应用数学和力学

2009 Vol. 30, No. 6

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Bifurcation of Piecewise-Linear Nonlinear Vibration System of Vehicle Suspension

ZHONG Shun, CHEN Yu-shu

2009, 30(6): 631-638. doi: 10.3879/j.issn.1000-0887.2009.06.001

Abstract(1711) PDF(909)

Abstract:
The kinetic model of piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring was established.The resonance solution's bifurcation of two-degree-of-freedom suspension system was investigated by means of singularity theory.The transition sets of the system and 40 groups of bifurcation diagrams were obtained.And the complicated local bifurcation was founded,which shows the bifurcation characteristic roundly.Furthermore,according to the relation between the parameters and the topological bifurcation solutions,the motion characteristic with different parameters was obtained.The results supply theoretical bases for optimal control of vehicle suspension system parameters.

Strong Convergence Theorem for a Generalized Equilibrium Problem and k-Strict Pseudocontraction in Hilbert Spaces

ZHANG Shi-sheng, RAO Ruo-feng, HUANG Jia-lin

2009, 30(6): 638-647. doi: 10.3879/j.issn.1000-0887.2009.06.002

Abstract(1417) PDF(823)

Abstract:
The main purpose is to introduce and study a new iterative algorithom for finding a common element of the set of solutions for a generalized equilibrium problem and the set of fixed points for a k-strict pseudocontractive mapping in Hilbert space.The results presented extend and improve the corresponding results announced by many others.

Minimizing Sequence of Variational Problems With Small Parameters

NI Ming-kang, LIN Wu-zhong

2009, 30(6): 648-654. doi: 10.3879/j.issn.1000-0887.2009.06.003

Abstract(1365) PDF(948)

Abstract:
A class of variational problems with small parameters had been studied.A zeroth order asymptotic solution of which was constructed.It was proved that the zeroth-order asymptotic solution is the minimizing sequence of variational problems when the small parameter approaches to zero.

Inversion of Dispersion Coefficient in Water Quality Model Using Optimal Perturbation Algorithm

NIE Hong-tao, TAO Jian-hua

2009, 30(6): 655-662. doi: 10.3879/j.issn.1000-0887.2009.06.004

Abstract(1522) PDF(838)

Abstract:
As one of the primary parameters in the water quality model for shallow bay,the dispersion coefficient is traditionally determined by trial and error method with time consuming and more experience.Based on the measured data of chemical oxygen demand (COD),the dispersion coefficient was calculated using inversion method.In this process,the regularization method was applied to treat the ill-posedness,and the operator identification perturbation method was used to obtain the solution.By running the model with the inverted dispersion coefficient,the distribution of COD,inorganic nitrogen (IN) and inorganic phosphorus (IP) in Bohai bay were predicted respectively and compared with the measured data.The results indicate that this method is feasible and the inverted dispersion coefficient can be used to predict other pollutant distribution.Moreover,this method may also be further extended to the inversion of other parameters in water quality model.

Direct Proof of the Uniqueness of the Square-Root of a Positive Semi-Definite Tensor

SHAO Yue, LÜ Cun-jing

2009, 30(6): 663-666. doi: 10.3879/j.issn.1000-0887.2009.06.005

Abstract(1871) PDF(793)

Abstract:
Understanding the basic properties of the positive semi-definite tensor is prerequisite for its wide application in theoretical and practical field,especially for its square-root.The uniqueness of the square-root of a positive semi-definite tensor was proven without resorting to the notion of eigenvalues,eigenvectors and the spectral decomposition of the second-order symmetric tensor.

Natural Frequencies of Composite Beams Having Variable Fiber Volume Fraction Including Rotary Inertia and Shear Deformation

Y. Bedjilili, A. Tounsi, H. M. Berrabah, I. Mechab, E. A. Adda Bedia, S. Benaissa

2009, 30(6): 667-676. doi: 10.3879/j.issn.1000-0887.2009.06.006

Abstract(1571) PDF(822)

Abstract:
The vibration analysis of symmetrically composite beams having a variable fiber volume fraction through the thickness was concerned with.First-order shear deformation and rotary inertia were included in the analysis.The solution procedure is applicable to arbitrary boundary conditions.Continuous gradation of the fiber volume fraction is modelled in the form of an mthpower polynomial of the coordinate axis in thickness direction of the beam.By varying the fiber volume fraction within the symmetric composite beam to create a functionally graded material (FGM),certain vibration characteristics can be affected.Results have been presented to demonstrate the effect of shear deformation,fiber volume fraction and boundary conditions on the natural frequencies and mode shapes of composite beams.

Global Existence of Weak Solutions to a Prey-Predator Model With Strong Cross-Diffusion

LI Hui-ling

2009, 30(6): 677-689. doi: 10.3879/j.issn.1000-0887.2009.06.007

Abstract(1389) PDF(913)

Abstract:
By using finite differences and entropy inequalities,the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained.Furthermore,the non-negativity of such solution is also given.

A Mixed Newton-Tikhonov Method for Nonlinear Ⅲ-Posed Problems

KANG Chuan-gang, HE Guo-qiang

2009, 30(6): 690-700. doi: 10.3879/j.issn.1000-0887.2009.06.008

Abstract(2233) PDF(908)

Abstract:
Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems and attract extensive attention of people.However,the computational cost of Newton type methods may be very large because of the complexity of practical problems.A mixed NewtonTikhonov method,i.e.,one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method was proposed.The convergence and stability of this method were proved under some conditions.Numerical experiments show that the new method has obvious improvement over the classical Newton method in the reduction of the computational cost.

Parametric Resonances of Convection Belts System Analysis

YANG Zhi-an, LI Gao-feng

2009, 30(6): 701-712. doi: 10.3879/j.issn.1000-0887.2009.06.009

Abstract(1451) PDF(825)

Abstract:
Based on Coriolis acceleration and Lagrangian strain formula,the transverse vibration sys-tem of convection belts equation generalized was derived by Newton.s second law .The method of multiple scales was applied directly to the governing equations,and approximate solution of primary parameter resonance of the system was obtained.The detuning parameter,cros-s section area,elastic and viscoelastic parameters,and an axial moving speed have a significant effect on the amplitudes of steady-state response and their existence boundaries.Some new dynamical phenomena were re-vealed.

Derivation of a Segregation-Mixing Equation for Particles in a Fluid Medium

Donald O. Besong

2009, 30(6): 713-718. doi: 10.3879/j.issn.1000-0887.2009.06.010

Abstract(1157) PDF(664)

Abstract:
The main purpose is to show that the gravity term of the segregation-mixing equation of fine mono-disperse particles in a fluid can be derived from elementary physics(i.e.first principles).The derivation of the gravity-driven flux of particles leads to the simplest case of the Richaidson and Zald correlation.Stokes velocity also naturally appears from the physical parameters of the particles and fluid by means of derivation only,for the first time.This derivation fmm first principle physics has never been presented before.It is applicable in small concentrations of fine particles

Nonlinear Dynamic Behaviors of Viscoelastic Shallow Arches

YI Zhuang-peng, WANG Lian-hua, ZHAO Yue-yu

2009, 30(6): 719-724. doi: 10.3879/j.issn.1000-0887.2009.06.011

Abstract(1459) PDF(793)

Abstract:
The nonlinear dynamic of nonlinear viscoelastic shallow arches subjected to the external excitation is investigated.Based on the d.Alembert principle and the Euler-Bernoulli assumption,the governing equation of shallow arch was obtained,where the Leaderman constitutive relation was applied.The Galerkin method and numerical integration were used to study the nonlinear dynamic properties of the viscoelastic shallow arches.Moreover,the effects of the rise,the material parameter and excitation on the nonlinear dynamic of shallow arch were investigated.The results show that viscoelastic shallow arches may have chaotic motion for certain condition.

Numerical Study of Attack Angle Characteristics for Integrated Hypersonic Vehicle

HUANG Wei, WANG Zhen-guo

2009, 30(6): 725-732. doi: 10.3879/j.issn.1000-0887.2009.06.012

Abstract(1561) PDF(701)

Abstract:
Two dimension coupled implicit NS equations and standard k epsilon viscous models were used to simulate the angle of attack characteristics of integrated hypersonic vehicle with hark head configuration under three kinds of working conditions,i.e.inlet cut off,engine through flow,engine ignition.The influence of each component on the aero propulsive performance of vehicle was dis cussed.It is concluded that the longitudinal static stability of vehicle is good;it has enough lift to drag ratio to satisfy the flying requirement of the vehicle.At the same time,it is very important to change the configurations of engine and upper surface of airframe to improve the aero propulsion of the vehicle.

Local and Parallel Finite Element Algorithms for the Time-Dependent Convection-Diffusion Equations

LIU Qing-fang, HOU Yan-ren

2009, 30(6): 733-740. doi: 10.3879/j.issn.1000-0887.2009.06.013

Abstract(1510) PDF(784)

Abstract:
Local and parallel finite element algorithms based on two-grid discretization for the timedependent convection-diffusion equations are presented.These algorithms are motivated by the observation that for a solution to the convection-diffusion problems,low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedure.Hence,these local and parallel algorithms only involve one small original problem on coarse mesh and some correction problems on local fine grid.One technical tool for the analysis is some local a priori estimates that are also obtained.Finally,some numerical examples are given to support our theoretical analysis.

Markov Chain-Based Stability Analysis of a Modified Cooper-Frieze Model

TONG Jin-ying, HOU Zhen-ting, SHI Ding-hua

2009, 30(6): 741-749. doi: 10.3879/j.issn.1000-0887.2009.06.014

Abstract(1098) PDF(693)

Abstract:
From the perspective of probability,the stability of a modified Cooper-Frieze model is studied.Based on the concept and technique of first-passage probability in Markov theory,a rigorous proof for existence of the steady-state degree distribution was provided,moreover the explicit formula was derived analytically.Finally,extensive numerical simulations of the model,including the degree distribution and the clustering were performed.

Lag Synchronization for Fuzzy Chaotic System Based on Fuzzy Observer

TANG Lin-jun, LI Dong, WANG Han-xing

2009, 30(6): 750-756. doi: 10.3879/j.issn.1000-0887.2009.06.015

Abstract(1445) PDF(701)

Abstract:
A new fuzzy observer for lag synchronization was given.By investigating synchronization of chaotic systems,the structure of drive response lag synchronization for fuzzy chaos system based on fuzzy observer was proposed,and a new lag synchronization criterion was derived by Liapunov sta bility theorem,in which control gains are obtained by LMI condition.The proposed approach is applied to well known Chens systems.And simulation example is presented to illustrate its effectiveness.