应用数学和力学

Two-Mode Galerkin Approach in Dynamic Stability Analysis of Viscoelastic Plates

ZHANG Neng-hui, CHENG Chang-jun

2003, 24(3): 221-228.

Abstract(2713) PDF(674)

Abstract:
The dynamic stability of viscoelastic thin plates with large deflections was investigated by using the largest Liapunov exponent analysis and other mumerical and analytical dynamic methods.The material behavior was described in terms of the Boltzmann superposition principle.The Galerkin method was used to simplify the original integro-partial-differential model into a two-mode approximate integral model, which further reduced to an ordinary differential model by introducing new variables.The dynamic properties of one-mode and two-mode truncated systems were numerically compared.The influence of viscoelastic properties of the material, the loading amplitude and the initial values on the dynamic behavior of the plate under in-plane periodic excitations was discussed.

Applications of Fractional Exterior Differential in Three-Dimensional Space

CHEN Yong, YAN Zhen-ya, ZHANG Hong-qing

2003, 24(3): 229-233.

Abstract(2246) PDF(806)

Abstract:
A brief survey of fractional calculus and fractional differential forms was firstly given.The fractional exterior transition to curvilinear coordinate at the origin were discussed and the two coordinate transformations for the fractional differentials for three-dimensional Cartesian coordinates to spherical and cylindrical coordinates are obtained, respectively.In particular, for v=m=1, the usual exterior transformations, between the spherical coordinate and Cartesian coordinate, as well as the cylindrical coordinate and Cartesian coordinate, are found respectively, from fractional exterior transformation.

Coexisting Periodic Orbits in Vibro-Impacting Dynamical Systems

LI Qun-hong, LU Qi-shao

2003, 24(3): 234-244.

Abstract(2303) PDF(625)

Abstract:
Abstract: A method is presented to seek for coexisting periodic orbits which may be stable or unstable in piecewise-linear vibro-impacting systems.The conditions for coexistence of single impact periodic orbits are derived, and in particular, it is investigated in details how to assure that no other impacts will happen in an evolution period of a single impact periodic motion.Furthermore, some criteria for nonexistence of single impact periodic orbits with specific periods are also established.Finally, the stability of coexisting periodic orbits is discussed, and the corresponding computation formula is given.Examples of numerical simulation are in good agreement with the theoretic analysis.

The Effect of Magnetic Fields on Low Frequency Oscillating Natural Convection With Pressure Gradient

G. C. Sharma, Madhu Jain, Mahesh Chandra

2003, 24(3): 245-252.

Abstract(2219) PDF(599)

Abstract:
The oscillating natural convection in the presence of transverse magnetic field with time depending pressure gradient is studied.The analysis of the problem is carried out by assuming that the fluid is flowing in a parallel plate configuration.The emphasis is on low frequency oscillating convective flows induced by g-jitter associated with micro gravity because of their importance to the space processing materials.A general solution for an oscillating flow in the presence of transverse magnetic field is carried out.Some special cases of the oscillating flow and its response to an applied magnetic field are performed.It was observed that the behavior of oscillating free convective flows depends on frequency, amplitude of the driving buoyancy forces, temperature gradient, magnetic field and the electric conditions of the channel walls.In the absence of magnetic field, buoyancy force plays a predominant role in driving the oscillatory flow pattern, and velocity magnitude is also affected by temperature gradients.To suppress the oscillating flow external magnetic field can be used.It is also found that the reduction of the velocity is inversely proportional to the square of the applied magnetic field with conducting wall but directly proportional to the inverse of the magnetic field with insulating wall.Detailed calculations and computational results are also carried out to depict the real situation.

Bifurcation Analysis of a Mitotic Model of Frog Eggs

Lü Jin-hu, ZHANG Zi-fan, ZHANG Suo-chun

2003, 24(3): 253-266.

Abstract(2765) PDF(615)

Abstract:
The mitotic model of frog eggs established by Borisuk and Tyson is qualitatively analyzed.The existence and stability of its steady states are further discussed.Furthermore, the bifurcation of above model is further investigated by using theoretical analysis and numerical simulations.At the same time, the numerical results of Tyson are verified by theoretical analysis.

Poisson Limit Theorem for Countable Markov Chains in Markovian Environments

FANG Da-fan, WANG Han-xing, TANG Mao-ning

2003, 24(3): 267-274.

Abstract(2495) PDF(749)

Abstract:
A countable Markov chain in a Markovian environment is considered.A Poisson limit theorem for the chain recurring to small cylindrical sets is mainly achieved.In order to prove this theorem,the entropy function h is introduced and the Shannon-McMillan-Breiman theorem for the Markov chain in a Markovian environment is shown.It.s well known that a Markov process in a Markovian environment is generally not a standard Markov chain, so an example of Poisson approximation for a process which is not a Markov process is given.On the other hand, when the environmental process degenerates to a constant sequence, a Poisson limit theorem for countable Markov chains, which is the generalization of Pitskel.s result for finite Markov chains is obtained.

Determination of Creep Parameters from Indentation Creep Experiments

YUE Zhu-feng, WAN Jian-song, Lü Zhen-zhou

2003, 24(3): 275-281.

Abstract(2776) PDF(777)

Abstract:
The possibilities of determining creep parameters for a simple Norton law material are explored from indentation creep testing.Using creep finite element analysis the creep indentation test technique is analyzed in terms of indentation rates at constant loads.Emphasis is placed on the relationships between the steady creep behavior of indentation systems and the creep property of the indented materials.The role of indenter geometry, size effects and macroscopic constraints is explicitly considered on indentation creep experiments.The influence of macroscopic constraints from the material systems becomes important when the size of the indenter is of the same order of magnitude as the size of the testing material.Two methods have been presented to assess the creep property of the indented material from the indentation experimental results on the single-phase-material and two-phase-material systems.The results contribute to a better mechanical understanding and extending the application of indentation creep testing.

Analysis of Disturbances Rejection for Lur’e Systems

HAO Fei, CHU Tian-guang, HUANG Lin

2003, 24(3): 282-288.

Abstract(2195) PDF(627)

Abstract:
The analysis of disturbance rejection for singe-input singe-output(SISO) Lur'e system with norm uncertainty was concerned through invariant set analysis using Lyapunov function method.The conditions on robust ellipsoidal attractor for uncertain Lur'e systems were given in terms of LMIs(Linear Matrix Inequality), which simultaneously ensure the absolute stability and disturbance rejection of the uncertain Lur'e systems.An estimate of the maximum set included in a robust ellipsoidal attractor was also presented.Finally, a numerical example was worked out to illustrate the main results.

IMD Based Nonlinear Galerkin Method

HOU Yan-ren, LI Kai-tai

2003, 24(3): 289-299.

Abstract(2398) PDF(589)

Abstract:
By taking example of the 2D Navier-Stokes equations, a kind of improved version of the nonlinear galerkin method of Marion-Temam type based on the new concept of the inertial manifold with delay(IMD) is presented, which is focused on overcoming the defect that the feasibility of the M-T type nonlinear Galerkin method heavily depended on the least solving scale.It is shown that the improved version can greatly reduce the feasible conditions as well as preserve the superiority of the former version.Therefore, the version obtained here is an applicable, high performance and stable algorithm.

Procedure for Computing the Possibility and Fuzzy Probability of Failure of Structures

GUO Shu-xiang, Lü Zhen-zhou

2003, 24(3): 300-304.

Abstract(2497) PDF(841)

Abstract:
Traditionally, the calculation of reliability of fuzzy random structures is based on the wellknown formulation of probability of fuzzy events.But sometimes the results of this formulation willnot indicating the real state of safety of fuzzy-random structures.Based on the possibility theory, a computational procedure for the reliability analysis of fuzzy failure problems and random-fuzzy failure problems of mechanical structures that contain fuzzy variables were presented .A procedure for the analysis of structural reliability of problems of fuzzy failure criterion was also proposed.The failure possibility of fuzzy structures and possibility distribution of the probability of failure of fuzzy-random structures can be given by the proposed methods.It is shown that for the hybrid probabilistic and fuzzy reliability problems, the probability of failure should be suitably taken as a fuzzy variable in order to indicate the real safety of system objectively.Two examples illustrate the validity and rationality of the proposed methods.

On the Existence of Common Fixed Points for a Pair of Lipschitzian Mappings in Banach Spaces

ZENG Lu-chuan

2003, 24(3): 305-314.

Abstract(2132) PDF(653)

Abstract:
The existence of common fixed points for a pair of Lipschitzian mappings in Banach Spaces is proved.By using this result, some common fixed point theorems are established for these mappings in Hilbert spaces, in L^pspaces, in Hardy spaces H^p, and in Sobolev spaces H^r,p, for 1< p< +∞ and r≥0.

A Positve Interior-Point Algorithm for Nonlinear Complementarity Problems

MA Chang-feng, LIANG Guo-ping, CHEN Xin-mei

2003, 24(3): 315-322.

Abstract(2363) PDF(735)

Abstract:
Anew iterative method, which is called positive interior-point algorithm, is presented for solving the nonlinear complementarity problems.This method is of the desirable feature of robustness.And the convergence theorems of the algorithm is established.In addition, some numerical results are reported.

Method of Model Analysis for Flexible Head Impacting With Elastic Plane

ZHAO Gui-fan, TAN Hui-fneg, DU Xing-wen

2003, 24(3): 323-330.

Abstract(2187) PDF(696)

Abstract:
The process of head impacting with elastic plane was modeled as a response of vibrant system, and the method of mechanical network figure and mechanical impedance was used to resolve this problem.Based on its structure, head was viewed as a vibrant model, which concludes the masses of scalp and bone in the impact area, the masses in the other part of the head and the brain, the stiffness of the head, and the damper of the scalp and brain.Also the elastic plane was simplified as a vibrant model including mass, stiffness and damper.The models were transformed into mechanical girding figure at violent vibration poin.When the initial impact speed is known, the impact force of the system,the impact acceleration of the head, the elastic deformation of the plane and the fixed frequency of the system can be worked out by calculating the velocity impedance at the violent vibration point, the results fit the test data well, which proves that this method is available for the analysis of the dynamic response of the system under impact.

2003 Vol. 24, No. 3