应用数学和力学

2008 Vol. 29, No. 8

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Floquet Instability of a Large Density Ratio Liquid-Gas Coaxial Jet With Periodic Fluctuation

LI Zhen, HU Guo-hui, ZHOU Zhe-wei

2008, 29(8): 883-892.

Abstract(2685) PDF(558)

Abstract:
By the numerical simulation of basic flow,Floquet stability analyis of interfacial flow with periodic fiuctuation into lage density ratio range were extended.The stability of a liquid aluminum jet in a coaxial nitrogen stream with velocity fiuctuation Was investigated by Chebyshev collocation method and the Floquet.The parametric resonance of the jet and the influences of different physical parameters on the instability were discussed.The results show qualitative agreement with the experimental data available.

Study on the Inflow Boundary Condition for DNS of Turbulent Boundary Layers on Supersonic Blunt Cones

DONG Ming, ZHOU Heng

2008, 29(8): 893-904.

Abstract(2742) PDF(766)

Abstract:
For the direct numerical simulation (DNS) of turbulent boundary layers,hou to generate an appropriate infow condition is problem that needs to be considered.Amethod was proposed,by which the infow condition for spatial-mode DNS of tolbulet boundary layers on supersonic blunt Cones with different Mach number,Reynolds number and wall temperature conditions can be generated,based only on a given instant flow field obtained by a temporal-mode DNS of a turulent boundary layer on a flat plate.the effectiveness of the proposed method is shown by three typical examples,thmugh comparing its results with those obtained by other methods.

Elasticity Solutions for Functionally Graded Plates in Cylindrical Bending

YANG Bo, DING Hao-jiang, CHEN Wei-qiu

2008, 29(8): 905-910.

Abstract(2702) PDF(664)

Abstract:
The plate theory of functionally graded materials suggested by Mian and fencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load.The expansion formula for displacements was adopted.While keeping the assumption that the material parameters can vary along the thiclmess direction in an arbitrary fashion,it was considerect orthotropic materials rather than isotropic materials.In addition,the traction-free condition on the top surface was replaced by the condition of uniform load applied on the top surface.The plate theory for the particular case of cylindrical bending was presented by considering an infinite extent in the y-direction.The effects of boundary conditions and material inhomogeneity on the static response of functionally graded plates were inwestigated through a numerical example.

Fracture Analysis for Torsion Problems of a Composite Cylinder With Curvilinear Cracks

PAN Tian-wei, WANG Yin-bang

2008, 29(8): 911-917.

Abstract(3215) PDF(687)

Abstract:
The Saint-Venant torsion problems of a composite cylinder with curvilinear crack were investigated.By means of considering the bimaterial interface as a boundary of outer bar or inner one,the problem was reduced to solving the boundary integral equations on crack,external boundary and interface.Using the new boundary element method,some typical torsion problems of a composite cylinder irnolving a straight or kinked crack were calculated.The obtained results were compared with the literature tada to prove the validity and applicability of the present method.

Steering Laws Analysis of SGCMGs Based on Singular Value Decomposition Theory

ZHANG Jing-rui

2008, 29(8): 918-926.

Abstract(3071) PDF(783)

Abstract:
The steering laws of single gunbal control moment gyros (SGCMGs) are analyzed and compared for a spacecraft attitude control system based on the singular value decomposition (SVD) theory.The mechanism of the steering laws escaping singularity,espeaally the steering laws of how to affect the singularity ofgimbal configuration and the output toque error,was researched via SVD theory.The perforn}ance of various steering laws was analyzed and compared quantitatively by simulation.The obtained results can be used as a reference for the engineering designers.

Changes of Natural Frequency of a Ferromagnetic Rod in Magnetic Field Due to Magnetoelastic Interaction

WANG Xing-zhe

2008, 29(8): 927-935.

Abstract(3048) PDF(613)

Abstract:
Based on magnetoelastic generalized variational principle and Hamilton's principle,a dynamic theoretical model characterizing the magnetoelastic interaction of a soft ferromagnetic medium in an applied magnetic field is developed.Fhom variational manipulation respectively on magnetic scale potential and elastic displacement,the all fundamental equations for the magnetic field and mechanical deformation,as well as the the magnetic body force and magnetic traction for describing magnetoelastic interaction,were derived.The theoretical model was applied to a ferromagnetic rod vibrating in an applied magnetic field by means of pertrubation technique and Galerldn method.The results show that the magnetic field will change the natural frequenaes of the ferromagnetic rod by decrease as the bending motion along the applied magnetic field where the magnetoelastic buckling will take place,but by increase when bending motion of the rod is perpendicular to the field.The prediction by the model qualitatively agrees with the natural fiequency changes of the ferromagnetic rod observed in the experiment.

Enhancement of Natural Convection Heat Transfer From a Fin by Triangular Perforations of Bases Parallel and Toward Its Tip

Abdullah H. AlEssa, Mohamad I. Al-Widyan

2008, 29(8): 936-946.

Abstract(2387) PDF(586)

Abstract:
Heat transfer enhancement from a horizontal recrtarrgular fin embedded with triangular perforations (their bases are parallel and toward to the fin tip) under natural convection is studied.Its heat dissipation rate was compared to that of the equivalent solid one.The parameters considered were geometrical dimensions and thermal properties of the fin and of the perforations.The gain in heat transfer enhancement and the fin weight reduction due to the perforations was considered.It is shown also that the heat dissipation from the perforated fin for certain range of triangular perforation dimension and spaces between perforations result in improvement in heat transfer over the equivalent solid fin.The heat transfer enhancement of the perforated fin increases as the fin thermal conductivity and its thicluress are increased.

Study of Stress Field Near Interface Crack Tip of Double Dissimilar Orthotropic Composite Materials

LI Jun-lin, ZHANG Shao-qin, YANG Wei-yang

2008, 29(8): 947-953.

Abstract(3388) PDF(8058)

Abstract:
A study of double dissintilar orthotropic composite materials interfacial crack was made by constivcting new stress functions and employing the method of composite material complex.In the case that the characteristic equations' discriminants are all more than zero,the theoretical fonmula of the stress field and the displacement field near the mode Ⅰ interface crack tip,without oscillation and inter-embedding between the interfaces of the crack were delved.

Magneto-Elastic Combination Resonances Analysis of Current-Conducting Thin Plate

HU Yu-da, LI Jing

2008, 29(8): 954-966.

Abstract(3006) PDF(622)

Abstract:
Based on Maxwell the nonlinear magneto-elastic vibration equations of a thin plate were derived.The electrodynamic equations and of electromagnetic forces were also derived.In addition,the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant magnetic filed were studied.by means of the Galerldn Method,the corresponding nonlinear vibration differential equatios were derived.The amplitude frequency response equation of the system in steady motion was obtained by the method of multiple scales.The exatation condition of combination resonances was analyzed.Based on the Liapunov stability theory,the stabilities of steady solutions were analyzed and the critical conditions of stability were also obtained.Through the numerical calculation,the curves which resonance-amplifades changing with detuning parameters,excitation amplitudes and magnetic intensity in the fast and the second order modality were obtained respectively.The time history response plots,the phase charts,the Poincare mapping charts and the spectrum plots of vibraiaons were also obtained.The effeet of electso-mangetic and mechanical parameters for the stabilities of solutions and the bifurcattion are further analyzed.Some complex dynamic performances such as the period-doubling motion and the quasi-period motion were discussed.

Stabilization Meshless Method for Convection Dominated Problems

ZHANG Xiao-hua, OUYANG Jie, WANG Jian-yu

2008, 29(8): 967-975.

Abstract(2640) PDF(778)

Abstract:
It is well luiown that the standard Galerlan is not ideally suited to deal with the spatial discretization of convection-dominated problems.Several techniques were proposed to overcome the instability issues in convection-dominated problems simulated by meshless method.These stable techniques included: the nodal refinement,the enlazgement of nodal influence domain,the full upwind meshless technique and the adaptive upwind meshless technique.Meanwile,these stable techniques were applied to RPIM to solve one and two-dimensional convection-diffusion equations.Numerical resalts for example problems show that these techniques are effective to solve convection-dominated preblems,and the adaptive upwind meshless technique is the most effective method of all.

Two Dimensional Analytical Solution for a Partially Vegetated Compound Channal Flow

HUAN Wen-xin, XU Zhi-gang, YANG Zhong-hua, ZENG Yu-hong

2008, 29(8): 976-982.

Abstract(2545) PDF(728)

Abstract:
The theory of eddy viscosity model is applied to the study of the flow in compound charurel which was partially vegetated.The governing equation was constituted by analyzing the longitudinal forces acted on the unit volume where the effect of the vegetation to the flow is considered as the drag force item.The compound channel was divided into 3 sub-regions in transverse direction,and the weffcients in every region's differential equations were solved simultaneously.Thus the analytical solulion of the transverse distribution of the depth-averaged velocity for uniform flow in partially vegetated compound channel is got.The results can also be used to predict the transverse distribution of the bed shear stress which has an important effect on the transportation of sediment.by comparing the analytical results with the measured data,the analytical solution was prnved to be sufficiently accurate to predict most hydraulic features for engineering design purpose.

Nonlinear Coupling Dynamics of Liquid Filled Spherical Container in Microgravity

YUE Bao-zeng

2008, 29(8): 983-990.

Abstract(2210) PDF(569)

Abstract:
Nonlinear coupled dynamics of liquid-filled spherical container in microgravity is investigated.The goveniing equations of the low-gravity liquid sloshing in a convex asymmetrical container subjected to lateral excitation was obtained by variational principle and solved by a modal analysis method.The variational formulas were transformed into a fiequency equation in the form of a standard eigenvalue problem by the Galerldn method,in which admissible functions for the velocity potential and the liquid free surface displacement were determined analytically in terns of the Gauss hypergeometric series.The coupled dynamic equations of the liquid-filled container were derived using Ia,grange's method,and are numerically solved.The time histories of the modal solutions were obtained by numerical simulations.

Magnetic Field and Hall Currents Influences on Blood Flow Through a Stenotic Artery

Kh. S. Mekheimer, M. A. El Kot

2008, 29(8): 991-1002.

Abstract(2574) PDF(646)

Abstract:
A micrnpolar model for blood of mag}etol}ydrodynamic flow through a horizontally nonsymmetric arterial but vertically symmetric artery with a mild stenosis is presented.To estimate the effect of the stenosis shape,a suitable geometry was considered such that the horizontal shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter).Flow parameters such as velocity,the resistance to flow (the resistance impedance),the wall shear stress distribution in the stenotic region and its magnitude at the maavmum height of the stenosis (stenosis throat) were computed for different shape parameter,the Hartrnann number and Hall parameter.It is shown that the resistance to flow decreases with increasing values of the parameter deterrninirrg the stenosis shape and Hall parameter,while the resistance to flow increase with increasing the Hartrnann number.The wall shear stress and the shearing stress on the wall at the maavmum height of the stenosis possess an inverse character to the resistance to flow with respect to any given values of Hartmann number and Hall parameter.Finally,the effect of the Hartrnann number and the Hall paruneter on the horizontal velocity was examined.

Singular Perturbation for the Weakly Nonlinear Reaction Diffusion Equation With Boundary Perturbation

MO Jia-qi

2008, 29(8): 1003-1008.

Abstract(2618) PDF(827)

Abstract:
A class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation is considered under suitable conditions.Firstly,by dint of regular perturbation method,the outer solution of the original problem was obtained.Secondly,by using the stretched variable and the expanding theory of power series,the initial layer term of solution was constructed.And then,by using the theory of differential inequalities the asymptotic behavior of solutions for the initial boundary value problems was studied.finally,using some relational inequalities the existence and uniqueness of solution for the original problem and the uniforntly valid asympfolic estimation were discussed.