应用数学和力学

On Star Product Fractal Surfaces and Their Dimensions

Xie Heping, Feng Zhigang, Chen Zhida

1999, 20(11): 1101-1106.

Abstract(2198) PDF(568)

Abstract:
In this paper, by using fractal curves, a family of fractal surfaces are defined. Each fractal surface of this family is called Star Product Fractal Surface (SPFS). A theorem of the dimensions of the SPFS is strictly proved. The relationship between the dimensions of the SPFS and the dimensions of the fractal curves constructing the SPFS is obtained.

Deformation Analysis of Laser Spectra Based on S-R Decomposition Theorem

Jiang Yaodong, An Liqian, Liu Yanhua, Chen Zhida

1999, 20(11): 1107-1114.

Abstract(2582) PDF(604)

Abstract:
In the Fourier spectral analyzer, the Fourier spectra or the Fraunhofer diffraction pattern of an image is formed on the back focal plane when a laser beam is directed on the image lying on the front focal plane. If the image is deformed, its Forier spectra are also subjected to change. Therefore the change of the Fourier spectra provides a particular beautiful insight into the deformation of that image. Through proposing the corresponding relationship between the image and its spectra, and analyzing the change of Fourier spectra, the deformation of the image can be obtained. Based on Fourier optical theory and S-R decomposition theorem of finite deformation, in this paper, a state of the art deformation measurement technique is presented by using laser spectral analysis. The theoretical foundation of this new technique related to mathematics and optics, experimental principle and the technique of automatic recognizing and processing of the deformed spectral image is discussed. The paper is as a special commemoration and memorial to the death anniversary of Professor Chen Zhida(1927～1998),who initially proposed the above academic idea in early 80s.

Variational Principles of Asymmetric Elasticity Theory of Finite Deformation

Song Yanqi, Chen Zhida

1999, 20(11): 1115-1120.

Abstract(2724) PDF(758)

Abstract:
In this paper, based on the finite deformation S-R decomposition theorem, the definition of the body moment is renewed as the sum of its internal and external. The expression of the increment rate of the deformation energy is derived and the physical meaning is clarified. The power variational principle and the complementary power variational principle for finite deformation mechanics are supplemented and perfected.

Effective Stress Laws for Multi-Porosity Media

Chen Mian, Chen Zhida

1999, 20(11): 1121-1127.

Abstract(2072) PDF(831)

Abstract:
In this paper, the effective stress for multi-porosity elasticity model is presented by means of stress analysis for double porosity media elements. It is found that the effective stress law is not unique, it depends on the hypothesis of constitutive equations for multi-porosity media. Diversified effective stress laws for multi-porosity are developed.

The Non-Linear Chaotic Model Reconstruction for the Exerimental Data Obtained From Different Dynamic System

Ma Junhai, Chen Yushu, Liu Zengrong

1999, 20(11): 1128-1134.

Abstract(2693) PDF(776)

Abstract:
The non-linear chaotic model reconstruction is the major important quantitative index for describing accurate experimental data obtained in dynamic analysis. A lot of work has been done to distinguish chaos from randomness, to calulate fractral dimension and Lyapunov exponent, to reconstruct the state space and to fix the rank of model. In this paper, a new improved EAR method is presented in modelling and predicting chaotic timeseries, and a successful approach to fast estimation algorithms is proposed. Some illustrative experimental data examples from known chaotic systems are presented, emphasising the increase in predicting error with time. The calculating results tell us that the parameter identification method in this paper can effectively adjust the initial value towards the global limit value of the single peak target function nearby. Then the model paremeter can immediately be obtained by using the improved optimization method rapidly, and non-linear chaotic models can not provide long period superior predictions. Applications of this method are listed to real data from widely different areas.

Inverse Problem for the Viscoelastic Medium with Discontinuous Wave Impedance

Chen Xianyao, Cheng Changjun

1999, 20(11): 1135-1142.

Abstract(2320) PDF(561)

Abstract:
In this paper, the inverse problem for the viscoelastic medium is investigated in the time domain, in which the wave impedance of the medium is discontinuous at the rear interface. The differentio-integral equations governing the behavior of the scattering and propagation operators are utilized to reconstruct the relaxation modulus of the viscoelastic medium. A new approach, in which only the one-side measurement reflection data for one round trip through the viscoelastic layer, is developed. The numerical examples are given at the end of the paper. It is shown that the curves of the reconstructed moduli coincide very well with the original relaxation moduli.

A Generalization of Recursion Operators of Differential Equations

Chen Yufu, Zhang Hongqing

1999, 20(11): 1143-1148.

Abstract(2509) PDF(689)

Abstract:
Most important recursion operators of differential equations are integro-differential operators. One often runs into difficulties in trying to obtain a full hierarchy of symmetries. The lack of precision sometimes leads to bogus symmetries. In this paper, a generalization of recursion operators is given, which eliminates the problem. Several examples are also given to demonstrate the generalization and the significance of the generalization is shown simultaneously.

Computational Intellectual Analytical Theory of Computational Analytical Approach to Rotating Flow of Non-Newtonian Fluid

Han Shifang

1999, 20(11): 1149-1160.

Abstract(2914) PDF(792)

Abstract:
A combination of the computational symbolic calculation, mathematical approach and physico-mechanical model leads to a computational intellectual analytical approach developed by the author. There is a principal difference between the computer proof and the computer derivation completed by the computer,also difference between the numerical and symbolic calculations. In this investigation the computational analytical approach is extended,and an unsteady flow of non-Newtonian fluid in the gap between two rotating coaxial cylinders is studied. The Oldroyd fluid B model is used by which the Weissenberg effects are explained in a good comparison with the experiments. The governing equations are reduced to a partial differential equation of 3rd order for the dimensionless velocity. Using the computer software Macsyma and an improved variational approach the problem with the initial and boundary conditions is then reduced to a problem of an ordinary differential equation for different approximations. The analytical solutions are given for the 1st, 2nd and 3rd approximations. The present investigation shows the ability of the computational symbolic manipulation in solving the problems of non-Newtonian fluid flows. There is a possibility of that to solve the problems in mathematics and mechanics. An important conclusion can be drawn from the results that the transition from a steady state to another steady state is non-unique.

Qualitative Analysis for the Solution of Kuramoto-Sivashinsky Equation

Jiang Chengshun, Gu Haiming

1999, 20(11): 1161-1167.

Abstract(2838) PDF(819)

Abstract:
In this paper, two kinds of initial boundary value problems for Kuramoto-Sivashinsky equation are considered. Some prior estimates are derived by Galerkin methods. The existence, uniqueness and regularities of the generalized global solutions and the classical global solutions for the equation are proved. Morever, the asymptotic behavior of these solutions are considered under some conditions.

A Solving Method for a System of Partial Differential Equations With an Application to the Bending Problem of a Thick Plate

Yin Yihui, Chen Gang, Chen Yuze

1999, 20(11): 1168-1174.

Abstract(2244) PDF(615)

Abstract:
A theorem of solving a system of linear non-homogeneous differential equations through integrating and adding its basic solutions is put forward and proved,the mathematical role and physical nature of the theorem is interpreted briefly. As an example,the theorem is applied to solve the problem of thermo-force bending of a thick plate.

Algebraic Structures and Poisson Integrals of Relativistic Dynamical Equations for Rotational Systems

Fu Jingli, Chen Xiangwei, Luo Shaokai

1999, 20(11): 1175-1182.

Abstract(2779) PDF(802)

Abstract:
The algebraic structures of the dynamical equations for the rotational relativistic systems are studied. It is found that the dynamical equations of holonomic conservative rotational relativistic systems and the special nonholonomic rotational relativistic systems have Lie's algebraic structure, and the dynamical equations of the general holonomic rotational relativistic systems and the general nonholonomic rotational relativistic systems have Lie admitted algebraic structure. At last the Poisson integrals of the dynamical equations for the rotational relativistic systems are given.

Configuration From Truth Vector to XOR Function

Hong Qinghua

1999, 20(11): 1183-1186.

Abstract(2279) PDF(699)

Abstract:
Kamaugh maps are widely used in the logic synthesis. However, the number of the variable it can deal with is limited. In this paper, two kinds of function shrinking techniques are proposed, and a fast algorithm to configure a truth vector into a XOR function is realized. There is no variable number limitation for this algorithm.

On the Repeated Natural Frequencies for Torsional Vibration of Shafts

Chen Kuifu, Jiao Qunying

1999, 20(11): 1187-1192.

Abstract(2045) PDF(537)

Abstract:
To investigate the repeated frequency condition (RFC) for torsional vibration of shafts' system, the transfer matrix method was adopted. Firstly, the transfer relationship from the boundary to engaging disks of double shafts' system(DSS) was constructed. Secondly, the RFC of DSS was deduced out and the methods to select mode shape were presented. Finally, the relationship was extended to multilevel transmission system (MTS), and the RFC of this system was explored. The conclusions is this:1) the necessary RFC requires the existence of joint engaging couple (JEC);2) for DSS, the sufficient is the number of boundary transfer factors (f_B) larger than 2;3) the whole system can be split into independent groups, the total multiplicity is the sum of independent solution number of every group, the latter is the number of independent f_B=0 inside the group minus 1.

New Points of View on the Nonlocal Field Theory and Their Applications to the Fracture Mechanics(Ⅲ)——Re-Discuss the Linear Theory of Nonlocal Elasticity

Huang Zaixing

1999, 20(11): 1193-1197.

Abstract(2856) PDF(949)

Abstract:
In this paper, it is proven that the balance equation of energy is the first integral of the balance equation of momentum in the linear theory of nonlocal elasticity. In other words, the balance equation of energy is not an independent one. It is also proven that the residual of nonlocal body force identically equals zero. This makes the transform formula of the nonlocal residual of energy much simpler. The linear nonlocal constitutive equations of elastic bodies are deduced in details, and a new formula to calculate the antisymmetric stress is given.

Quasi-Weak Convergence with Applications in Ordered Banach Space

Yang Guangchong

1999, 20(11): 1198-1202.

Abstract(2800) PDF(729)

Abstract:
In the paper quasi-weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of continuity and compactness in the sense of norm and weak compactness and is applied to the Hammerstein nonlinear intergal equation.

Generalized Diagonalization of Matrices Over Quaternion Field

Jiang Tongsong, Chen Li

1999, 20(11): 1203-1210.

Abstract(2969) PDF(730)

Abstract:
A concept of diagonalization matrix over quaternion field is given, the necessary and sufficient conditions for determining whether a quaternion matrix is a diagonalization one are discussed, and a method of diagonalization of matrices over quaternion field is given.

1999 Vol. 20, No. 11