应用数学和力学

1999 Vol. 20, No. 10

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Ma Zheng, Zhou Zhewei

1999, 20(10): 991-996.

Abstract(2237) PDF(593)

Abstract:
The instability theory of fluid flow is applied in gas atomization and the results show that the instability of interfacial wave is the main cause of gas atomization. The size of the droplets and its change with parameters are also studied, the results are compatible with the experiments.

On the Maximal Lyapunov Exponent for a Real Noise Parametrically Excited Co-Dimension Two Bifurcation System(Ⅱ)

Liu Xianbin, Chen Qiu, Chen Dapeng

1999, 20(10): 997-1003.

Abstract(2332) PDF(629)

Abstract:
Foraco-dimension two bifurcation system on a three-dimensional central manifold, which is parametrically excited by a real noise, a rather general model is obtained by assuming that the real noise is an output of a linear filter system-a zeromean stationary Gaussian diffusion process which satisfies detailed balance condition. By means of the asymptotic analysis approach given by L. Arnold and the expression of the eigenvalue spectrum of Fokker-Planck operator, the asymptotic expansions of invariant measure and maximal Lyapunov exponent for the relevant system are obtained.

Vibration and Damping Analysis of a Composite Plate With Active and Passive Damping Layer

Gao Jianxin, Shen Yapeng

1999, 20(10): 1004-1014.

Abstract(2390) PDF(606)

Abstract:
The equations of motion and boundary conditions governing the vibration of nonsymmetric composite plates with active and passive dampings layer are derived. The analytical solution is first obtained for frequencies and loss factors of the plates with active constrained layer damping treatments. The distributions of electric potential across the thickness of piezoelectric layer and relevant governing equations are obtained when the direct and inverse piezoelectric effects are considered. The influence of the direct and inverse piezoelectric effects on the frequencies and loss factors are investigated.

On a Class of Generalized Nonlinear Implicit Quasivariational Inclusions

Ding Xieping

1999, 20(10): 1015-1024.

Abstract(2405) PDF(963)

Abstract:
In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set-valued maximal monotone mapping are studied. A existence theorem of solutions for this class of generalized nonlinear implicit quasivariational inclusions is proved without compactness assumptions. A new iterative algorithm for finding approximate solutions of the generalized nonlinear implicit quasivariational inclusions is suggested and analysed and the convergence of iterative sequence generated by the new algorithm is also given. As special cases, some known results in this field are also discussed.

Investigation of a Griffith Crack Subject to Uniform Tension Using the Non-Local Theory by a New Method

Zhou Zhengong, Wang Biao

1999, 20(10): 1025-1032.

Abstract(2330) PDF(546)

Abstract:
Field equations of the non-local elasticity are solved to determine the state of stress in a plate with a Griffith crack subject to uniform tension. Then a set of dual-integral equations is solved using a new method, namely Schmidt's method. This method is more exact and more reasonable than Eringen's one for solving this kind of problem. Contrary to the solution of classical elasticity, it is found that no stress singularity is present at the crack tip. The significance of this result is that the fracture criteria are unified at both the macroscopic and the microscopic scales. The finite hoop stress at the crack tip depends on the crack length.

The Influence of Imperfections Upon the Critical Load of Structures

Zhu Zhengyou, Cong Yuhao

1999, 20(10): 1033-1039.

Abstract(2521) PDF(596)

Abstract:
By means of the theory of universal unfolding, the influence of multi-imperfections upon the critical load of structure in engineering is analysed in this paper. For the pitchfork problem, a lower bound of increments of the critical loads caused by imperfections of the structures is given. A simple and available numerical method for computing the lower bound is described.

On the Existence and Stability of Periodic Solutions for Hopfield Neural Network Equations With Delay

Huang Xiankai

1999, 20(10): 1040-1044.

Abstract(2042) PDF(704)

Abstract:
Sufficient conditions are obtained for the existence, uniqueness and stability of T _periodic solutions for the Hopfield neural network equations with delay .

Global Composite Element Iteration to Solve Seepage Free Surface

Chen Hongkai, Tang Hongmei, Xiao Shengxie

1999, 20(10): 1045-1050.

Abstract(1868) PDF(585)

Abstract:
As one of the most difficult topics of rock mass hydromechanics, seepage free surfece plays an important part in slope stability researches. Based on analysis of numerical methods to solve seepage free surface, global composite element iteration (GCEI) is presented in this paper. FEM program is made by using GCEI. Much calculating verifies that not only the program is simpler using GCEI, also the tolerance is higher after 5 iterations.

Boundary Integral Equations of Unique Solutions in Elasticity

Zhou Shenjie, Cao Zhiyuan, Sun Shuxun

1999, 20(10): 1051-1056.

Abstract(2500) PDF(688)

Abstract:
The properties of the fundamental solution are derived in linear elastostatics. These properties are used to show that the conventional displacement and traction boundary integral equations yield non-unique displacement solutions in a traction boundary value problem. The condition for the existence of unique displacement solutions is proposed for the traction boundary value problem. The degrees of freedom of the displacement solution are removed by the condition to obtain the boundary integral equations of unique solutions for the traction boundary value problems. Numerical example is presented to demonstrate the accuracy and efficiency of the present equations.

Elastic Modulus of Human Cementum

Ye Delin, Ni Haiying, Gong Yikang, Chen Xing

1999, 20(10): 1057-1064.

Abstract(3607) PDF(701)

Abstract:
In this paper, the elastic modulus measuring of human cementum is studied. The average value of the elastic modulus measured from 100 specimens is E=2.398±0.455 GPa. The specimens were made from incisors, canines, bicuspids, and molars. The testing was done on type AG——10TA electronic-mechanical universal material testing machine. It was verified by mathematical statistics that the probability distribution of measured data obeys normal distribution. By the great difference in elastic moduli between cementum and dentin it is explained that 1. why more cementum grows at the root apexes; 2.the behavior of cementum must be taken into consideration when the stress analysis for teeth is carried out.

Dynamic Thermal Shock in a Layered Cylinder With Initial Interface Pressure

Wang Xi

1999, 20(10): 1065-1071.

Abstract(2257) PDF(675)

Abstract:
An analytical method is developed to determine the transient response of dynamic thermostress in a two-layered cylinder with initial interface pressure. At first, the initial interface pressure in a two-layered cylinder caused by a heat-assembling method is considered as the initial condition of a thermal elastodynamic equilibrium equation. Thus, a thermal elastodynamic solution for a separate hollow cylinder with the initial stress field is found out by means of a series of simply mathematical transform. By making use of the boundary conditions and continuity conditions of a layered cylinders, the solution for the thermal shock exerting an influence on the initial interface pressure in a twolayered cylinder is also discussed.

Water Surface Wave Radiation Generated by Multiple Cylinders Oscillating With Identical Frequency

He Wuzhou

1999, 20(10): 1072-1080.

Abstract(2330) PDF(601)

Abstract:
The water surface wave radiation problem caused by multiple cylinders oscillating with identical frequency was solved in frequency domain by the boundary element method using simple Green's function in the inner water region combined with the eigenfunction expansions in the outer water region. The numerical method is suitable to the situation of constant depth of outer regions and complicated boundary conditions of inner region, while the oscillating modes, motion amplitudes and phases of the cylinders may be different from one another. The second order potential and hydrodynamic forces acting on ecah cylinder were evaluated completely by perturbation method. Compared with the case of single oscillating cylinder, hydrodynamic interference phenomena, such as wave resonance and negative added mass, of the radiation problem due to the oscillatory motions of multiple cylinders are identified which is of engineering importance to the design of moorings and other facilities involving multiple structures.

On Probabilistic Norm of a Linear Operators and Space of Operators

Fang Jinxuan

1999, 20(10): 1081-1086.

Abstract(2063) PDF(670)

Abstract:
Since the PN space (E, F) which satisfies condition (PN-5) is just a Menger PN-space (E, F, min), the results with regard to probabilistic norms of linear operators on PN-spaces obtained by Xiao Jianzhong have bigger limitations. In this paper, problems respecting pr obabilistic norms of linear operators and spaces of operators are studied on more general Menger PN spaces. The results presente dimprove and generalize the corresponding results by Xiao.

Modeling and Analysis of a Coupled Rigid- Flexible System

Hu Zhendong, Hong Jiazhen

1999, 20(10): 1087-1093.

Abstract(2969) PDF(809)

Abstract:
Correct predictions of the behavior of flexible bodies undergoing large rigid-body motions and small elastic vibrations is a subject of major concern in the field of flexible multibody system dynamics. Because of failing to account for the effects of dynamic stiffening, conventional methods based on the linear theories can lead to erroneous results in many practical applications. In this paper, the idea of "centrifugal potential field", which induced by large overall rotation is introduced, and the motion equation of a coupled rigid-flexible system by employing Hamilton's principle is established. Based on this equation, first it is proved that the elastic motion of the system has periodic property, then by using Frobenius. method its exact solution is obtained. The influences of large overall rigid motion on the elastic vibration mode shape and frequency are analysed through the numerical examples.

Chaotic Ocillation of a Nonlinear Power System

Zhang Weinian, Zhang Weidong

1999, 20(10): 1094-1100.

Abstract(2414) PDF(924)

Abstract:
For a nonlinear power transmission system, the residue calculus method is introduced and applied to study its heteroclinic bifurcation. There a cone region and a strip region of parameters are obtained in which the power transmission system displays chaotic ocillation. This gives a theoretic analysis and a computational method for the purpose to control the nonlinear system with deviation stably running.