应用数学和力学

2001 Vol. 22, No. 2

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New Conservation Laws of Energy and C-D Inequalities in Continua Without Microstructure

DAI Tian-min

2001, 22(2): 111-118.

Abstract(2610) PDF(918)

Abstract:
Fundamental laws and balance equations as well as C-D inequalities in continuum mechanics are carefully restudied, incompleteness of existing balance laws of angular momentum and conservation laws of energy as well as C-D inequalities are pointed out, and finally new and more general conservation laws of energy and corresponding balance equations of energy as well as C-D inequalities in local and nonlocal asymmetric continua are presented.

New Conservation Laws of Energy and C-D Inequalities in Continua With Microstructure

DAI Tian-min

2001, 22(2): 119-126.

Abstract(2236) PDF(798)

Abstract:
Existing fundamental laws, balance equations and Clausius-Duhem inequalities in continua with microstructure are systematically restudied, and the incomplete formulations of conservation laws of energy and related C-D inequalities are pointed out. Some remarks on existing results are made, and new conservation laws of energy and related C-D inequalities are presented.

C-L Method and Its Application to Engineering Nonlinear Dynamical Problems

CHEN Yu-shu, DING Qian

2001, 22(2): 127-134.

Abstract(2433) PDF(655)

Abstract:
The C-L method was generalized from Liapunov-Schmidt reduction method, combined with theory of singularities, for study of non-autonomous dynamical systems to obtain the typical bifurcating response curves in the system parameter spaces. This method has been used, as an example, to analyze the engineering nonlinear dynamical problems by obtaining the bifurcation programs and response curves which are useful in developing techniques of control to subharmonic instability of large rotating machinery.

Study on Stress Concentrations in an Intraply Hybrid Composite Sheet

ZENG Qing-dun, HUANG Xiao-qing, LIN Xue-hui

2001, 22(2): 135-139.

Abstract(1864) PDF(658)

Abstract:
A reasonably, simply and accurately modified shear-lag model was proposed. Based on the model, the stress redistributions due to the failure of some fibers in an intraply hybrid composite under tension were analyzed. The results show that the present calculating stress concentration factors very coincide with Fukuda and Chou's results, thus verifying the reasonableness and correctness of the present model and methods.

Qusi-Equilibrium Problems and Constrained Multiobjective Games in Generalized Convex Space

DING Xie-ping

2001, 22(2): 140-150.

Abstract(2236) PDF(758)

Abstract:
A class of quasi-equilibrium problems and a class of constrained multiobjective games were introduced and studied in generalized convex spaces without linear structure. First, two existence theorems of solutions for quasi-equilibrium problems are proved in noncompact generalized convex spaces. Then, as applications of the quasi-equilibrium existence theorem, several existence theorems of weighted Nash-equilibria and Pareto equilibria for the constrained multiobjective games are established in noncompact generalized convex spaces. These theorems improve, unify and generalize the corresponding results of the multiobjective games in recent literatures.

Direct Integration Methods With Integral Model for Dynamic Systems

LÜ He-xiang, YU Hong-jie, QIU Chun-hang

2001, 22(2): 151-156.

Abstract(3094) PDF(867)

Abstract:
A new approach which is a direct integration method with integral model (DIM-IM) to solve dynamic governing equations is presented. The governing equations are integrated into the integral equations. An algorithm with explicit and predict-correct and self-starting and four order accuracy to integrate the integral equations is given. Theoretical analysis and numerical examples show that DIM-IM discribed in this paper suitable for strong non-linear and non-conservative system have higher accuracy than central difference, Houbolt, Newmark and Wilson-Theta methods.

Attractors of Nonautonomous Schr-dinger Equations

LIU Yu-rong, LIU Zeng-rong, ZHENG Yong-ai

2001, 22(2): 157-166.

Abstract(2253) PDF(746)

Abstract:
The long-time behaviour of a two-dimensional nonautonomous nonlinear Schr-dinger equation is considered. The existence of uniform attractor is proved and the upper bound of the uniform attractor's Hausdorff dimension is given.

General Constitutive Equation of an ER Suspension Based on the Internal Variable Theory

WANG Biao, XIAO Zhong-min

2001, 22(2): 167-181.

Abstract(2498) PDF(574)

Abstract:
A microstructural constitutive theory of ER suspensions was formulated in this investigation. The framework was based on the internal variable theory and the mechanism analysis. The ER suspension consists of fine particles with high dielectric constant and the supporting fluid. Under the action of the electric field, the polarized particles will aggregate together to form the chain-like structures along the direction of the electric field. As the size and orientation of the particle aggregates are volatile, and they adjust according to the applied electric field and strain rate, the energy conservation equation and the force equilibrium equation were thus established to determine the orientation and size of the aggregates. Following that, a three-dimensional, explicit form of the constitutive equation was derived based on the interaction energy and the dissipation function of the system. The response of the system under the action of a simple shearing load was considered and discussed in detail. It is found that the shear-thinning viscosity of an ER suspension is well approximated by the power-law ∝(Mn)^-0.82.

Identification of Nonlinear Dynamic Systems:Time-Frequency Filtering and Skeleton Curves

WANG Li-li, ZHANG Jing-hui

2001, 22(2): 182-190.

Abstract(2509) PDF(695)

Abstract:
The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator on definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system(GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

Periodic Stream Lines in the Three-Dimensional Square Cell Pattern

LI Ji-bin, DUAN Wan-suo

2001, 22(2): 191-198.

Abstract(2457) PDF(666)

Abstract:
By using the theory of the generalized perturbed Hamiltonian systems, it is shown that there exist periodic stream lines in the three-dimensional square cell pattern of Rayleigh-Benard convection. The result means that our method enables this three-dimensional flow pattern to be described in an unambiguous manner, and some experimental results of other authors can be explained.

Singular Perturbation of Boundary Value Problem for Quasilinear Third Order Ordinary Differential Equations Involving Two Small Parameters

LIN Su-rong, TIAN Gen-bao, LIN Zong-chi

2001, 22(2): 199-205.

Abstract(3502) PDF(872)

Abstract:
The singularly perturbed boundary value problem for quasilinear third order ordinary differential equation involving two small parameters has been considered. For the three cases ε/μ²→0(μ→0);μ²/ε→0(ε→0) and ε=μ², the formal asymptotic solutions are constructed by the method of two steps expansions and the existences of solution are proved by using the differential inequality method. In addition, the uniformly valid estimations of the remainder term are given as well.

Pansystems Analysis:Mathematics, Methodology, Relativity and Dialectical Thinking

GUO Ding-he, WU Xue-mou, FENG Xiang-jun, LI Yong-li

2001, 22(2): 206-220.

Abstract(2409) PDF(813)

Abstract:
Based on new analysis modes and new definitions with relative mathematization and simplification or strengthening forms for concepts of generalized systems, panderivatives, pansymmetry, panbox principle, pansystems relativity, etc, the framework and related principles of pansystems methodology and pansystems relativity are developed. Related contents include:pansystems with relatively universal mathematizing forms, 200 types of dualities, duality transformation, pansymmetry transformation, pansystems dialectics, the 8-domain method, pansystems mathematical methods, generalized quantification, the principles of approximation-transforming, pan_equivalence theorems, supply-demand analysis, thinking experiment, generalized gray systems, etc.