应用数学和力学

2003 Vol. 24, No. 7

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Effect of Heat Exchange on the Interfacial Instability of Gas-Liquid Jet

WANG Zhi-liang, ZHOU Zhe-wei

2003, 24(7): 661-668.

Abstract(2263) PDF(588)

Abstract:
The classical linear instability theory was applied to the planar stratified two-layers flow with high speed compressible gas layer impacting on incompressible viscous liquid layer.The walls were kept at different temperatures,resulting in heat transfer across the layers.The thermal conductivity and the density of the gas were alerted when the temperature changes.After some treatment,a four-order stiff ordinary differential equation was derived,and numerical integration and multi-shooting method were used to solve this equation for its spatial mode calculation.The numerical results of characteristic parameters show good coincidence with other models.At the same time,when the wall temperature ratio decreases,as well as the Reynold number and the gas thermal conductivity change increases,the atomization would be more efficient and producing finer droplets.And the results show good fit with the experimental datum of HJE.Co.Inc(Glens Falls,NY,USA).

Optimal Control of Parabolic Variational Inequalities With Stat Constraint

GUO Xing-ming, ZHOU Shi-xing

2003, 24(7): 669-674.

Abstract(2371) PDF(633)

Abstract:
The optimal control problem of parabolic variational inequalities with the state constraint and nonlinear,discontinuous nonmonotone multivalued mapping term and its approximating problem are studied,which generalizes some obtained results.

Transversely Isotropic Hyper-Elastic Material Rectangular Plate With Voids Under a Uniaxial Extension

CHENG Chang-jun, REN Jiu-sheng

2003, 24(7): 675-683.

Abstract(2351) PDF(573)

Abstract:
The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper-elastic material with the generalized neo-Hookean strain energy function under a uniaxial extension are studied.The deformation functions of plates with voids that are symmetrically distributed in a certain manner are given and the functions are expressed by two parameters by solving the differential equations.The solution may be approximately obtained from the minimum potential energy principle.Thus,the analytic solutions of the deformation and stress of the plate are obtained.The growth of the voids and the distribution of stresses along the voids are analyzed and the influences of the degree of anisotropy,the size of the voids and the distance between the voids are discussed.The characteristics of the growth of the voids and the distribution of stresses of the plates with one void,three or five voids are obtained and compared.

General Solution for the Coupled Equations of Transversely Isotropic Magnetoelectroelastic Solids

LIU Jin-xi, WANG Xiang-qin, WANG Biao

2003, 24(7): 684-690.

Abstract(2381) PDF(775)

Abstract:
The coupling feature of transversely isotropic magnetoelectroelastic solids are governed by a system of five partial differnetial equations with respect to the elastic displacements,the electric potential and the magnetic potential.Based on the potential theory,the coupled equations are reduced to the five uncoupled generalized Laplace equations with respect to five potential functions.Further,the elastic fields and electromagnetic fields are expressed in terms of the potential functions.These expressions constitute the general solution of transversely isotropic magnetoelectroelastic media.

Elastic-Plastic Analytical Solutions For an Eccentric Crack Loaded by Two Pairs of Anti-Plane Point Forces

WANG Cheng, WU Cheng-ping

2003, 24(7): 691-698.

Abstract(2241) PDF(583)

Abstract:
The improved near crack line analysis method was used to investigate an eccentric cracked plate loaded by two pairs of anti-plane point forces at the crack surface in an elastic-perfectly plastic solid.The analytical solutions of the elastic-plastic stress fields and displacements near the crack line have been found without the assumptions of the small scale yielding.The law that the length of the plastic zone along the crack line is varied with an external loads and the bearing capacity of an eccentric cracked plate are obtained.

Three-Dimensional Instability of an Oscillating Viscous Flow Past a Circular Cylinder

LU Xi-yun, LING Guo-can

2003, 24(7): 699-707.

Abstract(2448) PDF(705)

Abstract:
A systematically numerical study of the sinusoidally oscillating viscous flow around a circular cylinder was performed to investigate vortical instability by solving the three-dimensional incompressible Navier-Stokes equations.The transition from twoto three-dimensional flow structures along the axial direction due to the vortical instability appears,and the three-dimensional structures lie alternatively on the two sides of the cylinder.Numerical study has been taken for the Keulegan-Carpenter(KC) numbers from 1 to 3.2 and frequency parameters from 100 to 600.The force behaviors are also studied by solving the Morison equation.Calculated results agree well with experimental data and theoretical prediction.

Perturbation Transfer Matrix Method for Eigendata of One-Dimensional Structural System With Parameter Uncertainties

LIU Bao-guo, YIN Xue-gang, JIAN Kai-lin, WU Yong

2003, 24(7): 708-714.

Abstract(2280) PDF(649)

Abstract:
A general method based on RICCATI transfer matrix is presented to calculate the 2nd order perturbations of eigendatas for one-dimensional structural system with parameter uncertainties.The method is applicable to both real and complex eigendatas of any one-dimensional structural system.The formulas for calculating the sensitivity derivatives of eigendatas based on this method are also pre sented.The method is applied to the perturbation analysis for the eigendatas of a rotor with gyroscopic moment,and the differences between the perturbation results and the accurate calculating results are small.

Elastic Wave Scattering and Dynamic Stress in Composite With Fiber

HU Chao, LI Feng-ming, HUANG Wen-hu

2003, 24(7): 715-722.

Abstract(2760) PDF(900)

Abstract:
Based on the theory of elastic dynamics,multiple scattering of elastic waves and dynamic stress concentrations in fiber-reinforced composite were studied.The analytical expressions of elastic waves in different region were presented and an analytic method to solve this problem was established.The mode coefficients of elastic waves were determined in accordance with the continuous conditions of displacement and stress on the boundary of the multi-interfaces.By making use of the addition theorem of Hankel funcitions,the formulations of scattered wave fields in different local coordinates were transformed into those in one local coordinate to determine the unknown coefficients and dynamic stress concentration factors.The influence of distance between two inclusions,material properties and structural size on the dynamic stress concentration factors near the interfaces was analyzed.It indicates in the analysis that distance between two inclusions,material properties and structural size has great influence on the dynamic properties of fiber-reinforced composite near the interfaces.As examples,the numerical results of dynamic stress concentration factors near the interfaces in a fiber-reinforced composite are presented and discussed.

Response of Nonlinear Oscillator Under Narrow-Band Random Excitation

RONG Hai-wu, WANG Xiang-dong, MENG Guang, XU Wei, FANG Tong

2003, 24(7): 723-729.

Abstract(2531) PDF(727)

Abstract:
The principal resonance of Duffing oscillator to narrow-band random parametric excitation was investigated.The method of multiple scales was used to determine the equations of modulation of amplitude and phase.The behavior,stability and bifurcation of steady state response were studied by means of qualitative analyses.The effects of damping,detuning,bandwidth and magnitudes of deterministic and random excitations were analyzed.The theoretical analyses were verified by numerical results.Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases,the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle.Under some conditions the system may have two steady state solutions.

New Method to Option Pricing for the General Black-Scholes Model-An Acturarial Approach

YAN Hai-feng, LIU San-yang

2003, 24(7): 730-738.

Abstract(2347) PDF(1275)

Abstract:
Using physical probability measure of price process and the principle of fair premium,the results of Mogens Bladt and Hina Hviid Rydberg are generalized.In two cases of paying intermediate divisends and no intermediate dividends,the Black-Scholes model is generalized to the case where the riskless asset(bond or bank account) earns a time-dependent interest rate and risky asset(stock) has time-dependent the continuously compounding expected rate of return,volatility.In these cases the accurate pricing formula and put-call parity of European option are obtained.The general approach of option pricing is given for the general Black-Scholes of the risk asset(stock) with a stochastic continuously compounding expected rate of return,volatility.The accurate pricing formula and put-call parity of European option on a stock whose price process is driven by general Ornstein-Uhlenback process are given by actuarial approach.

Two-Dimensional Nonlinear Dynamic System Model of Interspecific Interaction and Numerical Simulation Research on It

LI Zi-zhen, XU Cai-lin, WANG Wan-xiong

2003, 24(7): 739-746.

Abstract(2375) PDF(688)

Abstract:
The mechanism and the course of two-dimensional nonlinear dynamic system of interspecific interaction were dealt with systematically.By extending the Lotka-Volterra model from the viewpoint of biomechanics,it developed new models of two-dimensional nonlinear autonomous and nonautonomous dynamic systems,with its equilibrium point s stability and the existence and stability of its periodical solutions analyzed,and did numerical simulation experiments on its dynamics course.The results show that efficiency of interaction between two populations,time-varying effort,and change direction of action coefficient and reaction coefficient have important influences on the stability of dynamic system,that too large or too small interspecific interaction efficiency and contrary change direction of action coefficient and reaction coefficient may result in the nonstability of the system,and thus it is difficult for two populations to coexist,and that time-varying active force contributes to system stability.

Model Shift and Strange Attractor on M^Lbius Strip

CHEN Fang-yue, CHEN Feng-juan

2003, 24(7): 747-754.

Abstract(2759) PDF(595)

Abstract:
A new model shift mapping was given in bilateral symbol space.It is topologically conjugate with the traditional shift mapping.Similar to Smale Horseshoe,a model was constructed correspondent to the model shift mapping,i.e.a class of mapping on M^Lbius strip was given.Its attractors.structure and dynamical behaviour were described.

Research on a Systematic Methodology for Theory of Elasticity

LUO Jian-hui, LIU Guang-dong, SHANG Shou-ping

2003, 24(7): 755-763.

Abstract(2644) PDF(895)

Abstract:
The equivalence between differential form and integral form of a systematic methodology for theory of elasticity is proved.A uniform framework of the systematic methodology is established.New system includes differential form,integral form and mixed form.All kinds of variational principles are proved by the equivalence between differential form and integral form.The idea for generalized virtual work and virtual function is presented.

On Gauge Equivalent Integrable Systems and r-matrices for AKNS Hierarchy and A Coupled MKdV Hierarchy

LIU Xiang-lin, CHEN Qing-hui, ZHANG Bao-cai

2003, 24(7): 764-770.

Abstract(2323) PDF(604)

Abstract:
The new coupled MKdV hierarchy is obtained.By using gauge transformation,the constrained flow,the integrable system and Lax representation for the coupled MKdV hierarchy were first constructed from the AKNS hierarchy and then using the Lax representation the r-matrix for the constrained flow of the coupled MKdV hierarchy was constructed.The second set of conserved integrals of this constrained flow and their involutivity were also given.