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    01 April 2017, Volume 38 Issue 4
    Articles
    Analytical study of wrinkling in thin-film-on-elastomer system with finite substrate thickness
    Xianhong MENG, Guanyu LIU, Zihao WANG, Shuodao WANG
    2017, 38(4):  469-478.  doi:10.1007/s10483-017-2189-6
    Abstract ( 845 )   HTML   PDF (312KB) ( 331 )  
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    Surface wrinkling, a film bonded on a pre-strained elastomeric substrate can form periodic wrinkling patterns, is a common phenomenon in daily life. In existing theoretical models, the film is much thinner than the substrate so that the substrate can be considered to be elastomeric with infinite thickness. In this paper, the effect of finite substrate thickness is analyzed theoretically for free boundary condition cases. Based on the minimum potential energy principle, a theoretical model is established, and the wave length and amplitude of the wrinkling pattern are obtained. When the thickness of the substrate is more than 200 times larger than the thickness of the film, the results of this study agree well with the results obtained from the previous models for infinite substrate thickness. However, for thin substrates, the effect of finite substrate thickness becomes significant. The model given in this paper accurately describes the effect of finite substrate thickness, providing important design guidelines for future thin-film-on-substrate systems such as stretchable electronic devices.

    Three-dimensional magneto-thermo-elastic analysis of functionally graded cylindrical shell
    A. MEHDITABAR, G. H. RAHIMI, S. ANSARI SADRABADI
    2017, 38(4):  479-494.  doi:10.1007/s10483-017-2186-6
    Abstract ( 694 )   HTML   PDF (416KB) ( 235 )  
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    The present paper presents the three-dimensional magneto-thermo-elastic analysis of the functionally graded cylindrical shell immersed in applied thermal and magnetic fields under non-uniform internal pressure. The inhomogeneity of the shell is assumed to vary along the radial direction according to a power law function, whereas Poisson's ratio is supposed to be constant through the thickness. The existing equations in terms of the displacement components, temperature, and magnetic parameters are derived, and then the effective differential quadrature method (DQM) is used to acquire the analytical solution. Based on the DQM, the governing heat differential equations and edge boundary conditions are transformed into algebraic equations, and discretized in the series form. The effects of the gradient index and rapid temperature on the displacement, stress components, temperature, and induced magnetic field are graphically illustrated. The fast convergence of the method is demonstrated and compared with the results obtained by the finite element method (FEM).

    Geometric effects of cross sections on equilibrium of helical and twisted ribbon
    Ye XIAO, Zaixing HUANG
    2017, 38(4):  495-504.  doi:10.1007/s10483-017-2182-6
    Abstract ( 503 )   HTML   PDF (195KB) ( 159 )  
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    In the framework of elastic rod model, the Euler-Lagrange equations characterizing the equilibrium configuration of the polymer chain are derived from a free energy functional associated with the curvature, torsion, twisting angle, and its derivative with respect to the arc-length. The configurations of the helical ribbons with different crosssectional shapes are given. The effects of the elastic properties, the cross-sectional shapes, and the intrinsic twisting on the helical ribbons are discussed. The results show that the pitch angle of the helical ribbon decreases with the increase in the ratio of the twisting rigidity to the bending rigidity and approaches the intrinsic twisting. If the bending rigidity is much greater than the twisting rigidity, the bending and twisting of the helical ribbon always appear simultaneously.

    Axial control for nonlinear resonances of electrostatically actuated nanobeam with graphene sensor
    Canchang LIU, Qian DING, Qingmei GONG, Chicheng MA, Shuchang YUE
    2017, 38(4):  527-542.  doi:10.1007/s10483-017-2184-6
    Abstract ( 579 )   HTML   PDF (496KB) ( 167 )  
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    The nonlinear resonance response of an electrostatically actuated nanobeam is studied over the near-half natural frequency with an axial capacitor controller. A graphene sensor deformed by the vibrations of the nanobeam is used to produce the voltage signal. The voltage of the vibration graphene sensor is used as a control signal input to a closedloop circuit to mitigate the nonlinear vibration of the nanobeam. An axial control force produced by the axial capacitor controller can transform the frequency-amplitude curves from nonlinear to linear. The necessary and sufficient conditions for guaranteeing the system stability and a saddle-node bifurcation are studied. The numerical simulations are conducted for uniform nanobeams. The nonlinear terms of the vibration system can be transformed into linear ones by applying the critical control voltage to the system. The nonlinear vibration phenomena can be avoided, and the vibration amplitude is mitigated evidently with the axial capacitor controller.

    Neumann's method for boundary problems of thin elastic shells
    Y. S. NEUSTADT
    2017, 38(4):  543-556.  doi:10.1007/s10483-017-2190-6
    Abstract ( 600 )   HTML   PDF (310KB) ( 193 )  
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    The possibility of using Neumann's method to solve the boundary problems for thin elastic shells is studied. The variational statement of the static problems for the shells allows for a problem examination within the distribution space. The convergence of Neumann's method is proven for the shells with holes when the boundary of the domain is not completely fixed. The numerical implementation of Neumann's method normally requires significant time before any reliable results can be achieved. This paper suggests a way to improve the convergence of the process, and allows for parallel computing and evaluation during the calculations.

    Darcy-Forchheimer flow of variable conductivity Jeffrey liquid with Cattaneo-Christov heat flux theory
    M. A. MERAJ, S. A. SHEHZAD, T. HAYAT, F. M. ABBASI, A. ALSAEDI
    2017, 38(4):  557-566.  doi:10.1007/s10483-017-2188-6
    Abstract ( 702 )   HTML   PDF (241KB) ( 370 )  
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    The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the implementation of the Cattaneo-Christov heat flux. A liquid with variable thermal conductivity is considered in the Darcy-Forchheimer porous space. The mathematical expressions of momentum and energy are coupled due to the presence of mixed convection. A highly nonlinear coupled system of equations is tackled with the homotopic algorithm. The convergence of the homotopy expressions is calculated graphically and numerically. The solutions of the velocity and temperature are expressed for various values of the Deborah number, the ratio of the relaxation time to the retardation time, the porosity parameter, the mixed convective parameter, the Darcy-Forchheimer parameter, and the conductivity parameter. The results show that the velocity and temperature are higher in Fourier's law of heat conduction cases in comparison with the Cattaneo-Christov heat flux model.

    Hydroelastic interaction between water waves and thin elastic plate floating on three-layer fluid
    Qingrui MENG, Dongqiang LU
    2017, 38(4):  567-584.  doi:10.1007/s10483-017-2185-6
    Abstract ( 599 )   HTML   PDF (808KB) ( 175 )  
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    The wave-induced hydroelastic responses of a thin elastic plate floating on a three-layer fluid, under the assumption of linear potential flow, are investigated for two-dimensional cases. The effect of the lateral stretching or compressive stress is taken into account for plates of either semi-infinite or finite length. An explicit expression for the dispersion relation of the flexural-gravity wave in a three-layer fluid is analytically deduced. The equations for the velocity potential and the wave elevations are solved with the method of matched eigenfunction expansions. To simplify the calculation on the unknown expansion coefficients, a new inner product with orthogonality is proposed for the three-layer fluid, in which the vertical eigenfunctions in the open-water region are involved. The accuracy of the numerical results is checked with an energy conservation equation, representing the energy flux relation among three incident wave modes and the elastic plate. The effects of the lateral stresses on the hydroelastic responses are discussed in detail.

    Natural convection of SiO2-water nanofluid in square cavity with thermal square column
    Xiaopeng XIONG, Sheng CHEN, Bo YANG
    2017, 38(4):  585-602.  doi:10.1007/s10483-017-2183-6
    Abstract ( 568 )   HTML   PDF (6779KB) ( 228 )  
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    A square with a thermal square column is a simple but nontrivial research prototype for nanofluid research. However, until now, the effects of the temperature of the square column on the heat and mass transfer of nanofluids have not been revealed comprehensively, especially on entropy generation. To deepen insight into this important field, the natural convection of the SiO2-water nanofluid in a square cavity with a square thermal column is studied numerically in this study. The effects of the thermal column temperature (T=0.0, 0.5, 1.0, 1.5), the Rayleigh number (ranging from 103 to 106), and the volume fraction of the nanoparticle (varying from 0.01 to 0.04) on the fluid flow, heat transfer, and entropy generation are investigated, respectively. It is found that, no matter at a low or high Rayleigh number, the volume fraction of the nanoparticle shows no considerable effects on the flow field and temperature field for all the temperatures of the thermal column. With an increase in the volume fraction, the mean Nusselt number increases slightly. At the same time, it is found that, with an increase in the temperature of the thermal column, the average Nusselt number gradually decreases at all values of the Rayleigh number. Meanwhile, it is found that, at a high Rayleigh number, the heat transfer mechanism is the main parameter affecting the increase in the total entropy generation rather than the volume fraction. In addition, no matter at a high or low Rayleigh number, when T=0.5, the total entropy generation is the minimum.

    Global solution for quantum Zakharov equations
    Shujun YOU, Boling GUO
    2017, 38(4):  603-616.  doi:10.1007/s10483-017-2181-6
    Abstract ( 579 )   HTML   PDF (165KB) ( 201 )  
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    The initial value problem for the quantum Zakharov equation in three dimensions is studied. The existence and uniqueness of a global smooth solution are proven with coupled a priori estimates and the Galerkin method.

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