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2009年 第30卷 第9期    刊出日期：2009-09-01

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Articles

Free axisymmetric vibration of FGM circular plates

王云 徐荣桥 丁浩江

2009, 30(9):  1077-1082.  doi:10.1007/s10483-009-0901-x

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Based on the three-dimensional theory, this work presents a direct displacement method to investigate the free axisymmetric vibration of transversely isotropic circular plates, whose material is functionally graded and properties obey the exponential law along the thickness direction of the plate. Under two boundary conditions, the solution satisfies all basic equations and the corresponding boundary condition at every point. Thus, it is three-dimensional exact. Numerical examples are presented and compared with previous works. The present method can also be extended to the case of arbitrary distribution of the material properties along the thickness direction of the plate.

Homotopy analysis approach to Duffing-harmonic oscillator

冯少东 陈立群

2009, 30(9):  1083-1089.  doi:10.1007/s10483-009-0902-7

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This paper uses the homotopy analysis for the Duffing-harmonic oscillator. The auxiliary parameter in the deformation equation is numerically determined. The response and the frequency of the Duffing-harmonic oscillator are calculated. The analytical results are validated in numerical simulations.

Basic function scheme of polynomial type

吴望一 林光

2009, 30(9):  1091-1103.  doi:10.1007/s10483-009-0903-y

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A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as a basic function and applying the flux splitting method and the combination of central and upwind schemes to suppress non-physical fluctuation near shock waves, a second-order basic function scheme of polynomial type is proposed to solve inviscid compressible flows numerically. Numerical results of typical examples for two-dimensional inviscid compressible transonic and supersonic steady flows indicate that the new scheme has high accuracy and high resolution for shock waves. Combined with the adaptive remeshing technique, satisfactory results can be obtained.

论文

Generalized mixed equilibrium problem in Banach spaces

张石生

2009, 30(9):  1105-1112.  doi:10.1007/s10483-009-0904-6

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This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-φ-nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.

Articles

MHD natural convection in porous media-filled enclosures

F.G.Shehadeh H.M.Duwairi

2009, 30(9):  1113-1120.  doi:10.1007/s10483-009-0905-6

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In this work, the magnetohydrodynamics (MHD) natural convection heat transfer problem inside a porous medium filled with inclined rectangular enclosures is investigated numerically. The boundary conditions selected on the enclosure are two adiabatic and two isothermal walls. The governing equations, continuity, and Forchheimer extension of the Darcy law and energy are transformed into dimensionless forms by using
a set of suitable variables, and then solved by using a finite difference scheme. The governing parameters are the magnetic influence number, the Darcy Rayleigh number, the inclination angle, and the aspect ratio of the enclosure. It is found that the magnetic influence number and the inclination angle have pronounced effects on the fluid flow and heat transfer in porous media-filled enclosures.

Two-dimensional analytical solution for compound channel flows with vegetated floodplains

槐文信 高敏 曾玉红 李丹

2009, 30(9):  1121-1130.  doi:10.1007/s10483-009-0906-z

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This paper presents a two-dimensional analytical solution for compound channel flows with vegetated floodplains. The depth-integrated N-S equation is used for analyzing the steady uniform flow. The effects of the vegetation are considered as the drag force item. The secondary currents are also taken into account in the governing equations, and the preliminary estimation of the secondary current intensity coefficient K is discussed. The predicted results for the straight channels and the apex cross-section of meandering channels agree well with experimental data, which shows that the analytical model presented here can be applied to predict the flow in compound channels with vegetated floodplains.

Three-to-one internal resonance in multiple stepped beam systems

A.Tekin E.Ozkaya S.M.Bagdath

2009, 30(9):  1131-1142.  doi:10.1007/s10483-009-0907-x

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In this study, the vibrations of multiple stepped beams with cubic nonlinearities are considered. A three-to-one internal resonance case is investigated for the system. A general approximate solution to the problem is found using the method of multiple scales (a perturbation technique). The modulation equations of the amplitudes and the phases are derived for two modes. These equations are utilized to determine steady state
solutions and their stabilities. It is assumed that the external forcing frequency is close to the lower frequency. For the numeric part of the study, the three-to-one ratio in natural frequencies is investigated. These values are observed to be between the first and second natural frequencies in the cases of the clamped-clamped and clamped-pinned supports, and between the second and third natural frequencies in the case of the pinned-pinned support. Finally, a numeric algorithm is used to solve the three-to-one internal resonance. The first mode is externally excited for the clamped-clamped and clamped-pinned supports, and the second mode is externally excited for the pinned-pinned support. Then, the amplitudes of the first and second modes are investigated when the first mode is externally excited. The amplitudes of the second and third modes are investigated when the second mode is externally excited. The force-response, damping-response, and frequencyresponse curves are plotted for the internal resonance modes of vibrations. The stability analysis is carried out for these plots.

A convolution-type semi-analytic DQ approach to transient response of rectangular plates

彭建设 杨杰 袁玉全 罗光兵

2009, 30(9):  1143-1151.  doi:10.1007/s10483-009-0908-2

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The convolution-type Gurtin variational principle is known as the only variational principle that is, from the mathematics point of view, totally equivalent to the initial value problem system. In this paper, the equation of motion of rectangular thin plates is first transformed to a new governing equation containing initial conditions by using a convolution method. A convolution-type semi-analytical DQ approach, which involves differential quadrature (DQ) approximation in the space domain and an analytical series expansion in the time domain, is proposed to obtain the transient response solution. This approach offers the same advantages as the Gurtin variational principle and, at the same time, is much simpler in calculation. Numerical results show that it is very accurate yet computationally efficient for the dynamic response of plates.

Interface end stress field of antiplane of orthotropic bimaterials

李俊林 王小丽

2009, 30(9):  1153-1159.  doi:10.1007/s10483-009-0909-z

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The orthotropic bimaterial antiplane interface end of a flat lap is studied by constructing new stress functions and using the composite complex function method of material fracture. The expressions of stress fields, displacements fields and the stress intensity factor around the flat lap interface end are derived by solving a class of generalized bi-harmonic equations. The result shows that this type of problem has one singularity, the stress field has no singularity when two materials have constant ratio Γ > 0, the stress field has power singularity, and the singularity index has a trend to −1/2 as Γ increases. The derived equation is verified with FEM analysis.

Two-mode squeezed state of nanomechanical resonators

范瑞琴 羊红光 白志明

2009, 30(9):  1161-1167.  doi:10.1007/s10483-009-0910-y

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In this paper, we introduce a flexible model for the control and measurement of NAMRs (nanomechanical resonators). We obtain the free Hamiltonian of the dc-SQUID (direct current superconducting quantum interference device) and the interaction Hamiltonian between these two NAMRs and the dc-SQUID by introducing the annihilation and creation operators under the rotating wave approximation. We can treat the mode of the dc-SQUID as a classical field. In the Heisenberg picture, the generation of two-mode squeezed states of two nanomechanical resonators is shown by their collective coordinate and momentum operators.

Variational principle for a special Cosserat rod

刘东生 Charles H-T WANG

2009, 30(9):  1169-1176.  doi:10.1007/s10483-009-0911-y

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In this paper, we describe the nonlinear models of a rod in three-dimensional space based on the Cosserat theory. Using the pseudo-rigid body method and variational principle, we obtain the motion equations of a Cosserat rod including shear deformations.

Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation

尚月强 何银年

2009, 30(9):  1177-1182.  doi:10.1007/s10483-009-0912-6

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Schwarz methods are an important type of domain decomposition methods. Using the Fourier transform, we derive error propagation matrices and their spectral radii of the classical Schwarz alternating method and the additive Schwarz method for the biharmonic equation in this paper. We prove the convergence of the Schwarz methods from a new point of view, and provide detailed information about the convergence speeds and their dependence on the overlapping size of subdomains. The obtained results are independent of any unknown constant and discretization method, showing that the Schwarz alternating method converges twice as quickly as the additive Schwarz method.

Nonlinear implicit iterative method for solving nonlinear ill-posed problems

柳建军 贺国强 康传刚

2009, 30(9):  1183-1192.  doi:10.1007/s10483-009-0913-1

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In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.

Generalized elastic curves in the Lorentz flat space L⁴

黄荣培 商东虎

2009, 30(9):  1193-1200.  doi:10.1007/s10483-009-0914-x

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In this paper, we study the extremals of the curvature energy actions on non-null curves in the four-dimensional Lorentz-Minkowski space. We derive the motion equations and find three Killing fields along the generalized elastic curves. We also construct a cylindrical coordinate system using these Killing fields and express the generalized elastic curves by means of quadratures.

Discontinuous penalty approach with deviation integral for global constrained minimization

陈柳 姚奕荣 郑权

2009, 30(9):  1201-1210.  doi:10.1007/s10483-009-0915-x

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In this paper, we use the discontinuous exact penalty functions to solve the constrained minimization problems with an integral approach. We examine a general form of the constrained deviation integral and its analytical properties. The optimality conditions of the penalized minimization problems are proven. To implement the algorithm, the cross-entropy method and the importance sampling are used based on the Monte-Carlo technique. Numerical tests show the effectiveness of the proposed algorithm.