应用数学和力学

2002 Vol. 23, No. 1

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Quasi-Static and Dynamical Analysis for Viscoelastic Timoshenko Beam With Fractional Derivative Constitutive Relation

ZHU Zheng-you, LI Gen-guo, CHENG Chang-jun

2002, 23(1): 1-10.

Abstract(2781) PDF(819)

Abstract:
The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived.The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitutive relation.The quasi-static behavior of the viscoelastic Timoshenko beam under step loading is analyzed and the analytical solution is obtained.The influence of material paraeters on the deflection is investigated.The dynamical response of the viscoelastic Timoshenko beam subjected to a periodic excitation is studied by means of mode shape functions.And the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.

The Tensor Denotation of Beltrami Spherical Vortices and Their Symmetry Analysis

HUANG Yong-nian, HU Xin

2002, 23(1): 11-15.

Abstract(2601) PDF(624)

Abstract:
Discuss one kind of tensor denotation of nth Beltrami axisymmetric and nonaxisymmetric spherical vortices,their classification and symmetries were discussed.Chaotic phenomena will occur in the dynamic system of the nonaxisymmetric Beltrami spherical vortices.From these aspects,it is shown that the tensor denotation has more meaningful characters and nonaxisymmetric Beltrami shperical vortices are various and very complex.

Time Precise Integration Method for Constrained Nonlinear Control System

DENG Zi-chen, ZHONG Wan-xie

2002, 23(1): 16-22.

Abstract(2466) PDF(635)

Abstract:
For the constrained nonlinear optimal control problem,by taking the first term of Taylor series,the dynamic equation is linearized.Thus by introducing into the dual variable(Lagrange multiplier vector),the dynamic equation can be transformed into Hamilton system from Lagrange system on the basis of the original variable.Under the whole state,the problem discussed can be described from a new view,and the equation can be precisely solved by the time precise integration method established in linear dynamic system.A numerical example shows the effectiveness of the method.

A Family of Integrable Systems of Liouville and Lax Representation, Darboux Transformations for its Constrained Flows

ZHANG Yu-feng, ZHANG Hong-qing

2002, 23(1): 23-30.

Abstract(2044) PDF(675)

Abstract:
A family of integrable systems of Liouville are obtained by Tu pattern.Using higher-order potential-eigenfuction constraints,the integrable systems are fact orized to two x-and t_n-integrable Hamiltonian systems whose Lax representation and three kinds of Darboux transformations are presented.

Instability and Dispersivity of Wave Propagation in Inelastic Saturated/Unsaturated Porous Media

LI Xi-kui, ZHANG Jun-bo, ZHANG Hong-wu

2002, 23(1): 31-46.

Abstract(2080) PDF(607)

Abstract:
A model based on the Biot theory for simulating coupled hydro-dynamic behavior in saturated-unsaturated porous media was utilized with integration of the inertial coupling effect between the solid-fluid phases of the media into the model.Stationary instability and dispersivity of wave propagation in the media in one-dimensional problem were analyzed.The effects of the following factors on stationary instability and dispersivity were discussed.They are the viscous and inertial couplings between the solid and the fluid phases,compressibility of the mixture composed of solid grains and pore fluid,the degree of saturation,visco-plastic(rate dependent inelastic)constitutive behavior of the solid skeleton under high strain rate.The results and conclusion obtained by the present work will provide some bases or clues for overcoming the difficulties in numerical modelling of wave propagation in the media subjected to strong and shock loading.

A Form Invariance of Constrained Birkhoffian System

CHEN Xiang-wei, LUO Shao-kai, MEI Feng-xiang

2002, 23(1): 47-51.

Abstract(2576) PDF(829)

Abstract:
The form invariance of constrained Birkhoffian system is a kind of invariance of the constrained Birkhoffian equations under infinitesimal transformations.The definition and criteria of the form invariance of constrained Birkhoffian system are given,and the relation of the form invariance and the Noether symmetry is studied.

The Exact Solitary Wave Solution for the Klein-Gordon-Schr^Ldinger Equations

XIA Jing-na, HAN Shu-xia, WANG Ming-liang

2002, 23(1): 52-58.

Abstract(2656) PDF(714)

Abstract:
The solitary wave solutions for the Klein-Gordon-Schr^Ldinger Equations were obtained by using the homogeneous balance principle.The form of the solutions is more generalized than the result that has been proved by pure theoretical and qualitative method in literature;namely,the form of solutions in literature is a particular case of result of the present paper.

Stability Analysis of Hopfield Neural Networks With Time Delay

WANG Lin-shan, XU Dao-yi

2002, 23(1): 59-64.

Abstract(2525) PDF(883)

Abstract:
The global asymptotic stability for Hopfield neural networks with time delay was investigated.A theorem and two corollaries were obtained,in which the boundness and differentiability of f_j on R in some articles were deleted.Some sufficient conditions for the existence of global asymptotic stable equilibrium of the networks in this paper are better than the sufficient conditions in quoted articles.

The Extension Theorems of Cone Linear Operators

SHENG Bao-huai, LIU San-yang

2002, 23(1): 65-72.

Abstract(2049) PDF(617)

Abstract:
A kind of cone separation theorems is established,by which the extension theorems for cone linear continuous operators are developed.As application,the extension theorem for positive linear continuous operators is given.

Nonlinear Saturation of Baroclinic Instability in the Generalized Phillips Model (Ⅰ)—the Upper Bound on the Evolution of Disturbance to the Nonlinearly Unstable Basic Flow

ZHANG Gui, XIANG Jie, LI Dong-hui

2002, 23(1): 73-81.

Abstract(2051) PDF(579)

Abstract:
On the basis of the nonlinear stability theorem in the context of Arnol's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated.By choosing appropriate artificial stable basic flows,the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained,which are analytic completely and without the limitation of infinitesimal initial disturbance.

The Conservation Law of Nonholonomic System of Second-Order Non-Chetave’s Type in Event Space

FANG Jian-hui

2002, 23(1): 82-86.

Abstract(2406) PDF(717)

Abstract:
The conservation law of nonholonomic system of second-order non-Chataev's type in event space is studied.The Jourdain's principle in event space is presented.The invariant condition of the Jourdain's principle under infinitesimal transformation is given by introducing Jourdain's generators in event space.Then the conservation law of the system in event space is obtained under certain conditions.Finally a calculating example is given.

Exponential Stability of Interval Dynamical System With Multidelay

SUN JI-tao, ZHANG Yin-ping, LIU Yong-qing, DENG Fei-qi

2002, 23(1): 87-91.

Abstract(2002) PDF(637)

Abstract:
Using the matrix measure and delay differential inequality,the sufficient conditions were obtained for exponential stability of interval dynamical system with multidelay These conditions are an improvement and extension of the results achieved in earlier papers presented by Liao,Liu,Zhang,Sun,et al.

2T-Periodic Solution for m Order Neutral Type Differential Equations With Time Delays

ZHANG Bao-sheng, ZHU Guang-hui

2002, 23(1): 92-98.

Abstract(2349) PDF(592)

Abstract:
Periodic solution of m order linear neutral equations with constant coefficient and time delays was studied.Existence and uniqueness of 2T-periodic solutions for the equation were discussed by using the method of Fourier series.Some new necessary and sufficient conditions of existence and uniqueness of 2T-periodic solutions for the equation are obtained.The main result is used widely.It contains results in some correlation paper for its special case,improves and extends the main results in them.Existence of periodic solution for the equation in larger number of particular case can be checked by using the result,but cannot be checked in another paper.In other words,the main result in this paper is most generalized for(1),the better result by using the same method.

Computation of Supersonic Turbulent Flowfield With Transverse Injection

SUN De-chuan, HU Chun-bo, CAI Ti-min

2002, 23(1): 99-105.

Abstract(2534) PDF(749)

Abstract:
Three-dimensional steady flowfield generated by transverse sonic injection into a supersonic flow was simulated by solving the Favre-averaged Navier-Stokes equations using the weighted essentially nonoscillatory(WENO)schemes and Jones-Launder k-E model.Results indicate that in the upstream of the square injection there exist two main recirculation regions and the primary vortex induces the horseshoe vortex region.In the downstream there is a low pressure region which conduces a pair of helical vortex.

Preliminary Analysis of Skating Motion

HU Hui

2002, 23(1): 106-110.

Abstract(2358) PDF(487)

Abstract:
A mechanical model of skating motion was founded,and its solution was obtained by using the Rouths equations in nonholonomic dynamics.The two kinds of common,local meaning and scleronomic motions were discussed in detail.The computational results turn out in good agreement with observations.