Table of Content

10 September 2008, Volume 29 Issue 9

Previous Issue    Next Issue

Articles

Adaptive explicit Magnus numerical method for nonlinear dynamical systems

LI Wen-cheng;DENG Zi-chen;

2008, 29(9):  1111-1118 .  doi:10.1007/s10483-008-0901-5

Abstract ( 1612 )   PDF (190KB) ( 830 )  

Related Articles | Metrics

Based on the new explicit Magnusexpansion developed for nonlinear equations defined on a matrix Lie group, an efficient numerical method is proposed for nonlinear dynamical systems. To improve computational efficiency, the integration step size can be adaptively controlled. Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system, the van der Pol system with strong stiffness, and the nonlinear Hamiltonian pendulum system.

Dynamic stress intensity factor KIII and dynamic crack propagation characteristics of anisotropic materials

GAO Xin;WANG Han-gong;KANG Xing-wu

2008, 29(9):  1119-1129 .  doi:10.1007/s10483-008-0902-z

Abstract ( 1655 )   PDF (213KB) ( 1001 )  

Related Articles | Metrics

Based on the mechanics of anisotropic materials, the dynamic propagation problem of a mode III crack in an infinite anisotropic body is investigated. Stress, strain and displacement around the crack tip are expressed as an analytical complex function, which can be represented in power series. Constant coefficients of series are determined by boundary conditions. Expressions of dynamic stress intensity factors for a mode III crack are obtained. Components of dynamic stress, dynamic strain and dynamic displacement around the crack tip are derived. Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials, i.e., crack propagation velocity M and the parameter α. The faster the crack velocity is, the greater the maximums of stress components and dynamic displacement components around the crack tip are. In particular, the parameter α affects stress and dynamic displacement around the crack tip.

Adaptive neural network control for coordinated motion of a dual-arm space robot system with uncertain parameters

GUO Yi-shen;CHEN Li

2008, 29(9):  1131-1140 .  doi:10.1007/s10483-008-0903-z

Abstract ( 1840 )   PDF (198KB) ( 739 )  

Related Articles | Metrics

Control of coordinated motion between the base attitude and the arm joints of a free-floating dual-arm space robot with uncertain parameters is discussed. By combining the relation of system linear momentum conversation with the Lagrangian approach, the dynamic equation of a robot is established. Based on the above results, the free-floating dual-arm space robot system is modeled with RBF neural networks, the GL matrix and its product operator. With all uncertain inertial system parameters, an adaptive RBF neural network control scheme is developed for coordinated motion between the base attitude and the arm joints. The proposed scheme does not need linear parameterization of the dynamic equation of the system and any accurate prior-knowledge of the actual inertial parameters. Also it does not need to train the neural network offline so that it would present real-time and online applications. A planar free-floating dual-arm space robot is simulated to show feasibility of the proposed scheme.

Propagation of plane waves in poroviscoelastic anisotropic media

A. K. Vashishth;M.D.Sharma

2008, 29(9):  1141-1153 .  doi:10.1007/s10483-008-0904-x

Abstract ( 1541 )   PDF (299KB) ( 886 )  

Related Articles | Metrics

This study discusses wave propagation in perhaps the most general model of a poroelastic medium. The medium is considered as a viscoelastic, anisotropic and porous solid frame such that its pores of anisotropic permeability are filled with a viscous fluid. The anisotropy considered is of general type, and the attenuating waves in the medium are treated as the inhomogeneous waves. The complex slowness vector is resolved to define the phase velocity, homogeneous attenuation, inhomogeneous attenuation, and angle of attenuation for each of the four attenuating waves in the medium. A non-dimensional parameter measures the deviation of an inhomogeneous wave from its homogeneous version. An numerical model of a North-Sea sandstone is used to analyze the effects of the propagation direction, inhomogeneity parameter, frequency regime, anisotropy symmetry, anelasticity of the frame, and viscosity of the pore-fluid on the propagation characteristics of waves in such a medium.

Boundary slippage for generating hydrodynamic load-carrying capacity

ZHANG Yong-bin

2008, 29(9):  1155-1164 .  doi:10.1007/s10483-008-0905-y

Abstract ( 1573 )   PDF (175KB) ( 815 )  

Related Articles | Metrics

Boundary slippage is used to generate the load-carrying capacity of the hydrodynamic contact between two parallel plane surfaces. In the fluid inlet zone, the fluid-contact interfacial shear strength on a stationary surface is set at low to generate boundary slippage there, while in the fluid outlet zone the fluid-contact interfacial shear strength on the stationary surface is set at high enough to prevent the occurrence of boundary slippage. The fluid-contact interfacial shear strength on the entire moving surface is set at high enough to prevent boundary slippage on the moving surface. These hydrodynamic contact configurations are analyzed to generate the pronounced load-carrying capacity. The optimum ratio of the outlet zone width to the inlet zone width for the maximum load-carrying capacity of the whole contact is found to be 0.5.

Analytical model of sound transmission through laminated composite cylindrical shells considering transverse shear deformation

Kamran Daneshjou;Ali Nouri and Roohollah Talebitooti

2008, 29(9):  1165-1177 .  doi:10.1007/s10483-008-0906-x

Abstract ( 1437 )   PDF (531KB) ( 799 )  

Related Articles | Metrics

Composite structures are often used in the aerospace industry due to the advantages offered by a high strength to weight ratio. Sound transmission through an infinite laminated composite cylindrical shell is studied in the context of the transmission of airborne sound into the aircraft interior. The shell is immersed in an external fluid medium and contains internal fluid. Airflow in the external fluid medium moves with a constant velocity. An exact solution is obtained by simultaneously solving the first-order shear deformation theory (FSDT) of a laminated composite shell and the acoustic wave equations. Transmission losses (TL) obtained from numerical solutions are compared with those of other authors. The effects of structural properties and flight conditions on TL are studied for a range of values, especially, the Mach number, stack sequences, and the angle of warp. Additionally, omparisons of the transmission losses are made between the classical thin shell theory (CST) and FSDT for laminated composite nd isotropic cylindrical shells.

Effects of chemical reactions on MHD micropolar fluid flow past a vertical plate in slip-flow regime

R. C. Chaudhary;Abhay Kumar Jha

2008, 29(9):  1179-1194 .  doi:10.1007/s10483-008-0907-x

Abstract ( 1510 )   PDF (509KB) ( 1541 )  

Related Articles | Metrics

Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical reaction of the first order. A uniform magnetic field acts perpendicular to the porous surface absorb micropolar fluid with a suction velocity varying with time. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. Using the approximate method, the expressions for the velocity microrotation, temperature, and concentration are obtained. Further, the results of the skin friction coefficient, the couple stress coefficient, and the rate of heat and mass transfer at the wall are presented with various values of fluid properties and flow conditions.

Limit cycles and homoclinic orbits and their bifurcation of Bogdanov-Takens system

HUANG Cheng-biao;LIU Jia

2008, 29(9):  1195-1201 .  doi:10.1007/s10483-008-0908-6

Abstract ( 1610 )   PDF (180KB) ( 760 )  

Related Articles | Metrics

A quantitative analysis of limit cycles and homoclinic orbits, and the bifurcation curve for the Bogdanov-Takens system are discussed. The parameter incremental method for approximate analytical-expressions of these problems is given. These analytical-expressions of the limit cycle and homoclinic orbit are shown as the generalized harmonic functions by employing a time transformation. Curves of the parameters and the stability characteristic exponent of the limit cycle versus amplitude are drawn. Some of the limit cycles and homoclinic orbits phase portraits are plotted. The relationship curves of parameters μand αwith amplitude a and the bifurcation diagrams about the parameter are also given. The numerical accuracy of the calculation results is good.

Anisotropic rectangular nonconforming finite element analysis for Sobolev equations

SHI Dong-yang;WANG Hai-hong;GUO Cheng

2008, 29(9):  1203-1214 .  doi:10.1007/s10483-008-0909-2

Abstract ( 1662 )   PDF (252KB) ( 580 )  

Related Articles | Metrics

An anisotropic rectangular nonconforming finite element method for solving the Sobolev equations is discussed under semi-discrete and full discrete schemes. The corresponding optimal convergence error estimates and superclose property are derived, which are the same as the traditional conforming finite elements. Furthermore, the global superconvergence is obtained using a post-processing technique. The numerical results show the validity of the theoretical analysis.

Approximate analytical solutions and approximate value of skin friction coefficient for boundary layer of power law fluids

SU Xiao-hong;ZHENG Lian-cun and JIANG Feng;

2008, 29(9):  1215-1220 .  doi:10.1007/s10483-008-0910-4

Abstract ( 1802 )   PDF (144KB) ( 669 )  

Related Articles | Metrics

This paper presents a theoretical analysis for laminar boundary layer flow in a power law Non-Newtonian fluids. The Adomian analytical decomposition technique is presented and an approximate analytical solution is obtained. The approximate analytical solution can be expressed in terms of a rapid convergent power series with easily computable terms. Reliability and efficiency of the approximate solution are verified by comparing with numerical solutions in the literature. Moreover, the approximate solution can be successfully applied to provide values for the skin friction coefficient of the laminar boundary layer flow in power law non-Newtonian fluids.

A new alternating group explicit-implicit algorithm with high accuracy for dispersive equation

ZHANG Qing-jie;WANG Wen-qia

2008, 29(9):  1221-1230 .  doi:10.1007/s10483-008-0911-y

Abstract ( 1467 )   PDF (452KB) ( 847 )  

Related Articles | Metrics

In this paper, a new alternating group explicit-implicit (nAGEI) scheme for dispersive equations with a periodic boundary condition is derived. This new unconditionally stable scheme has a fourth-order truncation error in space and a convergence ratio faster than some known alternating methods such as ASEI and AGE. Comparison in accuracy with the AGEI and AGE methods is presented in the numerical experiment.

Convergence of gradient method for Elman networks

WU Wei;XU Dong-po;LI Zheng-xue

2008, 29(9):  1231-1238 .  doi:10.1007/s10483-008-0912-z

Abstract ( 1502 )   PDF (165KB) ( 606 )  

Related Articles | Metrics

The gradient method for training Elman networks with a finite training sample set is considered.Monotonicity of the error function in the iteration is shown. Weak and strong convergence results are proved, indicating that the gradient of the error function goes to zero and the weight sequence goes to a fixed point, respectively. A numerical example is given to support the theoretical findings.

The dividend function in the jump-diffusion dual model with barrier dividend strategy

LI Bo;WU Rong

2008, 29(9):  1239-1249 .  doi:10.1007/s10483-008-0913-z

Abstract ( 1428 )   PDF (274KB) ( 886 )  

Related Articles | Metrics

A dual model of the perturbed classical compound Poisson risk model is considered under a constant dividend barrier. A new method is used in deriving the boundary condition of the equation for the expectation function by studying the local time of a related process. We obtain the expression for the expected discount dividend function in terms of those in the corresponding perturbed compound Poisson risk model without barriers. A special case in which the gain size is phase-type distributed is illustrated. We also consider the existence of the optimal dividend level.