LINEAR ACTIVE STRUCTURES AND MODES （ Ⅱ ） — DISCRETE SYSTEMS AND BEAMS

The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes ( Ⅰ ) “. The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.     

Analysis of nonlinear dynamic stability of liquid-converying pipes

Nonlinearly dynamic stability of flexible liquid-conveying pipe in fluid structure interaction was analyzed by using modal disassembling technique. The effects of Poisson, Junction and Friction couplings in the wave-flowing-vibration system on the pipe dynamic stability were included in the analytical model constituted by four nonlinear differential equations. An analyzing example of cantilevered pipe was done to illustrate the dynamic stability characteristics of the pipe in the full coupling mechanisms, and the phase curves related to the first four modal motions were drawn. The results show that the dynamic stable characteristics of the pipe are very complicated in the complete coupling mechanisms, and the kinds of the singularity points corresponding to the various modal motions are different. Foundation items: the National Natural Science Foundation of China (50079007); the Hydraulic Science Foundation of China Hydraulic Ministry (SZ9830); the Natural Science Foundation of Yunnan Provicce (98E003G) Biographies: ZHANG Li-xiang (1959−) HUANG Wen-hu (1926−)     

On the formal solution of initial value problem of Navier-Stokes equation

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IMPULSIVE CONTROL FOR THE STABILIZATION AND SYNCHRONIZATION OF LUR＇ E SYSTEMS

An impulsive control scheme of the Lur‘e system and several theorems on stability of impulsive control systems was presented, these theorems were then used to find the conditions under which the Lur‘e system can be stabilized by using impulsive control with varying impulsive intervals. The parameters of Lur‘e system and impulsive control law are given, a theory of impulsive synchronization of two Lur‘e system is also presented. A numerical example is used to verify the theoretical result.     

Poincaré-cartan integral invariants of Birkhoffian systems

Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré-Cartan’s type is constructed for Birkhoffian systems. Finally, one-dimensional damped vibration is taken as an illustrative example and an integral invariant of Poincaré’s type is found.     

TheC k instability of navier-Stokes equation appending polynomials of unknown functions

Applying the theory of stratification, the solution space structure about a class of deformed Navier-Stokes equation isdetermined. It is proved that such kind of equation has no C^k (k≥2) stable solution by the fact that the strate transversale is a null set. Foundation item: the National Natural Science Foundation of China (19971054), Shanghai Natural Science Foundation (99ZA14034) Biography: HE You-hua (1960-)     

Applications of the signs of Melnikov's function

The existence and stability of peridic solutions for the two-dimensional system x′=f(x)+g(x, a), O<ε<1,a∈R whoseunperturbed system is Hamlitonan be decided by using the signs of Melnikov's function. Theresults can be applied to the comstuction of phase portralts in the bifiacation set of codimension two bifurcations of flows with double aero eignvahues.     

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL(Ⅱ)-THE LOWER BOUND ON THE DISTURBANCE ENERGY AND POTENTIAL ENSTROPHY TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol’d’s second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigatedThe lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance     

MIXED FINITE ELEMENT METHODS FOR THE SHALLOWWATER EQUATIONS INCLUDING CURRENT AND SILTSEDIMENTATION （Ⅱ）——THE DISCRETE-TIMECASE ALONG CHARACTERISTICS

The mixed finite element(MFE) methods for a shallow water equation systemconsisting of water dynamics equations, silt transport equation, and the equation of bottomtopography change were derived. A fully discrete MFE scheme for the discrete-time alongcharacteristics is presented and error estimates are established. The existence andconvergence of MFE solution of the discrete current velocity, elevation of the bottomtopography, thickness of fluid column, and mass rate of sediment is demonstrated.     

DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL

The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli’s gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.     

MAXIMAL ELEMENTS FOR G-B-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅱ)

By applying existence theorems of maximal elements for a family of G_B-majorized mappings in a product space of G-convex spaces, some coincidence theorem, Fan-Browder type fixed point theorem and some existence theorems of solutions for a system of minimax inequalities are proved under noncompact setting of G-convex spaces. These theorems improve and generalize many important known results in literature. Contributed by Duping Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province ([2000]25) Biography: Duping Xie-ping (1938∼), Professor (E-mail: dingxip@sichu.edu.cn)     

Hamiltonian structure for rigid body with flexible attachments in a circular orbit

Hamiltonian structure of a rigid body in a circular orbit is established in this paper. With the reduction technique, the Hamiltonian structure of a rigid body in a circular orbit is derived from Lie-Poisson structure of semidirect product, and Hamiltonian is derived from Jacobi's integral. The above method can be generalized to establish the Hamiltonian structure of a rigid body with a flexible attachment in a circular orbit. At last, an example of stability analysis is given. The project supported by National Natural Science Foundation of China and Aeronautic Science Foundation.     

An automatic constraint violation stabilization method for differential/ algebraic equations of motion in multibody system dynamics

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MAXIMAL ELEMENTS FOR GB-MAJORIZED MAPPINGS IN PRODUCT G-CONVEX SPACES AND APPLICATIONS (Ⅰ)

A new family of set-valued mappings from a topological space into generalized convex spaces was introduced and studied. By using the continuous partition of unity theorem and Brouwer fixed point theorem, several existence theorems of maximal elements for the family of set-valued mappings were proved under noncompact setting of product generalized convex spaces. These theorems improve, unify and generalize many important results in recent literature. Contributed by DING Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province of China ([2000]25) Biography: DING Xie-ping (1938∼)     

Bifurcation in two-dimensional neural network model with delay

A kind of 2-dimensional neural network model with delay is considered. By analyzing the distribution of the roots of the characteristic equation associated with the model, a bifurcation diagram was drawn in an appropriate parameter plane. It is found that a line is a pitchfork bifurcation curve. Further more, the stability of each fixed point and existence of Hopf bifurcation were obtained. Finally, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were determined by using the normal form method and centre manifold theory. Foundation item: the National Natural Science, Foundation of China (19831030) Biography: WEI Jun-jie, Professor, Doctor, E-mail: weijj@hit.edu.cn     

Similarity reductions for 2+1-dimensional variable coefficient generalized kadomtsev-petviashvili equation

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LINEAR ACTIVE STRUCTURES AND MODES （ Ⅰ ） — BASIC CONCEPTS AND PROPERTIES

Some basic concepts about the active structures were firstly explained, and the main subjects to study in the field of active structure dynamics were synthesized. For the linear active structures, the annotations on the modes were done in detail. The physical meanings of the right and left eigenvectors were explained. The right eigenvectors are the modal shapes and the modal responses of an active structure depend on the left ones. The adjoint structure of an active structure was defined and the reciprocity theorem was interpreted. For two active structures, which are adjoint to each other and with the reciprocal gain-matrices, the right and left eigenvector are reciprocal The relationship between an active structure and the corresponding passive structure is expressed with the transfer functions, which is employed to resolve the estimation problems.     

A class of nonlinear boundary value problems for the second-order<Emphasis Type="Italic">E</Emphasis><Subscript>2</Subscript> class elliptic systems in general form

A class of nonlinear boundary value problems (BVP) for the second-order E₂ class elliptic systems in general form is discussed. By introducing a kind of transformation, this kind of BVP is reduced to a class of generalized nonlinear Riemann-Hilbert BVP. And then some singular integral operators are introduced to establish the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of the properties of singular integral operators and the function theoretic methods. Foundation items: the National Natural Science Foundation of China (19671056); Shanghai Municipal Natural Scientific Foundation (99ZA14030, 01ZA14023); Jiangxi Provincial Natural Scientific Foundation (981102, 0211014) Biographies: LI Ming-zhong (1935−); XU Ding-hua (1967−)     

Constrained multiobjective games in locally convex<Emphasis Type="Italic">H</Emphasis>-spaces

A new class of constrained multiobjective games with infinite players in noncompact locally convex H-spaces without linear structure are introduced and studied. By applying a Fan-Glicksberg type fixed point theorem for upper semicontinuous set-valued mappings with closed acyclic values and a maximum theorem, several existence theorems of weighted Nath-equilibria and Pareto equilibria for the constrained multiobjective games are proved in noncompact locally convex H-spaces. These theorems improve, unify and generalize the corresponding results of the multiobjective games in recent literatures. Contributed by Ding Xie-ping Foundation items: the National Natural Science Foundation of China (19871059); the Natural Science Foundation of Education Department of Sichuan Province ([2000]25) Biography: Ding Xie-ping (1938-)