应用数学和力学

2004 Vol. 25, No. 12

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Pseudospectral Analysis of the Interfacial Stability of Free Jets With Different Velocity Profiles

SU Hai-rong, HU Guo-hui, ZHOU Zhe-wei

2004, 25(12): 1211-1219.

Abstract(2308) PDF(616)

Abstract:
A double fluid model for a liquid jet surrounded by a coaxial gas stream was constructed. The interfacial stability of the model was studied by Chebyshev pseudospectral method for different basic velocity profiles.The physical variables were mapped into computational space using a nonlinear coordinates transformation.The general eigenvalues of the dispersion relation obtained are solved by QZ method,and the basic characteristics and their dependence on the flow parameters are analyzed.

Flood Routing Models in Confluent and Dividing Channels

FAN Ping, LI Jia-chun, LIU Qing-quan

2004, 25(12): 1220-1229.

Abstract(1848) PDF(658)

Abstract:
By introducing a water depth connecting formula,the hydraulic equations in the dividing channel system were coupled and the relation of discharge distribution between the branches of the dividing channels can be yielded.In this manner,a numerical model for the confluent channels was established to study the variation of backwater effects with the parameters in the channel junction.The meeting of flood peaks in the mainstream and tributary can be analyzed with this model.The flood peak meeting is found to be a major factor for the extremely high water level in the mainstream during the 1998 Yangtze River flood'subsequently the variations of discharge distribution and water level with channel parameters between each branch in this system were studied as well.As a result,flood evolution caused by Jingjiang River shortcut and sediment deposition in the entrance of dividing channels of the Yangtze River may be qualitatively elucidated.It is suggested to be an effective measure for flood mitigation to enhance regulation capability of reservoirs available upstream of the tributaries and harness branch entrance channels.

Scattering of Anti-Plane Shear Waves by a Single Crack in an Unbounded Transversely Isotropic Electro-Magneto-Elastic Medium

DU Jian-ke, SHEN Ya-peng, GAO Bo

2004, 25(12): 1230-1238.

Abstract(2422) PDF(654)

Abstract:
A theoretical treatment of the scattering of anti-plane shear(SH)waves is provided by a single crack in an unbounded transversely isotropic electro-magneto-elastic medium.Based on the differential equations of equilibrium,electric displacement and magnetic induction intensity differ ential equations,the governing equations for SH waves were obtained.By means of a linear transform,the governing equations were reduced to one Helmholtz and two Laplace equations.The Cauchy singular integral equations were gained by making use of Fourier transform and adopting electro-magneto impermeable bo undary conditions.The closed for m expression for the resulting stress intensity factor at the crack was achieved by solving the appropriate singular integral equations using Chebyshev polynomial.Typical examples are provided to show the loading frequency upon the local stress fields around the crack tips.The study reveals the importance of the electro-magneto-mechanical coupling terms upon the resulting dynamic stress intensity factor.

Stability of the Crossflow Pattern Around a Slender and Influence of Disturbance

LI Guo-hui, DENG Xue-ying

2004, 25(12): 1239-1248.

Abstract(2524) PDF(893)

Abstract:
Topological structure and stability of a slender cross flow is discussed by the stability theory of dynamic system.The inner boundary of flow field was limiting streamline and it was proved that the topological structure connected saddles by limiting streamline is stable.It is proved that the development of slender vortices leads to the change of topological structure about cross flow.And it is the change from stable and symmetrical vortices flow pattern to unstable and symmetrical vortices flow pattern,and then to stable and asymmetrical vortices flow pattern due to little disturbance which leads to the development of asymmetrical slender vortices.The influence of disturbance to flowfield structure was discussed by unfolding theory too.

Investigation on Elasto-Plastic Constitutive Model Coupled With Damage for Localization Phenomena

SHEN Xin-pu, SHEN Guo-xiao, CHEN Li-xin

2004, 25(12): 1249-1256.

Abstract(2678) PDF(713)

Abstract:
On the basis of existing plasticity-based damage model for plasticity coupled with damage for localization analysis,constitutive parameter identification was carried out through a series of numerical tests at local level.And then improvements were made on the expressions of the evolution laws of damage'strain localization phenomena were simulated with a typical double-notched specimen under tensions.Numerical results indicate the validity of the proposed theory.

Study on Dynamic Constitutive Relations for Concrete With Finite Deformation

CHEN Shu-yu, SHEN Cheng-kang, JIN Wu-gen

2004, 25(12): 1257-1263.

Abstract(2870) PDF(906)

Abstract:
The differences between finite deformation and infinitesimal deformation are discussed. They are exercised on elasto-viscoplastic constitutive relations of concrete.Then,a Rate-dependent mechanics model was presented on the basis of Ottosen's four-parameter yield criterion,where different loading surface transferring laws were taken into account,when material was in hardening stage or in softening stage,respectively.The model is well established,so that it can be applied to simulate the response of concrete subject to impact loading.Green-Naghdi stress rate was introduced as objective stress rate.Appropriate hypothesis was postulated in accordance with many experimental results, which could reflect the mechanical behaviour of concrete with large deformation.Available thoughts as well as effective methods are also provided for the research on related engineering problems.

Nontrivial Equilibrium Solutions for a Semilinear Reaction-Diffusion System

GU Yong-geng, SUN Wen-jun

2004, 25(12): 1264-1270.

Abstract(2792) PDF(824)

Abstract:
By the degree theory on positive cone together with the technique of a priori estimate,the nontrivial equilibrium solutions of a strong nonlinearity and weak coupling reaction diffusion system and the structure of the equilibrium solutions are discussed.

Turbulence, Vortex and External Explosion Induced by Venting

JIANG Xiao-hai, FAN Bao-chun, YE Jin-fang

2004, 25(12): 1271-1277.

Abstract(2259) PDF(516)

Abstract:
The process of explosion venting to air in a cylindrical vent vessel connected to a duct,filling with a stoichiometric methane-oxygen gas mixture,was simulated numerically by using a colocated grid SIMPLE scheme based on k-epsilon turbulent model and Eddy-dissipation combustion model. The characteristics of the combustible cloud,flame and pressure distribution in the external flow field during venting were analyzed in terms of the predicted results.The results show that the external explosion is generated due to violent turbulent combustion in the high pressure region within the external combustible cloud ignited by a jet flame.And the turbulence and vortex in the external flow field were also discussed in detail.After the jet flame penetrating into the external combustible cloud,the turbulent intensity is greater in the regions with greater average kinetic energy gradient,rather than in the flame front;and the vortex in the external flow field is generated primarily due to the baroclinic effect,which is greater in the regions where the pressure and density gradients are nearly perpendicular.

Torsional Impact Response of a Penny-Shaped Crack in a Functional Graded Strip

FENG Wen-jie, LI Xiang-guo, WANG Shou-dong

2004, 25(12): 1278-1284.

Abstract(2508) PDF(532)

Abstract:
The torsional impact response of a penny-shaped crack in a nonhomogeneous strip is considered.The shear modulus is assumed to be functionally graded such that the mathematics is tractable.Laplace and Hankel transforms were used to reduce the problem to solving a Fredholm integral equation.The crack tip stress field is obtained by considering the asymptotic behavior of Bessel function.Explicit expressions of both the dynamic stress intensity factor and the energy density factor were derived.And it is shown that,as crack driving force,they are equivalent for the present crack problem.Investigated are the effects of material nonhomogeneity and strip's highness on the dynamic fracture behavior.Numerical results reveal that the peak of the dynamic stress intensity factor can be suppressed by increasing the nonhomogeneity parameter of the shear modulus,and that the dynamic behavior varies little with the adjusting of the strip's highness.

GP-Stability of Rosenbrock Methods for System of Delay Differential Equation

CONG Yu-hao, CAI Jia-ning, XIANG Jia-xiang

2004, 25(12): 1285-1291.

Abstract(2264) PDF(948)

Abstract:
The stability analysis of the Rosenbrock method for the numerical solutions of system of delay differential equations was studied.The stability behavior of Rosenbrock method was analyzed for the solutions of linear test equation.The result that the Rosenbrock method is GP-stable if and only if it is A-stable is obtained.

On the Redundancy of Complex Modal Parameters

CHEN Kui-fu, JIAO Qun-ying

2004, 25(12): 1292-1298.

Abstract(2542) PDF(1127)

Abstract:
Generating the simulation transfer function(TF)is indispensable to modal analysis,such as examining modal parameters identification algorithm,and assessing modal analysis software.Comparing 3 feasible algorithms to simulate TF shows that,one of them is preperable,which is expressing the TF as the function of the complex modal parameters(CMPs),because the deliberate behaviors of CMPs can be implemented easily,such as,dense modals,large damping,and complex modal shape, etc.Nonetheless,even this preferable algorithms is elected,the complex modal shapes cannot be specified arbitrarily,because the number of CMPs far more exceeds that in physical coordinate'so for physical realizable system,there are redundant constraints in CMPs.By analyzing the eigenvalue problem of a complex modal system,and the inversion equations from CMPs to physical parameters,the explicit redundancy constraints were presented.For the special cases,such as the real modal,the damping free modal,and non-complete identification,the specific forms of the redundancy constraints were discussed,along with the number of independent parameters.It is worthy of noting that,redundancy constraints are automatically satisfied for the real modal case.Their equivalent forms on the transfer matrix and a column of transfer matrix were also provided.These results are applicable to generate TF,to implement identification by optimization and appreciate the identification results,to evaluate residual modal,and to verify the complementary of identified modal orders.

Chaos in the Softening Duffing System Under Multi-Frequency Periodic Forces

LOU Jing-jun, HE Qi-wei, ZHU Shi-jian

2004, 25(12): 1299-1304.

Abstract(2356) PDF(832)

Abstract:
The chaotic dynamics of the softening-spring Duffing system with multi-frequency external periodic forces is studied.It is found that the mechanism for chaos is the transverse heteroclinic tori. The Poincar map,the stable and the unstable manifolds of the system under two incommensurate periodic forces were set up on a two-dimensional torus.Utilizing a global perturbation technique of Melnikov the criterion for the transverse interaction of the stable and the unstable manifolds was given. The system under more but finite incommensurate periodic forces was also studied.The Melnikov's global perturbation technique was therefore generalized to higher dimensional systems.The region in parameter space where chaotic dynamics may occur was given.It was also demonstrated that increasing the number of forcing frequencies will increase the area in parameter space where chaotic behavior can occur.

Electroelastic Interaction Between a Piezoelectric Screw Dislocation and a Circular Inhomogeneity With Interfacial Cracks

LIU You-wen, FANG Qi-hong

2004, 25(12): 1305-1312.

Abstract(2504) PDF(619)

Abstract:
A piezoelectric screw dislocation in the matrix interacting with a circular inhomogeneity with interfacial cracks under antiplane shear and in-plane electric loading at infinity was dealt with. Using complex variable method,a general solution to the problem was presented.For a typical case, the closed form expressions of complex potentials in the inhomogeneity and the matrix regions and the electroelastic field intensity factors were derived explicitly when the interface contains single crack. The image force acting on the piezoelectric screw dislocation was calculated by using the perturbation technique and the generalized Peach-Koehler formula.As a result,numerical analysis and discussion show that the perturbation influence of the interfacial crack on the interaction effects of the dislocation and the inhomogeneity is significant which indicates the presence of the interfacial crack will change the interaction mechanism when the length of the crack goes up to a critical value.It is also shown that soft inhomogeneity can repel the dislocation due to their intrinsic electromechanical coupling behavior.

Controlling Lü-System Using Partial Linearization

YU Yong-guang, ZHANG Suo-chun

2004, 25(12): 1313-1318.

Abstract(2235) PDF(455)

Abstract:
Partial linearization method is proposed for controlling Lü-system.Through partially cancelling the nonlinear cross-coupling terms the stabilization of the resulting system was realized.This method can be easily realized.The robust behavior was proved with respect to an uncertain system. Numerical simulation are provided to show the effectiveness and feasibility of the method.