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Table of Content

    01 May 2016, Volume 37 Issue 5
    Articles
    Synchronization of networked multibody systems using fundamental equation of mechanics
    Jun LIU, Jinchen JI, Jin ZHOU
    2016, 37(5):  555-572.  doi:10.1007/s10483-016-2071-8
    Abstract ( 684 )   HTML   PDF (1654KB) ( 186 )  
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    From the analytical dynamics point of view, this paper develops an optimal control framework to synchronize networked multibody systems using the fundamental equation of mechanics. A novel robust control law derived from the framework is then used to achieve complete synchronization of networked identical or non-identical multibody systems formulated with Lagrangian dynamics. A distinctive feature of the developed control strategy is the introduction of network structures into the control requirement. The control law consists of two components, the first describing the architecture of the network and the second denoting an active feedback control strategy. A corresponding stability analysis is performed by the algebraic graph theory. A representative network composed of ten identical or non-identical gyroscopes is used as an illustrative example. Numerical simulation of the systems with three kinds of network structures, including global coupling, nearest-neighbour, and small-world networks, is given to demonstrate effectiveness of the proposed control methodology.

    Boundary layer flow of Oldroyd-B fluid by exponentially stretching sheet
    T. HAYAT, M. IMTIAZ, A. ALSAEDI
    2016, 37(5):  573-582.  doi:10.1007/s10483-016-2072-8
    Abstract ( 614 )   HTML   PDF (201KB) ( 314 )  
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    The present paper investigates the steady flow of an Oldroyd-B fluid. The fluid flow is induced by an exponentially stretched surface. Suitable transformations reduce a system of nonlinear partial differential equations to a system of ordinary differential equations. Convergence of series solution is discussed explicitly by a homotopy analysis method (HAM). Velocity, temperature and heat transfer rates are examined for different involved parameters through graphs. It is revealed that for a larger retardation time constant, the velocity is enhanced and the temperature is lowered. It is noted that relaxation time constant and the Prandtl number enhance the heat transfer rate.

    Nonlinear beam formulation incorporating surface energy and size effect: application in nano-bridges
    A. KOOCHI, H. HOSSEINI-TOUDESHKY, M. ABADYAN
    2016, 37(5):  583-600.  doi:10.1007/s10483-016-2073-8
    Abstract ( 570 )   HTML   PDF (693KB) ( 261 )  
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    A nonlinear beam formulation is presented based on the Gurtin-Murdoch surface elasticity and the modified couple stress theory. The developed model theoretically takes into account coupled effects of the energy of surface layer and microstructures sizedependency. The mid-plane stretching of a beam is incorporated using von-Karman nonlinear strains. Hamilton's principle is used to determine the nonlinear governing equation of motion and the corresponding boundary conditions. As a case study, pull-in instability of an electromechanical nano-bridge structure is studied using the proposed formulation. The nonlinear governing equation is solved by the analytical reduced order method (ROM) as well as the numerical solution. Effects of various parameters including surface layer, size dependency, dispersion forces, and structural damping on the pullin parameters of the nano-bridges are discussed. Comparison of the results with the literature reveals capability of the present model in demonstrating the impact of nanoscale phenomena on the pull-in threshold of the nano-bridges.

    Modelling of thrust generated by oscillation caudal fin of underwater bionic robot
    Xinyan YIN, Lichao JIA, Chen WANG, Guangming XIE
    2016, 37(5):  601-610.  doi:10.1007/s10483-016-2074-8
    Abstract ( 607 )   HTML   PDF (805KB) ( 168 )  
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    A simplified model of the thrust force is proposed based on a caudal fin oscillation of an underwater bionic robot. The caudal fin oscillation is generalized by central pattern generators (CPGs). In this model, the drag coefficient and lift coefficient are the two critical parameters which are obtained by the digital particle image velocimetry (DPIV) and the force transducer experiment. Numerical simulation and physical experiments have been performed to verify this dynamic model.

    Numerical investigation of dual-porosity model with transient transfer function based on discrete-fracture model
    Yizhao WAN, Yuewu LIU, Weiping OUYANG, Guofeng HAN, Wenchao LIU
    2016, 37(5):  611-626.  doi:10.1007/s10483-016-2075-8
    Abstract ( 658 )   HTML   PDF (1358KB) ( 240 )  
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    Based on the characteristics of fractures in naturally fractured reservoir and a discrete-fracture model, a fracture network numerical well test model is developed. Bottom hole pressure response curves and the pressure field are obtained by solving the model equations with the finite-element method. By analyzing bottom hole pressure curves and the fluid flow in the pressure field, seven flow stages can be recognized on the curves. An upscaling method is developed to compare with the dual-porosity model (DPM). The comparisons results show that the DPM overestimates the inter-porosity coefficient λ and the storage factor ω. The analysis results show that fracture conductivity plays a leading role in the fluid flow. Matrix permeability influences the beginning time of flow from the matrix to fractures. Fractures density is another important parameter controlling the flow. The fracture linear flow is hidden under the large fracture density. The pressure propagation is slower in the direction of larger fracture density.

    RBF collocation method and stability analysis for phononic crystals
    Chunqiu WEI, Zhizhong YAN, Hui ZHENG, Chuanzeng ZHANG
    2016, 37(5):  627-638.  doi:10.1007/s10483-016-2076-8
    Abstract ( 556 )   HTML   PDF (606KB) ( 155 )  
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    The mesh-free radial basis function (RBF) collocation method is explored to calculate band structures of periodic composite structures. The inverse multi-quadric (MQ), Gaussian, and MQ RBFs are used to test the stability of the RBF collocation method in periodic structures. Much useful information is obtained. Due to the merits of the RBF collocation method, the general form in this paper can easily be applied in the high dimensional problems analysis. The stability is fully discussed with different RBFs. The choice of the shape parameter and the effects of the knot number are presented.

    Modelling and analysis of circular bimorph piezoelectric actuator for deformable mirror
    Hairen WANG, Ming HU, Zhenqin LI
    2016, 37(5):  639-646.  doi:10.1007/s10483-016-2077-8
    Abstract ( 600 )   HTML   PDF (223KB) ( 141 )  
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    A theoretical model of a circular flexure-mode piezoelectric bimorph actuator is established. The circular bimorph structure, consisting of two flexible layers of piezoelectric material and a layer of metallic material in the middle, is powered to the flexural deformation. The analytical solutions including the statics solution and the dynamics solution are derived from the 3D equations of the linear theory of piezoelectricity. Numerical results are included to show the circular bimorph piezoelectric actuator (CBPA) performance, depending on the physical parameters.

    Reduced-order finite element method based on POD for fractional Tricomi-type equation
    Jincun LIU, Hong LI, Yang LIU, Zhichao FANG
    2016, 37(5):  647-658.  doi:10.1007/s10483-016-2078-8
    Abstract ( 735 )   HTML   PDF (2506KB) ( 226 )  
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    The reduced-order finite element method (FEM) based on a proper orthogonal decomposition (POD) theory is applied to the time fractional Tricomi-type equation. The present method is an improvement on the general FEM. It can significantly save memory space and effectively relieve the computing load due to its reconstruction of POD basis functions. Furthermore, the reduced-order finite element (FE) scheme is shown to be unconditionally stable, and error estimation is derived in detail. Two numerical examples are presented to show the feasibility and effectiveness of the method for time fractional differential equations (FDEs).

    Analysis of diffusion induced elastoplastic bending of bilayer lithium-ion battery electrodes
    Dawei LI, Zongzan LI, Yicheng SONG, Junqian ZHANG
    2016, 37(5):  659-670.  doi:10.1007/s10483-016-2079-8
    Abstract ( 677 )   HTML   PDF (311KB) ( 193 )  
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    Bilayer electrode, composed of a current collector layer and an active material layer, has great potential in applications of in-situ electrochemical experiments due to the bending upon lithiation. This paper establishes an elastoplastic theory for the lithiation induced deformation of bilayer electrode with consideration of the plastic yield of current collector. It is found that the plastic yield of current collector reduces the restriction of current collector to an active layer, and therefore, enhances in-plane stretching while lowers down the rate of electrode bending. Key parameters that influence the elastoplastic deformation are identified. It is found that the smaller thickness ratio and lower elastic modulus ratio of current collector to an active layer would lead to an earlier plastic yield of the current collector, the larger in-plane strain, and the smaller bending curvature, due to balance between the current collector and the active layer. The smaller yield stress and plastic modulus of current collector have similar impacts on the electrode deformation.

    Symbolic dynamics of Belykh-type maps
    Denghui LI, Jianhua XIE
    2016, 37(5):  671-682.  doi:10.1007/s10483-016-2080-9
    Abstract ( 526 )   HTML   PDF (629KB) ( 99 )  
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    The symbolic dynamics of a Belykh-type map (a two-dimensional discontinuous piecewise linear map) is investigated. The admissibility condition for symbol sequences named the pruning front conjecture is proved under a hyperbolicity condition. Using this result, a symbolic dynamics model of the map is constructed according to its pruning front and primary pruned region. Moreover, the boundary of the parameter region in which the map is chaotic of a horseshoe type is given.

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