Table of Content

09 April 2014, Volume 35 Issue 4

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Articles

Open-plus-closed-loop control for chaotic motion of 3D rigid pendulum

GE Xin-Sheng;ZOU Kui

2014, 35(4):  403-412.  doi:10.1007/s10483-014-1800-8

Abstract ( 635 )   HTML   PDF (419KB) ( 421 )  

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An open-plus-closed-loop (OPCL) control problem for the chaotic motion of a 3D rigid pendulum subjected to a constant gravitational force is studied. The 3D rigid pendulum is assumed to be consist of a rigid body supported by a fixed and frictionless pivot with three rotational degrees. In order to avoid the singular phenomenon of Euler’s angular velocity equation, the quaternion kinematic equation is used to describe the motion of the 3D rigid pendulum. An OPCL controller for chaotic motion of a 3D rigid pendulum at equilibrium position is designed. This OPCL controller contains two parts: the open-loop part to construct an ideal trajectory and the closed-loop part to stabilize the 3D rigid pendulum. Simulation results show that the controller is effective and efficient.

Impact dynamics analysis of free-floating space manipulator capturing satellite on orbit and robust adaptive compound control algorithm design for suppressing motion

DONG Qiu-Huang;CHEN Li

2014, 35(4):  413-422.  doi:10.1007/s10483-014-1801-7

Abstract ( 673 )   HTML   PDF (467KB) ( 450 )  

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The impact dynamics, impact effect, and post-impact unstable motion suppression of free-floating space manipulator capturing a satellite on orbit are analyzed. Firstly, the dynamics equation of free-floating space manipulator is derived using the second Lagrangian equation. Combining the momentum conservation principle, the impact dynamics and effect between the space manipulator end-effector and satellite of the capture process are analyzed with the momentum impulse method. Focusing on the unstable motion of space manipulator due to the above impact effect, a robust adaptive compound control algorithm is designed to suppress the above unstable motion. There is no need to control the free-floating base position to save the jet fuel. Finally, the simulation is proposed to show the impact effect and verify the validity of the control algorithm.

Harmonic balance method with alternating frequency/time domain technique for nonlinear dynamical system with fractional exponential

ZHANG Zhi-Yong;CHEN Yu-Shu

2014, 35(4):  423-436.  doi:10.1007/s10483-014-1802-9

Abstract ( 582 )   HTML   PDF (747KB) ( 960 )  

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Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time (HB-AFT) domain technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.

Improved modal truncation method for eigensensitivity analysis of asymmetric matrix with repeated eigenvalues

ZHANG Zhen-Yu

2014, 35(4):  437-452.  doi:10.1007/s10483-014-1803-6

Abstract ( 621 )   HTML   PDF (174KB) ( 451 )  

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An improved modal truncation method with arbitrarily high order accuracy is developed for calculating the second- and third-order eigenvalue derivatives and the first- and second-order eigenvector derivatives of an asymmetric and non-defective matrix with repeated eigenvalues. If the different eigenvalues λ₁, λ₂, · · · , λ_r of the matrix satisfy |λ₁| <= · · ·<= |λ_r| and |λ_s| < |λ_s+1| (s <= r−1), then associated with any eigenvalue λ_i (i <=s), the errors of the eigenvalue and eigenvector derivatives obtained by the qth-order approximate method are proportional to |λ_i/λ_s+1|^q+1, where the approximate method only uses the eigenpairs corresponding to λ₁, λ₂, · · · , λ_s. A numerical example shows the validity of the approximate method. The numerical example also shows that in order to get the approximate solutions with the same order accuracy, a higher order method should be used for higher order eigenvalue and eigenvector derivatives.

Investigation on charge parameters of underwater contact explosion based on axisymmetric SPH method

MING Fu-Ren;SUN Feng-Nan;ZHANG A-Man

2014, 35(4):  453-468.  doi:10.1007/s10483-014-1804-6

Abstract ( 630 )   HTML   PDF (1179KB) ( 380 )  

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This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics (SPH) method. The dynamic boundary particle is proposed to improve the pressure fluctuation and numerical accuracy near the symmetric axis. An in-depth study is carried out over the influence of charge shapes and detonation modes on the near-field loads in terms of the peak pressure and impulse of shock waves. For different charge shapes, the cylindrical charge with different length-diameter ratios may cause strong directivity of peak pressure and impulse in the near field. Compared with spherical charge, the peak pressure of cylindrical charge may be either weakened or enhanced in different directions. Within a certain range, the greater the length-diameter ratio is, the more obvious the effect will be. The weakened ratio near the detonation end may reach 25% approximately, while the enhanced ratio may reach around 20% in the opposite direction. However, the impulse in different directions seems to be uniform. For different detonation modes, compared with point-source explosion, the peak pressure of plane-source explosion is enhanced by about 5%. Besides, the impulse of plane-source explosion is enhanced by around 5% near the
detonation end, but close to those of the point-source explosion in other directions. Based on the material constitutive relation in the axisymmetric coordinates, a simple case of underwater contact explosion is simulated to verify the above conclusions, showing that the charge parameters of underwater contact explosion should not be ignored.

Peristaltic flow of couple stress fluid through uniform porous medium

A. ALSAEDI;N.ALI;D.TRIPATHI;T. HAYAT

2014, 35(4):  469-480.  doi:10.1007/s10483-014-1805-8

Abstract ( 647 )   HTML   PDF (291KB) ( 432 )  

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Investigation concerning peristaltic motion of couple stress fluid is made. An incompressible couple stress fluid occupies the porous medium. Mathematical analysis is presented through large wavelength and low Reynolds number. Exact analytical expressions of axial velocity, volume flow rate, pressure gradient, and stream function are calculated as a function of couple stress parameter. The essential feature of the analysis is a full description of influence of couple stress parameter and permeability parameter on the pressure, frictional force, mechanical efficiency, and trapping.

Modified asymptotic Adomian decomposition method for solving Boussinesq equation of groundwater flow

CHEN Fang;LIU Qing-Quan

2014, 35(4):  481-488.  doi:10.1007/s10483-014-1806-7

Abstract ( 595 )   HTML   PDF (367KB) ( 428 )  

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The Adomian decomposition method (ADM) is an approximate analytic method for solving nonlinear equations. Generally, an approximate solution can be obtained by using only a few terms. However, in applications, we need to use it flexibly according to the real problem. In this paper, based on the ADM, we give a modified asymptotic Adomian decomposition method and use it to solve the nonlinear Boussinesq equation describing groundwater flows. The example shows effectiveness of the modified asymptotic Adomian decomposition method.

Heat transfer analysis of Williamson fluid over exponentially stretching surface

S. NADEEM; S. T. HUSSAIN

2014, 35(4):  489-502.  doi:10.1007/s10483-014-1807-6

Abstract ( 620 )   HTML   PDF (342KB) ( 958 )  

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This study explores the effects of heat transfer on the Williamson fluid over a porous exponentially stretching surface. The boundary layer equations of the Williamson fluid model for two dimensional flow with heat transfer are presented. Two cases of heat transfer are considered, i.e., the prescribed exponential order surface temperature (PEST) case and the prescribed exponential order heat flux (PEHF) case. The highly nonlinear partial differential equations are simplified with suitable similar and non-similar variables, and finally are solved analytically with the help of the optimal homotopy analysis method (OHAM). The optimal convergence control parameters are obtained, and the physical features of the flow parameters are analyzed through graphs and tables. The skin friction and wall temperature gradient are calculated.

Modified iterative method for augmented system

SHAO Xin-Hui;JI Cui;SHEN Hai-Long;LI Chang-Jun

2014, 35(4):  503-514.  doi:10.1007/s10483-014-1808-8

Abstract ( 507 )   HTML   PDF (199KB) ( 366 )  

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The successive overrelaxation-like (SOR-like) method with the real parameters ω is considered for solving the augmented system. The new method is called the modified SOR-like (MSOR-like) method. The functional equation between the parameters and the eigenvalues of the iteration matrix of the MSOR-like method is given. Therefore, the necessary and sufficient condition for the convergence of the MSOR-like method is derived. The optimal iteration parameter ω of the MSOR-like method is derived. Finally, the proof of theorem and numerical computation based on a particular linear system are given, which clearly show that the MSOR-like method outperforms the SOR-like (Li, C. J., Li, B. J., and Evans, D. J. Optimum accelerated parameter for the GSOR method. Neural, Parallel & Scientific Computations, 7(4), 453–462 (1999)) and the modified symmetric SOR-like (MSSOR-like) methods (Wu, S. L., Huang, T. Z., and Zhao, X. L. A modified SSOR iterative method for augmented systems. Journal of Computational and Applied Mathematics, 228(4), 424–433 (2009)).

Long time behavior of solutions to coupled Burgers-complex Ginzbury-Landau (Burgers-CGL) equations for flames governed by sequential reaction

GUO Chang-Hong;FANG Shao-Mei;GUO Bai-Ling

2014, 35(4):  515-534.  doi:10.1007/s10483-014-1809-7

Abstract ( 568 )   HTML   PDF (227KB) ( 377 )  

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This paper studies the existence and long time behavior of the solutions to the coupled Burgers-complex Ginzburg-Landau (Burgers-CGL) equations, which are derived from the nonlinear evolution of the coupled long-scale oscillatory and monotonic instabilities of a uniformly propagating combustion wave governed by a sequential chemical reaction, having two flame fronts corresponding to two reaction zones with a finite separation distance between them. This paper firstly shows the existence of the global solutions to these coupled equations via subtle transforms, delicate a priori estimates and a so-called continuity method, then prove the existence of the global attractor and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the attractor.