Authors:Ye Xiao; Zaixing Huang Pages: 495 - 504 Abstract: 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: 2017-04-01 DOI: 10.1007/s10483-017-2182-6 Issue No:Vol. 38, No. 4 (2017)

Authors:Jianghong Yuan; Weiqiu Chen Pages: 505 - 526 Abstract: 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: 2017-04-01 DOI: 10.1007/s10483-017-2187-6 Issue No:Vol. 38, No. 4 (2017)

Authors:Canchang Liu; Qian Ding; Qingmei Gong; Chicheng Ma; Shuchang Yue Pages: 527 - 542 Abstract: 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: 2017-04-01 DOI: 10.1007/s10483-017-2184-6 Issue No:Vol. 38, No. 4 (2017)

Authors:Qingrui Meng; Dongqiang Lu Pages: 567 - 584 Abstract: Abstract 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. PubDate: 2017-04-01 DOI: 10.1007/s10483-017-2185-6 Issue No:Vol. 38, No. 4 (2017)

Authors:Xiaopeng Xiong; Sheng Chen; Bo Yang Pages: 585 - 602 Abstract: 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: 2017-04-01 DOI: 10.1007/s10483-017-2183-6 Issue No:Vol. 38, No. 4 (2017)

Authors:Shujun You; Boling Guo Pages: 603 - 616 Abstract: Abstract 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. PubDate: 2017-04-01 DOI: 10.1007/s10483-017-2181-6 Issue No:Vol. 38, No. 4 (2017)

Authors:Yiqiang Chen; Wenjuan Yao; Shaofeng Liu Abstract: Abstract In this paper, the effect of fluid in a tunnel of Corti (TC) on organ of Corti (OC) is studied. A three-dimensional OC model including basilar membrane (BM), tectorial membrane (TM), inner and outer hair cells (OHCs), and reticular lamina (RL) is established by COMSOL. An initial pressure is applied to the fluid in the TC. The frequency response of the structure is analyzed, and the displacement of the BM is achieved. The results are in good agreement with the experimental data, confirming validity of the finite element model. Based on the model, the effect of fluid in the TC on the OC is studied. The results show that, when the pressure gradient is absent in the fluid, with the increase of the initial fluid pressure, the displacement of the BM increases. However, when the initial fluid pressure increases to a certain value, the increase rate of the displacement of the BM becomes very slow. The movement of the fluid amplifies the BM movement. Furthermore, the movement of the fluid can strengthen the movement of the OHCs and the shear movement of the stereocilia, especially in the vicinity of the characteristic frequency at which the amplification effect reaches a peak. Nevertheless, a pressure gradient in the fluid affects the BM movement. PubDate: 2017-04-03 DOI: 10.1007/s10483-017-2197-9

Authors:Yan Zhou; Wei Zhang Abstract: Abstract The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e., 1:3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed. By numerical simulation, periodic vibration and quasi-periodic vibration responses of the composite laminated piezoelectric plate are obtained. PubDate: 2017-04-03 DOI: 10.1007/s10483-017-2196-9

Authors:Jianzhong Zhao; Xingming Guo; Lu Lu Abstract: Abstract The paper investigates continuously changing wrinkle patterns of thin films bonded to a gradient substrate. Three types of gradient substrates including exponential, power-law, and symmetry models are considered. The Galerkin method is used to discretize the governing equation of film bonded to gradient substrates. The wavelength and the normalized amplitude of the wrinkles for substrates of various material gradients are obtained. The numerical simulation based on the finite element method (FEM) is used to evolve the wrinkle patterns. The result agrees well with that of the analytical model. It is concluded that localization of wrinkle patterns strongly depends on the material gradient. The critical membrane force depends on both the minimum value of wrinkle stiffness and the gradient of wrinkle stiffness when the wrinkle stiffness is at its minimum. This work provides a better understanding for local wrinkle formation caused by gradient substrates. PubDate: 2017-04-03 DOI: 10.1007/s10483-017-2199-9

Authors:D. V. Dung; N. T. Nga; L. K. Hoa Abstract: Abstract In this paper, Donnell’s shell theory and smeared stiffeners technique are improved to analyze the postbuckling and buckling behaviors of circular cylindrical shells of stiffened thin functionally graded material (FGM) sandwich under an axial loading on elastic foundations, and the shells are considered in a thermal environment. The shells are stiffened by FGM rings and stringers. A general sigmoid law and a general power law are proposed. Thermal elements of the shells and reinforcement stiffeners are considered. Explicit expressions to find critical loads and postbuckling load-deflection curves are obtained by applying the Galerkin method and choosing the three-term approximate solution of deflection. Numerical results show various effects of temperature, elastic foundation, stiffeners, material and geometrical properties, and the ratio between face sheet thickness and total thickness on the nonlinear behavior of shells. PubDate: 2017-04-03 DOI: 10.1007/s10483-017-2198-9

Authors:Chenggong Li; J. P. Y. Maa Abstract: Abstract Large eddy simulation (LES) using the Smagorinsky eddy viscosity model is added to the two-dimensional nine velocity components (D2Q9) lattice Boltzmann equation (LBE) with multi-relaxation-time (MRT) to simulate incompressible turbulent cavity flows with the Reynolds numbers up to 1 × 107. To improve the computation efficiency of LBM on the numerical simulations of turbulent flows, the massively parallel computing power from a graphic processing unit (GPU) with a computing unified device architecture (CUDA) is introduced into the MRT-LBE-LES model. The model performs well, compared with the results from others, with an increase of 76 times in computation efficiency. It appears that the higher the Reynolds numbers is, the smaller the Smagorinsky constant should be, if the lattice number is fixed. Also, for a selected high Reynolds number and a selected proper Smagorinsky constant, there is a minimum requirement for the lattice number so that the Smagorinsky eddy viscosity will not be excessively large. PubDate: 2017-04-03 DOI: 10.1007/s10483-017-2194-9

Authors:Yanqing Wang; J. W. Zu Abstract: Abstract The vibration of a longitudinally moving rectangular plate submersed in an infinite liquid domain is studied analytically with the Rayleigh-Ritz method. The liquid is assumed to be incompressible, inviscid, and irrotational, and the velocity potential is used to describe the fluid velocity in the whole liquid field. The classical thin plate theory is used to derive mechanical energies of the traveling plate. As derivative of transverse displacement with respect to time in the compatibility condition equation exists, an exponential function is introduced to depict the dynamic deformation of the moving plate. It is shown that this exponential function works well with the Rayleigh- Ritz method. A convergence study shows a quick convergence speed for the immersed moving plate. Furthermore, the parametric study is carried out to demonstrate the effect of system parameters including the moving speed, the plate location, the liquid depth, the plate-liquid ratio, and the boundary condition. Results show that the above system parameters have significant influence on the vibration characteristics of the immersed moving plate. To extend the study, the method of added virtual mass incremental (AVMI) factor is used. The results show good agreement with those from the Rayleigh-Ritz method. PubDate: 2017-04-03 DOI: 10.1007/s10483-017-2192-9

Authors:Yongan Zhu; Fan Wang; Renhuai Liu Abstract: Abstract Nonlinear stability of sensor elastic element—corrugated shallow spherical shell in coupled multi-field is studied. With the equivalent orthotropic parameter obtained by the author, the corrugated shallow spherical shell is considered as an orthotropic shallow spherical shell, and geometrical nonlinearity and transverse shear deformation are taken into account. Nonlinear governing equations are obtained. The critical load is obtained using a modified iteration method. The effect of temperature variation and shear rigidity variation on stability is analyzed. PubDate: 2017-04-01 DOI: 10.1007/s10483-017-2201-7

Authors:Yiqiang Chen; Wenjuan Yao; Shaofeng Liu Abstract: Abstract According to the vibration characteristics of the organ of Corti (OC), seven hypotheses are made to simplify the structure of the model, and a mechanical OC model is established. Using the variational principle, a displacement analytical expression is solved under a certain pressure. The results are in good agreement with experimental data, showing the validity of the formula. Combined with the damage caused by noise in clinic, it is found that the hardening of outer hair cells and outer stereocilia can lead to loss of hearing and generation of threshold shift. In addition, the results show that high frequency resonance occurs at the bottom of the basilar membrane (BM), and low frequency resonance occurs at the top of the BM. This confirms the frequency selective characteristics of the BM. Further, using this formula can avoid interference of the environment and the technical level of the test personnel, and can evaluate performance of the OC objectively. PubDate: 2017-04-01 DOI: 10.1007/s10483-017-2203-8

Authors:Xiangming Xiong; Jianjun Tao Abstract: Abstract The relationship between stabilities of the buoyancy boundary layers along an inclined plate and a vertical plate immersed in a stratified medium is studied theoretically and numerically. The eigenvalue problem of energy stability is solved with the method of descending exponentials. The disturbance energy is found to be able to grow to 11.62 times as large as the initial disturbance energy for Pr = 0.72 when the Grashof number is between the critical Grashof numbers of the energy stability and the linear stability. We prove that, with a weighted energy method, the basic flow of the vertical buoyancy boundary layer is stable to finite-amplitude streamwise-independent disturbances. PubDate: 2017-04-01 DOI: 10.1007/s10483-017-2202-8

Authors:Chao Zhang; Zhenhua Wan; Dejun Sun Abstract: Abstract The reduced-order model (ROM) for the two-dimensional supersonic cavity flow based on proper orthogonal decomposition (POD) and Galerkin projection is investigated. Presently, popular ROMs in cavity flows are based on an isentropic assumption, valid only for flows at low or moderate Mach numbers. A new ROM is constructed involving primitive variables of the fully compressible Navier-Stokes (N-S) equations, which is suitable for flows at high Mach numbers. Compared with the direct numerical simulation (DNS) results, the proposed model predicts flow dynamics (e.g., dominant frequency and amplitude) accurately for supersonic cavity flows, and is robust. The comparison between the present transient flow fields and those of the DNS shows that the proposed ROM can capture self-sustained oscillations of a shear layer. In addition, the present model reduction method can be easily extended to other supersonic flows. PubDate: 2017-03-23 DOI: 10.1007/s10483-017-2195-9

Authors:Xianhong Meng; Guanyu Liu; Zihao Wang; Shuodao Wang Abstract: 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: 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: 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: 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