Applied Mathematics and Mechanics (English Edition)

Bifurcation of piecewise-linear nonlinear vibration system of vehicle suspension

钟顺陈予恕

2009, 30(6): 677-684. doi:10.1007/s10483-009-0601-z

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A kinetic model of the piecewise-linear nonlinear suspension system that consists of a dominant spring and an assistant spring is established. Bifurcation of the resonance solution to a suspension system with two degrees of freedom is investigated with the singularity theory. Transition sets of the system and 40 groups of bifurcation diagrams are obtained. The local bifurcation is found, and shows the overall characteristics of bifurcation. Based on the relationship between parameters and the topological bifurcation solutions, motion characteristics with different parameters are obtained. The results provides a theoretical basis for the optimal control of vehicle suspension system parameters.

Strong convergence theorem for a generalized equilibrium problem and a k-strict pseudocontraction in Hilbert spaces

张石生饶若峰黄家琳

2009, 30(6): 685-694. doi:10.1007/s10483-009-0602-z

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The main purpose of this paper is to study a new iterative algorithm 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 the Hilbert space. The presented results extend and improve the corresponding results reported in the literature.

Minimizing sequences of variational problems with small parameters

倪明康林武忠

2009, 30(6): 695-701. doi:10.1007/s10483-009-0603-z

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A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of variational problems as the small parameter approaches to zero.

Inversion of dispersion coefficient in water quality model using optimal perturbation algorithm

聂红涛陶建华

2009, 30(6): 703-712. doi:10.1007/s10483-009-0604-x

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As a primary parameter in the water quality model for shallow bays, the dispersion coefficient is traditionally determined with a trial-and-error method, which is time-consuming and requires much experience. In this paper, based on the measured data of chemical oxygen demand (COD), the dispersion coefficient is calculated using an inversion method. In the process, the regularization method is applied to treat the ill-posedness, and an operator identity perturbation method is used to obtain the solution. Using the model with an inverted dispersion coefficient, the distributions of COD, inorganic nitrogen (IN), and inorganic phosphorus (IP) in Bohai Bay are predicted and compared with the measured data. The results indicate that the method is feasible and the inverted dispersion coefficient can be used to predict other pollutant distribution. This method may also be further extended to the inversion of other parameters in the water quality model.

A direct proof of uniqueness of square-root of a positive semi-definite tensor

邵玥吕存景

2009, 30(6): 713-716. doi:10.1007/s10483-009-0605-1

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Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without resorting to the notion of eigenvalues, eigenvectors and the spectral decomposition of the second-order symmetric tensor.

Natural frequencies of composite beams with a 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): 717-726. doi:10.1007/s10483-009-0606-z

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The present study is concerned with the vibration analysis of symmetric composite beams with a variable fiber volume fraction through thickness. First-order shear deformation and rotary inertia have been included in the analysis. The solution procedure is applicable to arbitrary boundary conditions. Continuous gradation of the fiber volume fraction is modeled in the form of an m-th power polynomial of the coordinate axis in the 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 are affected. Results are presented to demonstrate the effects 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

李慧玲

2009, 30(6): 727-740. doi:10.1007/s10483-009-0607-x

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Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown.

A mixed Newton-Tikhonov method for nonlinear ill-posed problems

康传刚贺国强

2009, 30(6): 741-752. doi:10.1007/s10483-009-0608-2

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Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems, which have attracted extensive attention. However, computational cost of Newton type methods is high because practical problems are complicated. We propose a mixed Newton-Tikhonov method, i.e., one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method. Convergence and stability of this method are proved under some conditions. Numerical experiments show that the proposed method has obvious advantages over the classical Newton method in terms of computational costs.

Parametric resonances of convection belt system

杨志安李高峰

2009, 30(6): 753-764. doi:10.1007/s10483-009-0609-y

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Based on the Coriolis acceleration and the Lagrangian strain formula, a generalized equation for the transverse vibration system of convection belts is derived using Newton’s second law. The method of multiple scales is directly applied to the governing equations, and an approximate solution of the primary parameter resonance of the system is obtained. The detuning parameter, cross-section area, elastic and viscoelastic parameters, and axial moving speed have a significant influences on the amplitudes of steady-state response and their existence boundaries. Some new dynamical phenomena are revealed.

Derivation of a segregation-mixing equation for particles in a fluid medium

Donald O.Besong

2009, 30(6): 765-770. doi:10.1007/s10483-009-0610-6

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

Nonlinear dynamic behaviors of viscoelastic shallow arches

易壮鹏王连华赵跃宇

2009, 30(6): 771-777. doi:10.1007/s10483-009-0611-y

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The nonlinear dynamic behaviors of nonlinear viscoelastic shallow arches subjected to external excitation are investigated. Based on the d’Alembert principle and the Euler-Bernoulli assumption, the governing equation of a shallow arch is obtained, where the Leaderman constitutive relation is applied. The Galerkin method and numerical integration are 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 behaviors of the shallow arch are investigated. The results show that viscoelastic shallow arches may appear to have a chaotic motion for certain conditions.

Numerical study of attack angle characteristics for integrated hypersonic vehicle

黄伟王振国

2009, 30(6): 779-786. doi:10.1007/s10483-009-0612-y

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The two-dimensional coupled implicit Navier-Stokes equations and standard k-ε viscous models are used to simulate the angle of attack characteristics of an integrated hypersonic vehicle with a hark head configuration under three kinds of working conditions: inlet cut-off, engine through-flow, and engine ignition. Influence of each component on aero-propulsive performance of the vehicle is discussed. It is concluded that the longitudinal static stability of the vehicle is good, and there is enough lift-to-drag ratio to satisfy the flying requirement of the vehicle. At the same time, it is important to change configurations of engine and upper surface of airframe to improve aero-propulsive performance of the vehicle.

Local and parallel finite element algorithms for time-dependent convection-diffusion equations

刘庆芳侯延仁

2009, 30(6): 787-794. doi:10.1007/s10483-009-0613-x

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Local and parallel finite element algorithms based on two-grid discretization for the time-dependent convection-diffusion equations are presented. These algorithms are motivated by the observation that, for a solution to the convection-diffusion problem, 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 procedures. Hence, these local and parallel algorithms only involve one small original problem on the coarse mesh and some correction problems on the local fine grid. One technical tool for the analysis is the local a priori estimates that are also obtained. Some numerical examples are given to support our theoretical analysis.

Markov chain-based analysis of a modified Cooper-Frieze model

童金英侯振挺史定华

2009, 30(6): 795-802. doi:10.1007/s10483-009-0614-6

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From the perspective of probability, the stability of a modified Cooper- Frieze model is studied in the present paper. Based on the concept and technique of the first-passage probability in the Markov theory, we provide a rigorous proof for the existence of the steady-state degree distribution, and derive the explicit formula analytically. Moreover, we perform extensive numerical simulations of the model, including the degree distribution and the clustering.

Lag synchronization for fuzzy chaotic system based on fuzzy observer

唐林俊李东王汉兴

2009, 30(6): 803-810. doi:10.1007/s10483-009-0615-y

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A new fuzzy observer for lag synchronization is given in this paper. By investigating synchronization of chaotic systems, the structure of drive-response lag synchronization for fuzzy chaos system based on fuzzy observer is proposed. A new lag synchronization criterion is derived using the Lyapunov stability theorem, in which control gains are obtained under the LMI condition. The proposed approach is applied to the well-known Chen’s systems. A simulation example is presented to illustrate its effectiveness.

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