应用数学和力学

2006 Vol. 27, No. 8

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Floquet Stability Analysis of Two-Layer Flows With Periodic Fluctuation in a Vertical Pipe

WANG Yan-xia, HU Guo-hui, ZHOU Zhe-wei

2006, 27(8): 883-890.

Abstract(2893) PDF(581)

Abstract:
Based on linear stability theory,parametric resonance of a liquid-gas cylindrical flow with periodic fluctuation in a vertical pipe was discussed by using Floquet theory and Chebyshev collocation method.The effects of different physical parameters on the instability of flow and the properties of parametric resonance were investigated.

Linear and Nonlinear Dielectric Properties of Particulate Composites at Finite Concentration

ZHOU Xiao-ming, HU Geng-kai

2006, 27(8): 891-898.

Abstract(2467) PDF(540)

Abstract:
An analytical method was proposed to calculate effective linear and nonlinear dielectric properties for particulate composites.The method is based on an approximate solution of two-particle interaction problem,and it can be applied to relatively high volume concentration of particles (upto 50%).Nonlinear dielectric property was also examined by means of secant method.It is found that for low applied electric filed the propose dmethod is close to Stroud and Hui's method and for high applied electric filed it is close to Yu.s method.

Minimum Size of 180 Degree Domains in Ferroelectric Thin Films Covered by Electrodes

CHEN Yong-qiu, LIU Yu-lan, WANG Biao

2006, 27(8): 899-903.

Abstract(2003) PDF(603)

Abstract:
Ferroelectric domain switching under low voltage or short pulses is of interest to the development of high-density random access memory(FRAM)devices.Being necessarily very small in size,instability and back switching often occurs when the external voltage is removed,and creates serious problems.A general approach to determine the minimum size of ferroelectric domain to avoid back switching was developed,and as an example,a 180 degree domain in a ferroelectric thin film covered by the upper and lower electrodes was considered in detail.The results show that the approach is generally applicable to many other fields,including phase transformation,nucleation and expansion of dislocation loops in thin films,etc.

Parametric Variational Principle Based Elastic-Plastic Analysis of Heterogeneous Materials With Voronoi Finite Element Method

ZHANG Hong-wu, WANG Hui

2006, 27(8): 904-912.

Abstract(2735) PDF(859)

Abstract:
The Voronoi cell finite element method(VCFEM) is adopted to overcome the limitations of the classic displacement based finite element method in numerical simulation of heterogeneous materials.The parametric variational principle and quadratic programming method were developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems.Finite element formulations were derived and a standard quadratic programming model was deduced from the elastic-plastic equations.Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail.Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.

Rayleigh Lamb Waves in a Micropolar Isotropic Elastic Plate

Rajneesh Kumar, Geeta Partap

2006, 27(8): 913-922.

Abstract(3104) PDF(559)

Abstract:
The propagation of waves in a homogeneous isotropic micropolar elastic cylindrical plate subjected to stress free conditions is investigated.The secular equations for symmetric and skew symmetric wave mode propagation were derived.At short wave limit,the secular equations for symmetric and skew symmetric waves in a stress free circular plate reduces to Rayleigh surface wave frequency equation.Thin plate results are also obtained.The amplitude of displacements and microrotation components are obtained and depicted graphically.Some special cases are also deduced from the present investigations.The secular equations for symmetric and skew symmetric modes are also presented graphically.

Periodic Motions of a Spinning Rigid Spacecraft Under the Influence of the Gravitional and Magnetic Fields

Yehia A. Abdel-aziz, M. H. Yehia, F. A. Abd El-Salam, M. Radwan

2006, 27(8): 923-930.

Abstract(2099) PDF(593)

Abstract:
The motion of a magnetized axisymmetric spacecraft about its center of mass in a circular orbit is considered,taking the gravitational and magnetic effects of the central body into account.Equations of motion of the redueced system are transformed to equations of plane motion of a charged particle under the action of electric and magnetic fields.Stationary motions of the system were determined and periodic motions near them are conustructed using the Liapounov theorem of the holomorphic integral.

Conditional Recursive Equations on Excess-of-Loss Reinsurance

YANG Jing-ping, WANG Xiao-qian, CHENG Shi-hong

2006, 27(8): 931-939.

Abstract(2435) PDF(660)

Abstract:
The marginal recursive equations on excess-of-loss reinsurance treaty were investigated,under the assumption that the number of claims belongs to the family consisting of Poisson,binomial and negative binomial,and that the severity distribution had bounded continuous density function.On condition of the numbers of claims associated with the the reinsurer and the cedent,some recursive equations are obtained for the marginal distributions of the total payments of the reinsurer and the cedent.

Nonsmooth Model for Plastic Limit Analysis and Its Smoothing Algorithm

LI Jian-yu, PAN Shao-hua, LI Xing-si

2006, 27(8): 940-946.

Abstract(2794) PDF(523)

Abstract:
By means of Lagrange duality theory of the convex program,a dual problem of Hill's maximum plastic work principle under Mises.yielding condition was derived and whereby a non-differentiable convex optimization model for the limit analysis were developed.With this model,it is not necessary to linearize the yielding condition and its discrete form becomes a minimization problem of the sum of Euclidean norms subjected to linear constraints.Aimed at resolving the non-differentiability of Euclidean norms,a smoothing algorithm for the limit analysis of perfect-plastic continuum media was prposed.Its efficiency was demonstrated by computing the limit load factor and the collapse state for some plane stress and plain strain problems.

Application of Variable-Fidelity Models to Aerodynamic Optimization

XIA Lu, GAO Zheng-hong

2006, 27(8): 947-953.

Abstract(1959) PDF(559)

Abstract:
For aerodynamic shape optimization,the approximation management framework(AMF) method was used to organize and manage the variable-fidelity models.The method can take full advantage of the low-fidelity,cheaper models to concentrate the main workload on the low-fidelity models in optimization iterative procedure.Furthermore,it can take high-fidelity,more expensive models to monitor the procedure to make the method globally convergent to a solution of high-fidelity problem.Finally,zero order variable-fidelity aerodynamic optimization management framework and search algorithm were demonstrated on an airfoil optimization of UAV with a flying wing.Compared with the original shape,the aerodynamic performance of the optimal shape is improved.The results show the method has good feasibility and applicability.

Dealing With Movings and Collisions of Arbitrary Many Discontinuities in a Conservative Front-Tracking Method

LIU Yan, MAO De-kang

2006, 27(8): 954-962.

Abstract(2529) PDF(458)

Abstract:
An approach to deal with movings and collisions of arbitrary many discontinuities in the conservative front tracking method was developed.Using this approach one may develop an "all-purposed and robust" front-tracking algorithm.The algorithm with this approach may have some inconsistency and thus will have O(1) magnitude errors in some grid cells some time.Nevertheless,these errors will be eliminated by the conservation-preserving property of the front-tracking method in the following computation.Numerical examples were presented to illustrate the efficiency of the approach.

System of Vector Quasi-Equilibrium Problems and Its Applications

PENG Jian-wen, YANG Xin-min, ZHU Dao-li

2006, 27(8): 963-970.

Abstract(2664) PDF(603)

Abstract:
A new system of vector quasi-equilibrium problems was introduced and its existence of a solution was proved.As applications,some existence results of weak Pareto equilibrium for both constrained multicriteria games and multicriteria games without constrained correspondences were also shown.

Stair Matrices and Their Generalizations With Applications to Iterative Methods

SHAO Xin-hui, SHEN Hai-long, LI Chang-jun

2006, 27(8): 971-977.

Abstract(2449) PDF(663)

Abstract:
Stair matrices and their generalizations are introduced.The definitions and some properties of the matrices were first given by Lu Hao.This class of matrices provided bases of matrix splittings for iterative methods.The remarkable feature of iterative methods based on the new class of matrices is that the methods were easily implemented for parallel computation.In particular,a generalization of the accelerated overrelaxation method(GAOR) was introduced.Some theories of the AOR method were extended to the generalized method to include a wide class of matrices.The convergence of the new method was derived for Hermitian positive definite matrices.Finally,some examples are given in order to show the superiority of the new method.

Temperature Profiles of Local Thermal Nonequilibrium for Thermal Developing Forced Convection in a Porous Medium Parallel Plate Channel

YANG Xiao, LIU Xue-mei

2006, 27(8): 978-986.

Abstract(2976) PDF(698)

Abstract:
Based on the two energy equation model,taking into account viscous dissipation due to the interaction between solid skeleton and pore fluid flow,temperature expressions of the solid skeleton and pore fluid flow were obtained analytically for the thermally developing forced convection in a saturated porous medium parallel plate channel,with walls being at constant temperature.It was proved that the temperatures of the two phases for the local thermal nonequilibrium will approach the temperature derived from the one-energy equation model for the local thermal equilibrium when the heat exchange coefficient goes to infinite.The temperature profiles were shown in figures for different dimensionless parameters and the effects of the parameters on the local thermal nonequilibrium is revealed by the parameter study.

Research on Rounded Flowing States of Obstructed Buoyant Jet

HUAI Wen-xin, FANG Shen-guang

2006, 27(8): 987-993.

Abstract(2637) PDF(563)

Abstract:
The mutual relationships of three effective factors,the diameter D/d(d is the diameter of exit) of obstructed plate,exit densimetric Froude number and the distance H/d of the plate from jet orifice for obstructed buoyant jet in static ambient,were analyzed to explain normal and abnormal rounded flowing(reverberated and bifurcated flowing).The critical Froude numbers for obstructed buoyant jets with H/d=2,4,6,8 which distinguished normal and abnormal flowing pattern were obtained.Normal rounded flowing is found only for a plate under a special value of H/d.A fitted formula of critical Froude numbers with H/d and D/d was presented to distinguish rounded flowing types.The occurring of reverberated or bifurcated flowing in abnormal rounded flow was analyzed.Based on the results of obstructed buoyant jets with D/d=1,normal rounded flowing occurred only for all conditions and axial dilution behind the plate under different H/D is obtained.

On the Stability of Solutions of Certain Fourth-Order Delay Differential Equations

Cemil Tun

2006, 27(8): 994-1000.

Abstract(2614) PDF(876)

Abstract:
By the use of the Liapunov functional approach,a new result is obtained to ascertain the asymptotic stability of zero solution of a certain fourth-order non-linear differential equation with delay.The established result is less restrictive than those reported in the literature.

Spatio-Temporal Chaotic Synchronization for Modes Coupled Two Ginzburg-Landau Equations

HU Man-feng, XU Zhen-yuan

2006, 27(8): 1001-1008.

Abstract(2463) PDF(621)

Abstract:
On the basis of numerical computation,the conditions of the modes coupling were proposed.The high-frequency modes are coupled,but the low frequency modes are uncoupled.It was proved that the existence of an absorbing set and a global finite dimensional attractor which is compact,connected in the function space for the high-frequency modes coupled two Ginzburg-Landau equations(MGLE).The trajectory of driver equation may be spatio-temporal chaotic.One associats with MGLE,a truncated form of the equations.The prepared equations will persist in long time dynamical behavior of MGLE.MGLE possess the squeezing properties under some conditions.It was proved that the complete spatio-temporal chaotic synchronization for MGLE can occur.Synchronization phenomenon of infinite dimensional dynamical system(IFDDS) was illustrated on the mathematical theory qualitatively.The method is different from Liapunov function methods and approximate linear methods.