Authors:I. A. Mirza; M. Abdulhameed; S. Shafie Pages: 379 - 392 Abstract: The non-Newtonian blood flow, together with magnetic particles in a stenosed artery, is studied using a magneto-hydrodynamic approach. The wall slip condition is also considered. Approximate solutions are obtained in series forms under the assumption that the Womersley frequency parameter has small values. Using an integral transform method, analytical solutions for any values of the Womersley parameter are obtained. Numerical simulations are performed using MATHCAD to study the influence of stenosis and magnetic field on the flow parameters. When entering the stenosed area, blood ve- locity increases slightly, but increases considerably and reaches its maximum value in the stenosis throat. It is concluded that the magnitude of axial velocity varies considerably when the applied magnetic field is strong. The magnitude of maximum fluid velocity is high in the case of weak magnetic fields. This is due to the Lorentz’s force that opposes motion of an electrically conducting fluid. The effect of externally transverse magnetic field is to decelerate the flow of blood. The shear stress consistently decreases in the presence of a magnetic field with increasing intensity. PubDate: 2017-03-01 DOI: 10.1007/s10483-017-2172-7 Issue No:Vol. 38, No. 3 (2017)

Authors:Shan Jiang; Longxiang Dai; Hao Chen; Hongping Hu; Wei Jiang; Xuedong Chen Pages: 411 - 422 Abstract: A folding beam-type piezoelectric phononic crystal model is proposed to isolate vibration. Two piezoelectric bimorphs are joined by two masses as a folding structure to comprise each unit cell of the piezoelectric phononic crystal. Each bimorph is connected independently by a resistive-inductive resonant shunting circuit. The folding structure extends the propagation path of elastic waves, while its structure size remains quite small. Propagation of coupled extension-flexural elastic waves is studied by the classical laminated beam theory and transfer matrix method. The theoretical model is further verified with the finite element method (FEM). The effects of geometrical and circuit parameters on the band gaps are analyzed. With only 4 unit cells, the folding beam-type piezoelectric phononic crystal generates two Bragg band gaps of 369Hz to 1 687Hz and 2 127Hz to 4 000Hz. In addition, between these two Bragg band gaps, a locally resonant band gap is induced by resonant shunting circuits. Appropriate circuit parameters are used to join these two Bragg band gaps by the locally resonant band gap. Thus, a low-frequency and broad band gap of 369Hz to 4 000Hz is obtained. PubDate: 2017-03-01 DOI: 10.1007/s10483-017-2171-7 Issue No:Vol. 38, No. 3 (2017)

Authors:Yadong Huang; Benmou Zhou; Zhaolie Tang Pages: 439 - 452 Abstract: Instability of a wake controlled by a streamwise Lorentz force is investigated through a Floquet stability analysis. The streamwise Lorentz force, which is a two-dimens- ional control input created by an electromagnetic actuator located on the cylinder surface, adjusts the base flow to affect the three-dimensional wake instability and achieve wake stabilization and transition delay. The instability mode at a Reynolds number Re = 300 can be transformed from B to A with N = 1.0, where N is an interaction number repre- senting the strength of the Lorentz force relative to the inertial force in the fluid. The wake flow is Floquet stable when N increases to 1.3. The spanwise perturbation wavelengths are 3.926D and 0.822D in the modes A and B, respectively, where D is the cylinder diameter. In addition, the oscillating amplitudes of drag and lift are reduced with the increase in the interaction number. Particle tracing is used to explore the essential physical mechanism for mode transformation. The path lines show that suppression of flow separation hinders the fluid deformation and rotation, leading to the decrease in elliptic and hyperbolic instability regions, which is the material cause of mode transformation. All of the results indicate that wake stabilization and transition delay can be achieved under open-loop active control via the streamwise Lorentz force. PubDate: 2017-03-01 DOI: 10.1007/s10483-017-2174-8 Issue No:Vol. 38, No. 3 (2017)

Authors:Chenyue Xie; Jianjun Tao; Ji Li Pages: 263 - 270 Abstract: The approximate but analytical solution of the viscous Rayleigh-Taylor instability (RTI) has been widely used recently in theoretical and numerical investigations due to its clarity. In this paper, a modified analytical solution of the growth rate for the viscous RTI of incompressible fluids is obtained based on an approximate method. Its accuracy is verified numerically to be significantly improved in comparison with the previous one in the whole wave number range for different viscosity ratios and Atwood numbers. Furthermore, this solution is expanded for viscous RTI including the concentration-diffusion effect. PubDate: 2017-02-01 DOI: 10.1007/s10483-017-2169-9 Issue No:Vol. 38, No. 2 (2017)

Authors:Xianhong Meng; Guanyu Liu; Zihao Wang; Shuodao Wang Abstract: 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. PubDate: 2017-02-23 DOI: 10.1007/s10483-017-2189-6

Authors:M. A. Meraj; S. A. Shehzad; T. Hayat; F. M. Abbasi; A. Alsaedi Abstract: 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. PubDate: 2017-02-23 DOI: 10.1007/s10483-017-2188-6

Authors:Y. S. Neustadt Abstract: 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. PubDate: 2017-02-23 DOI: 10.1007/s10483-017-2190-6

Authors:A. Mehditabar; G. H. Rahimi; S. Ansari Sadrabadi Abstract: 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). PubDate: 2017-02-23 DOI: 10.1007/s10483-017-2186-6

Authors:Ye Xiao; Zaixing Huang Abstract: 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 cross-sectional 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. PubDate: 2017-02-23 DOI: 10.1007/s10483-017-2182-6

Authors:Jianghong Yuan; Weiqiu Chen Abstract: Circular plates with radially varying thickness, stiffness, and density are widely used for the structural optimization in engineering. The axisymmetric flexural free vibration of such plates, governed by coupled differential equations with variable coefficients by use of the Mindlin plate theory, is very difficult to be studied analytically. In this paper, a novel analytical method is proposed to reduce such governing equations for circular plates to a pair of uncoupled and easily solvable differential equations of the Sturm-Liouville type. There are two important parameters in the reduced equations. One describes the radial variations of the translational inertia and flexural rigidity with the consideration of the effect of Poisson’s ratio. The other reflects the comprehensive effect of the rotatory inertia and shear deformation. The Heun-type equations, recently well-known in physics, are introduced here to solve the flexural free vibration of circular plates analytically, and two basic differential formulae for the local Heun-type functions are discovered for the first time, which will be of great value in enriching the theory of Heun-type differential equations. PubDate: 2017-02-23 DOI: 10.1007/s10483-017-2187-6

Authors:Canchang Liu; Qian Ding; Qingmei Gong; Chicheng Ma; Shuchang Yue Abstract: 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 closed-loop 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. PubDate: 2017-02-23 DOI: 10.1007/s10483-017-2184-6

Authors:Xiaopeng Xiong; Sheng Chen; Bo Yang Abstract: 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. PubDate: 2017-02-23 DOI: 10.1007/s10483-017-2183-6

Authors:Xinhui Si; Haozhe Li; Yanan Shen; Liancun Zheng Abstract: Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions, the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud (Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237 (2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution. PubDate: 2017-01-24 DOI: 10.1007/s10483-017-2178-8

Authors:Lihua Liu; Chaolu Temuer Abstract: In this paper, a symmetry analysis of the modified 2D Burgers vortex equation with a flow parameter is presented. A general form of classical and non-classical symmetries of the equation is derived. These are fundamental tools for obtaining exact solutions to the equation. In several physical cases of the parameter, the specific classical and non-classical symmetries of the equation are then obtained. In addition to rediscovering the existing solutions given by different methods, some new exact solutions are obtained with the symmetry method, showing that the symmetry method is powerful and more general for solving partial differential equations (PDEs). PubDate: 2017-01-24 DOI: 10.1007/s10483-017-2180-8

Authors:Wei Su; Zhenyu Tang; Bijiao He; Guobiao Cai Abstract: A stable high-order Runge-Kutta discontinuous Galerkin (RKDG) scheme that strictly preserves positivity of the solution is designed to solve the Boltzmann kinetic equation with model collision integrals. Stability is kept by accuracy of velocity discretization, conservative calculation of the discrete collision relaxation term, and a limiter. By keeping the time step smaller than the local mean collision time and forcing positivity values of velocity distribution functions on certain points, the limiter can preserve positivity of solutions to the cell average velocity distribution functions. Verification is performed with a normal shock wave at a Mach number 2.05, a hypersonic flow about a two-dimensional (2D) cylinder at Mach numbers 6.0 and 12.0, and an unsteady shock tube flow. The results show that, the scheme is stable and accurate to capture shock structures in steady and unsteady hypersonic rarefied gaseous flows. Compared with two widely used limiters, the current limiter has the advantage of easy implementation and ability of minimizing the influence of accuracy of the original RKDG method. PubDate: 2017-01-24 DOI: 10.1007/s10483-017-2177-8

Authors:Bohua Sun Abstract: Compatibility conditions of a deformation field in continuum mechanics have been revisited via two different routes. One is to use the deformation gradient, and the other is a pure geometric one. Variations of the displacement vector and the displacement density tensor are obtained explicitly in terms of the Riemannian curvature tensor. The explicit relations reconfirm that the compatibility condition is equivalent to the vanishing of the Riemann curvature tensor and reveals the non-Euclidean nature of the space in which the dislocated continuum is imbedded. Comparisons with the theory of Kr¨oner and Le-Stumpf are provided. PubDate: 2017-01-24 DOI: 10.1007/s10483-017-2176-8

Authors:Renjie Jiang; Pengjun Zheng Abstract: Flow around an oscillating cylinder in a subcritical region are numerically studied with a lattice Boltzmann method (LBM). The effects of the Reynolds number, oscillation amplitude and frequency on the vortex wake modes and hydrodynamics forces on the cylinder surface are systematically investigated. Special attention is paid to the phenomenon of resonance induced by the cylinder oscillation. The results demonstrate that vortex shedding can be excited extensively under subcritical conditions, and the response region of vibration frequency broadens with increasing Reynolds number and oscillation amplitude. Two distinct types of vortex shedding regimes are observed. The first type of vortex shedding regime (VSR I) is excited at low frequencies close to the intrinsic frequency of flow, and the second type of vortex shedding regime (VSR II) occurs at high frequencies with the Reynolds number close to the critical value. In the VSR I, a pair of alternately rotating vortices are shed in the wake per oscillation cycle, and lock-in/synchronization occurs, while in the VSR II, two alternately rotating vortices are shed for several oscillation cycles, and the vortex shedding frequency is close to that of a stationary cylinder under the critical condition. The excitation mechanisms of the two types of vortex shedding modes are analyzed separately. PubDate: 2017-01-24 DOI: 10.1007/s10483-017-2175-8

Authors:S. Maiti; S. K. Pandey Abstract: This paper presents a theoretical study of a non-linear rheological fluid transport in an axisymmetric tube by cilia. An attempt has been made to explain the role of cilia motion in the transport of fluid through the ductus efferent of the male reproductive tract. The Ostwald-de Waele power-law viscous fluid is considered to represent the rheological fluid. We analyze pumping by means of a sequence of cilia beats from row-to-row of cilia in a given row of cells and from one row of cells to the next (metachronal wave movement). For this purpose, we consider the conditions that the corresponding Reynolds number is small enough for inertial effects to be negligible, and the wavelength-to-diameter ratio is large enough so that the pressure can be considered uniform over the cross section. Analyses and computations of the fluid motion reveal that the time-average flow rate depends on ϵ, a non-dimensional measure involving the mean radius a of the tube and the cilia length. Thus, the flow rate significantly varies with the cilia length. Moreover, the flow rate has been reported to be close to the estimated value 6×10−3 ml/h for human efferent ducts if ϵ is near 0.4. The estimated value was suggested by Lardner and Shack (Lardner, T. J. and Shack, W. J. Cilia transport. Bulletin of Mathematical Biology, 34, 325–335 (1972)) for human based on the experimental observations of flow rates in efferent ducts of other animals, e.g., rat, ram, and bull. In addition, the nature of the rheological fluid, i.e., the value of the fluid index n strongly influences various flow-governed characteristics. An interesting feature of this paper is that the pumping improves the thickening behavior for small values of ϵ or in free pumping (ΔP = 0) and pumping (ΔP > 0) regions. PubDate: 2017-01-24 DOI: 10.1007/s10483-017-2179-8

Authors:Y. Protserov; N. Vaysfeld Abstract: An axisymmetric tangent stress is applied to a lateral surface of a multilayered elastic finite cylinder with a fixed bottom face. The problem is solved for an arbitrary number of layers. The layers are coaxial, and the conditions of an ideal mechanical contact are fulfilled between them. A circular crack is situated parallel to the cylinder’s faces in the internal layer with branches free from stress. The upper face of the cylinder is also free from stress. Concretization of the problem is done on examples of two- and three-layered cylinders. An analysis of cylinders’ stress state is conducted and the stress intensity factor is evaluated depending on the crack’s geometry, its location and ratio of the shear modulus. Advantages of the proposed method include reduction of the solution constants’ number regardless of the number of layers, and presentation of the mechanical characteristics in a form of uniformly convergent series. PubDate: 2017-01-05 DOI: 10.1007/s10483-017-2173-7

Authors:Haitao Liu; Zhengong Zhou Abstract: The dynamic behavior of a rectangular crack in a three-dimensional (3D) orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional (2D) Fourier transform is applied, and the mixed-boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite. PubDate: 2016-12-23 DOI: 10.1007/s10483-017-2161-9