS

In this paper the of inequality in solid mechanics,the contents of which consistof some main concepts,methods and results of the stationary and evolutionary aswell as determinate and random problems in variational principle and variational ine-quality studied in detail.     

SOLUTIONS OF MAGNETOHYDRODYNAMICS EQUATIONS-THE THEORY OF FUNCTIONS OF A COMPLEX VARIABLE UNDER DIRAC-PAULI REPRESENTATION AND ITS APPLICATION IN FLUID DYNAMICS (Ⅳ)

This work is the continuation of the discussion of Refs.[1 3].(A) We turn the Magnetohydrodynamics equaitons of isentropic compresible andnon-dissipative magneto-flow into the form of the ideal hydrodynamics equations in thispaper;we can obtain the general Chaplygin equation from Ref.[3],and the generalsduction of this equation.(B)We apply the theory of functions of a complex rariable under Dirac-paulirepresentation,turn the general Magnetohydrodyamics equations of incompressiblemageto-flow into two nonlinear equaitons for flow function and"magneto-flow function",and obtain the exact stable solution of incompressible magnetohydrodynamics equationsunder the condition of stable magnetic field(i.e.under conditon of equality for kinematicalviscid coefficient or viscid diffusion coefficient with magnetic diffusion coefficient).     

On the general equation and the general solution in problems for plastodynamics with rigid-plastic material

This work is the continuation of the discussion of refs. [1–2]. We discuss the dynamics problems of ideal rigid — plastic material in the flow theory of plasticity in this paper. From introduction of the theory of functions of complex variable under Dirac-Pauli representation we can obtain a group of the so-called general equations (i.e. have two scalar equations) expressed by the stream function and the theoretical ratio. In this paper we also testify that the equation of evolution for time in plastodynamics problems is neither dissipative nor disperive, and the eigen-equation in plastodynamics problems is a stationary Schrödinger equation, in which we take partial tensor of stress-increment as eigenfunctions and take theoretical ratio as eigenvalues. Thus, we turn nonlinear plastodynamics problems into the solution of linear stationary Schrödinger equation, and from this we can obtain the general solution of plastodynamics problems with rigid-plastic material.     

Simple waves of a seven-dimensional subalgebra of all translations in gas dynamics

A differentially invariant solution of rank 1 for gas dynamics equations is considered in a seven-dimensional subalgebra of all translations including Galilean translations. Exact solutions with a uniformly accelerated plane of the level of invariant functions are obtained. A nonisentropic wave depends on two arbitrary functions and constants. A general solution of an isentropic simple wave depends on the constants only.     

A particular solution for the chaplygin equation

In the theoretical studies of several gasdynamic problems a major role is played by the hodograph plane, where the equations in terms of velocity component variables are linear. In these studies a primary role is played by the Chaplygin equation for the stream function . Chaplygin [1] obtained a general solution for the equation of motion in the hodograph plane. Particular exact solutions of the hodograph are also known [2]: radial flow, spiral flow, etc. Below we consider a particular solution of the Chaplygin equation.     

An algorithm for isentropic flow

An efficient algorithm is presented for the solution of the equations of isentropic gas dynamics with a general convex gas law. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only two function evaluations in each computational cell are required. The scheme is applied to a standard test problem in gas dynamics for a polytropic gas.     

Global convergence of inexact Newton methods for transonic flow

In computational fluid dynamics, non-linear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these non-linear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modelled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.     

The Schrödinger equation in theory of plates and shells with orthorhombic anisotropy

This work is the continuation of the discussion of Refs. [1-5]. In this paper:[A] The Love-Kirchhoff equations of vibration problem with small deflection for orthorhombic misotropic thin shells or orthorhombic anisotropic thin plates on Winkler’s base are classified as several of the same solutions of Schrodmger equation, and we can obtain the general solutions for the two above-mentioned problems by the method in Refs. [1] and [3-5].[B] The. von Karman-Vlasov equations of large deflection problem for shallow shells with orthorhombic anisotropy (their special cases are the von Harmon equations of large deflection problem for thin plates with orthorhombic anisotropy) are classified as the solutions of AKNS equation or Dirac equation, and we can obtain the exact solutions for the two abovementioned problems by the inverse scattering method in Refs. [4-5].The general solution of small deflection problem or the exact solution of large deflection problem for the corrugated or rib-reinforced plates and shells as special cases is included in this paper.     

Delta Shock Wave Solution of the Riemann Problem for the Non-homogeneous Modified Chaplygin Gasdynamics

The motivation of the present study is to derive the solution of the Riemann problem for modified Chaplygin gas equations in the presence of constant external force. The analysis leads to the fact that in some special circumstances delta shock appears in the solution of the Riemann problem. Also, the Rankine–Hugoniot relations for delta shock wave which are utilized to determine the strength, position and propagation speed of the delta shocks have been derived. Delta shock wave solution to the Riemann problem for the modified Chaplygin gas equation is obtained. It is found that the external force term, appearing in the governing equations, influences the Riemann solution for the modified Chaplygin gas equation.

     

Interaction of a centered isentropic compression wave with the bow shock ahead of a body in a rarefied gas

Rarefied gas flow with a centered isentropic compression wave is investigated using direct Monte Carlo simulation of the solution of the Boltzmann equation. For monatomic gas flow the pattern of formation of a suspended compression shock near the geometric center of the compression wave is considered. The flow pattern is compared with the results obtained within the framework of gas dynamics. For a diatomic gas the interference of a centered compression wave with the bow shock ahead of a cylinder is investigated. The dependence of the pressure and the heat transfer to the surface on the Reynolds number and the wave center position relative to the cylinder center is analyzed. The results are compared with those of numerical simulation of the Euler and boundary-layer equations.     

Conservation laws and group properties of equations of isentropic gas motion

A system of equations of isentropic gas motion with n ⩾ 2 is classified in terms of zero-order conservation laws with the use of the method of A-operators. New conservation laws are found to be valid only for potential isentropic motion of the Chaplygin gas. In this case, the greatest number of nontrivial conservation laws is obtained, with n scalar conservation laws being nonlocal. Additional properties of symmetry of the considered equations associated with these conservation laws are indicated.