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Table of Content

    01 September 2017, Volume 38 Issue 9
    Articles
    Interplay of surface geometry and vorticity dynamics in incompressible flows on curved surfaces
    Qian SHI, Yu CHEN, Xilin XIE
    2017, 38(9):  1191-1212.  doi:10.1007/s10483-017-2238-8
    Abstract ( 382 )   HTML   PDF (7184KB) ( 133 )  
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    Incompressible viscous flows on curved surfaces are considered with respect to the interplay of surface geometry, curvature, and vorticity dynamics. Free flows and cylindrical wakes over a Gaussian bump are numerically solved using a surface vorticitystream function formulation. Numerical simulations show that the Gaussian curvature can generate vorticity, and non-uniformity of the Gaussian curvature is the main cause. In the cylindrical wake, the bump dominated by the positive Gaussian curvature can significantly affect the vortex street by forming velocity depression and changing vorticity transport. The results may provide possibilities for manipulating surface flows through local change in the surface geometry.

    Mechanism of three-dimensional boundary-layer receptivity
    Luyu SHEN, Changgen LU
    2017, 38(9):  1213-1224.  doi:10.1007/s10483-017-2232-7
    Abstract ( 425 )   HTML   PDF (697KB) ( 102 )  
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    Boundary-layer receptivity is always a hot issue in laminar-turbulent transition. Most actual laminar-turbulent transitions belong to three-dimensional flows. An infinite back-swept flat-plate boundary layer is a typical three-dimensional flow. Study of its receptivity is important both in theory and applications. In this paper, a freestream turbulence model is established. A modified fourth-order Runge-Kutta scheme is used for time marching, and compact finite difference schemes are used for space discretization. On these bases, whether unsteady cross-flow vortices can be excited in the three-dimensional boundary layer (the infinite back-swept flat-plate boundary layer) by free-stream turbulence is studied numerically. If so, effects of the level and the direction of free-stream turbulence on the three-dimensional boundary-layer receptivity are further studied. Differences of the three-dimensional boundary-layer receptivity are then discussed by considering the non-parallel effect, influence of the leading-edge stagnation point of the flat plate, and variation of the back-swept angle separately. Intensive studies on the three-dimensional boundary-layer receptivity will benefit the development of the hydrodynamic stability theory, and provide a theoretical basis for prediction and control of laminar-turbulent transition.

    Structure-preserving properties of Störmer-Verlet scheme for mathematical pendulum
    Weipeng HU, Mingzhe SONG, Zichen DENG
    2017, 38(9):  1225-1232.  doi:10.1007/s10483-017-2233-8
    Abstract ( 464 )   HTML   PDF (225KB) ( 98 )  
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    The structure-preserving property, in both the time domain and the frequency domain, is an important index for evaluating validity of a numerical method. Even in the known structure-preserving methods such as the symplectic method, the inherent conservation law in the frequency domain is hardly conserved. By considering a mathematical pendulum model, a Störmer-Verlet scheme is first constructed in a Hamiltonian framework. The conservation law of the Störmer-Verlet scheme is derived, including the total energy expressed in the time domain and periodicity in the frequency domain. To track the structure-preserving properties of the Störmer-Verlet scheme associated with the conservation law, the motion of the mathematical pendulum is simulated with different time step lengths. The numerical results illustrate that the Störmer-Verlet scheme can preserve the total energy of the model but cannot preserve periodicity at all. A phase correction is performed for the Störmer-Verlet scheme. The results imply that the phase correction can improve the conservative property of periodicity of the Störmer-Verlet scheme.

    Bifurcation characteristics analysis of a class of nonlinear dynamical systems based on singularity theory
    Kuan LU, Yushu CHEN, Lei HOU
    2017, 38(9):  1233-1246.  doi:10.1007/s10483-017-2234-8
    Abstract ( 651 )   HTML   PDF (233KB) ( 123 )  
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    A method for seeking main bifurcation parameters of a class of nonlinear dynamical systems is proposed. The method is based on the effects of parametric variation of dynamical systems on eigenvalues of the Frechet matrix. The singularity theory is used to study the engineering unfolding (EU) and the universal unfolding (UU) of an arch structure model, respectively. Unfolding parameters of EU are combination of concerned physical parameters in actual engineering, and equivalence of unfolding parameters and physical parameters is verified. Transient sets and bifurcation behaviors of EU and UU are compared to illustrate that EU can reflect main bifurcation characteristics of nonlinear systems in engineering. The results improve the understanding and the scope of applicability of EU in actual engineering systems when UU is difficult to be obtained.

    Arm motion control model based on central pattern generator
    Zhigang ZHENG, Rubin WANG
    2017, 38(9):  1247-1256.  doi:10.1007/s10483-017-2240-8
    Abstract ( 343 )   HTML   PDF (781KB) ( 77 )  
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    According to the theory of Matsuoka neural oscillators and with the consideration of the fact that the human upper arm mainly consists of six muscles, a new kind of central pattern generator (CPG) neural network consisting of six neurons is proposed to regulate the contraction of the upper arm muscles. To verify effectiveness of the proposed CPG network, an arm motion control model based on the CPG is established. By adjusting the CPG parameters, we obtain the neural responses of the network, the angles of joint and hand of the model with MATLAB. The simulation results agree with the results of crank rotation experiments designed by Ohta et al., showing that the arm motion control model based on a CPG network is reasonable and effective.

    Optimal control of attitude for coupled-rigid-body spacecraft via Chebyshev-Gauss pseudospectral method
    Xinsheng GE, Zhonggui YI, Liqun CHEN
    2017, 38(9):  1257-1272.  doi:10.1007/s10483-017-2236-8
    Abstract ( 455 )   HTML   PDF (416KB) ( 98 )  
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    The attitude optimal control problem (OCP) of a two-rigid-body spacecraft with two rigid bodies coupled by a ball-in-socket joint is considered. Based on conservation of angular momentum of the system without the external torque, a dynamic equation of three-dimensional attitude motion of the system is formulated. The attitude motion planning problem of the coupled-rigid-body spacecraft can be converted to a discrete nonlinear programming (NLP) problem using the Chebyshev-Gauss pseudospectral method (CGPM). Solutions of the NLP problem can be obtained using the sequential quadratic programming (SQP) algorithm. Since the collocation points of the CGPM are Chebyshev-Gauss (CG) points, the integration of cost function can be approximated by the Clenshaw-Curtis quadrature, and the corresponding quadrature weights can be calculated efficiently using the fast Fourier transform (FFT). To improve computational efficiency and numerical stability, the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of state and control variables. Furthermore, numerical float errors of the state differential matrix and barycentric weights can be alleviated using trigonometric identity especially when the number of CG points is large. A simple yet efficient method is used to avoid sensitivity to the initial values for the SQP algorithm using a layered optimization strategy from a feasible solution to an optimal solution. Effectiveness of the proposed algorithm is perfect for attitude motion planning of a two-rigid-body spacecraft coupled by a ball-in-socket joint through numerical simulation.

    Analytical method for evaluating stress field in casing-cementformation system of oil/gas wells
    Wei LIU, Baohua YU, Jingen DENG
    2017, 38(9):  1273-1294.  doi:10.1007/s10483-017-2237-8
    Abstract ( 401 )   HTML   PDF (2183KB) ( 82 )  
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    In this paper, we present an analytical method for evaluating the stress field within a casing-cement-formation system of oil/gas wells under anisotropic in-situ stresses in the rock formation and uniform pressure within the casing. The present method treats the in-situ stresses in the formation as initial stresses since the in-situ stresses have already developed in the formation before placement of cement and casing into the well. It is demonstrated that, via this treatment, the present method excludes additional displacements within the formation predicted by the existing method, and gives more reasonable stress results. An actual tight-oil well is analyzed using the present and existing analytical methods, as well as the finite element method. Good agreement between the analytical results and the finite element analysis (FEA) results is obtained, validating the present method. It is also evident that, compared with the present method, the existing method overestimates the compressive stress level within the casing and the cement. Finally, the effects of elastic properties of the formation, cement, and inner pressure of casing on stresses within the casing and cement are illustrated with a series of sensitivity analyses.

    Layer-element analysis of multilayered saturated soils subject to axisymmetric vertical time-harmonic excitation
    Zhiyong AI, Lihua WANG
    2017, 38(9):  1295-1312.  doi:10.1007/s10483-017-2241-8
    Abstract ( 370 )   HTML   PDF (735KB) ( 84 )  
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    The analytical layer-elements for a single poroelastic soil layer and the underlying half-space are established using an algebraic manipulation and Hankel transform. According to the boundary conditions and adjacent continuity conditions of general stresses and displacements, a global matrix equation in the transform domain for multilayered saturated soil media is assembled and solved. Solutions in the frequency domain can be further obtained with an inverse Hankel transform. Numerical examples are used to examine accuracy of the present method and demonstrate effects of soil parameters and load conditions on dynamic responses of the multilayered poroelastic saturated soils.

    Dispersion and attenuation of torsional wave in a viscoelastic layer bonded between a layer and a half-space of dry sandy media
    P. ALAM, S. KUNDU, S. GUPTA
    2017, 38(9):  1313-1328.  doi:10.1007/s10483-017-2239-8
    Abstract ( 488 )   HTML   PDF (479KB) ( 71 )  
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    Propagation of a torsional wave in a doubly-layered half-space structure of an initially stressed heterogeneous viscoelastic layer sandwiched between a layer and a half-space of heterogeneous dry sandy media is studied. A closed form complex expression for the velocity profile is obtained under effective boundary conditions. The real part of the complex expression provides a dispersion equation, and the imaginary part yields a damping equation. The derived dispersion and damped equations are in well agreement with the classical Love wave condition. In addition, to study the effect of the dissipation factor, the attenuation coefficient, the sandy parameters, the initial stress, the heterogeneity parameters, and the thickness ratio parameter, some noteworthy contemplations are made by numerical calculations and graphical visuals. The results of this paper may present a deeper insight into the behaviour of propagation phenomena in heterogeneous viscoelastic and heterogeneous dry sandy materials that can provide a theoretical guide for the design and optimization in the field of earthquake engineering. The study also reveals that the presence of a damping part due to viscoelasticity affects the torsional wave propagation significantly.

    Complex variable solution for boundary value problem with X-shaped cavity in plane elasticity and its application
    Hang ZHOU
    2017, 38(9):  1329-1346.  doi:10.1007/s10483-017-2235-8
    Abstract ( 385 )   HTML   PDF (1387KB) ( 92 )  
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    A new type of displacement pile, the X-section cast-in-place concrete (XCC) pile, has recently been developed in China. Extensive field tests and laboratory experiments are undertaken to evaluate its performance and quantify the non-uniform deformation effect (NUDE) of the X-shaped cross section during installation. This paper develops a simplified theoretical model that attempts to capture the NUDE. Based on the theory of complex variable plane elasticity, closed-form solutions of the stress and displacement for the X-shaped cavity boundary value problem are given. Subsequently, the analytical solution is used to evaluate the NUDE, the concrete filling index (CFI), and the perimeter reduction coefficient of the XCC pile cross section. The computed results are compared with field test results, showing reasonable agreement. The present simplified theoretical model reveals the deformation mechanism of the X-shaped cavity and facilitates application of the newly developed XCC pile technique in geotechnical engineering.

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