Authors:Bohua Sun Pages: 765 - 778 Abstract: Spatial scaling laws of velocity kinetic energy spectra for the compressible turbulence flow and the density-weighted counterparts are formulated in terms of the wavenumber, dissipation rate, and Mach number by using a dimensional analysis. We apply the Barenblatt’s incomplete similarity theory to both kinetic and density-weighted energy spectra. It shows that, within the initial subrange, both energy spectra approach the –5/3 and –2 power laws of the wavenumber when the Mach number tends to unity and infinity, respectively. PubDate: 2017-06-01 DOI: 10.1007/s10483-017-2204-8 Issue No:Vol. 38, No. 6 (2017)

Authors:Xiangming Xiong; Jianjun Tao Pages: 779 - 796 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 P r = 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: 2017-06-01 DOI: 10.1007/s10483-017-2202-8 Issue No:Vol. 38, No. 6 (2017)

Authors:Jun Hu; Shudao Zhang Pages: 797 - 814 Abstract: Surrogate models are usually used to perform global sensitivity analysis (GSA) by avoiding a large ensemble of deterministic simulations of the Monte Carlo method to provide a reliable estimate of GSA indices. However, most surrogate models such as polynomial chaos (PC) expansions suffer from the curse of dimensionality due to the high-dimensional input space. Thus, sparse surrogate models have been proposed to alleviate the curse of dimensionality. In this paper, three techniques of sparse reconstruction are used to construct sparse PC expansions that are easily applicable to computing variance-based sensitivity indices (Sobol indices). These are orthogonal matching pursuit (OMP), spectral projected gradient for L 1 minimization (SPGL1), and Bayesian compressive sensing with Laplace priors. By computing Sobol indices for several benchmark response models including the Sobol function, the Morris function, and the Sod shock tube problem, effective implementations of high-dimensional sparse surrogate construction are exhibited for GSA. PubDate: 2017-06-01 DOI: 10.1007/s10483-017-2208-8 Issue No:Vol. 38, No. 6 (2017)

Authors:J. Nagler Pages: 815 - 830 Abstract: A Jeffery-Hamel (J-H) flow model of the non-Newtonian fluid type inside a convergent wedge (inclined walls) with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical (numerical) solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature. PubDate: 2017-06-01 DOI: 10.1007/s10483-017-2206-8 Issue No:Vol. 38, No. 6 (2017)

Authors:A. K. Singh; A. Das; A. Ray Pages: 851 - 866 Abstract: The propagation of the Rayleigh-type wave in a fluid layer overlying a corrugated substrate is studied. The corrugated substrate is considered as a fluid saturated poroelastic substrate and a quadratically heterogeneous isotropic elastic substrate in Case I and Case II, respectively. Closed form expressions of dispersion relation for Case I and Case II are obtained. The influence of corrugation, porosity, and heterogeneity on the phase velocity of Rayleigh-type wave, for both cases, is highlighted and demonstrated through numerical computation and graphical discussion. Neglecting corrugation at the common interface, expressions of phase velocity of the Rayleigh-type wave for both cases are derived in a closed form as a special case of the problem. Comparison between the presence and the absence of both heterogeneity and poroelasticity in the substrate of the composite structure is a key in the present study. PubDate: 2017-06-01 DOI: 10.1007/s10483-017-2205-8 Issue No:Vol. 38, No. 6 (2017)

Authors:Yiqiang Chen; Wenjuan Yao; Shaofeng Liu Pages: 867 - 876 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 envi- ronment and the technical level of the test personnel, and can evaluate performance of the OC objectively. PubDate: 2017-06-01 DOI: 10.1007/s10483-017-2203-8 Issue No:Vol. 38, No. 6 (2017)

Authors:Yongan Zhu; Fan Wang; Renhuai Liu Pages: 877 - 888 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: 2017-06-01 DOI: 10.1007/s10483-017-2201-7 Issue No:Vol. 38, No. 6 (2017)

Authors:Chao Zhang; Zhenhua Wan; Dejun Sun Pages: 723 - 736 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: 2017-05-01 DOI: 10.1007/s10483-017-2195-9 Issue No:Vol. 38, No. 5 (2017)

Authors:Xuezhi Lu; Jisheng Luo Abstract: The nth-order expansion of the parabolized stability equation (EPSEn) is obtained from the Taylor expansion of the linear parabolized stability equation (LPSE) in the streamwise direction. The EPSE together with the homogeneous boundary conditions forms a local eigenvalue problem, in which the streamwise variations of the mean flow and the disturbance shape function are considered. The first-order EPSE (EPSE1) and the second-order EPSE (EPSE2) are used to study the crossflow instability in the swept NLF(2)-0415 wing boundary layer. The non-parallelism degree of the boundary layer is strong. Compared with the growth rates predicted by the linear stability theory (LST), the results given by the EPSE1 and EPSE2 agree well with those given by the LPSE. In particular, the results given by the EPSE2 are almost the same as those given by the LPSE. The prediction of the EPSE1 is more accurate than the prediction of the LST, and is more efficient than the predictions of the EPSE2 and LPSE. Therefore, the EPSE1 is an efficient e N prediction tool for the crossflow instability in swept-wing boundary-layer flows. PubDate: 2017-05-15 DOI: 10.1007/s10483-017-2214-6

Authors:Zeqing Wan; Shirong Li Abstract: Thermal buckling behavior of cylindrical shell made of functionally graded material (FGM) is studied. The material constituents are composed of ceramic and metal. The material properties across the shell thickness are assumed to be graded according to a simple power law distribution in terms of the volume fraction rule of mixtures. Based on the Donnell shell theory, a system of dimensionless partial differential equations of buckling in terms of displacement components is derived. The method of separation of variables is used to transform the governing equations to ordinary differential equations (ODEs). A shooting method is used to search for the numerical solutions of the differential equations under two types of boundary conditions. Effects of the power law index, the dimensionless geometrical parameters, and the temperature ratio on the critical buckling temperature are discussed in detail. PubDate: 2017-05-10 DOI: 10.1007/s10483-017-2225-7

Authors:Dan Wang; Yajun Yin; Jiye Wu; Zheng Zhong Abstract: Based on the viewpoint of duality, this paper studies the interaction between a curved surface body and an inside particle. By convex/concave bodies with geometric duality, interaction potentials of particles located outside and inside the curved surface bodies are shown to have duality. With duality, the curvature-based potential between a curved surface body and an inside particle is derived. Furthermore, the normal and tangential driving forces exerted on the particle are studied and expressed as a function of curvatures and curvature gradients. Numerical experiments are designed to test accuracy of the curvature-based potential. PubDate: 2017-05-09 DOI: 10.1007/s10483-017-2223-9

Authors:Caixi Liu; Shuai Tang; Yuhong Dong Abstract: The effect of inertial particles with different specific heat on heat transfer in particle-laden turbulent channel flows is studied using the direct numerical simulation (DNS) and the Lagrangian particle tracking method. The simulation uses a two-way coupling model to consider the momentum and thermal interactions between the particles and turbulence. The study shows that the temperature fields display differences between the particle-laden flow with different specific heat particles and the particle-free flow, indicating that the particle specific heat is an important factor that affects the heat transfer process in a particle-laden flow. It is found that the heat transfer capacity of the particle-laden flow gradually increases with the increase of the particle specific heat. This is due to the positive contribution of the particle increase to the heat transfer. In addition, the Nusselt number of a particle-laden flow is compared with that of a particle-free flow. It is found that particles with a large specific heat strengthen heat transfer of turbulent flow, while those with small specific heat weaken heat transfer of turbulent flow. PubDate: 2017-05-06 DOI: 10.1007/s10483-017-2224-9

Authors:Xinsheng Xu; Zhenzhen Tong; Dalun Rong; Xianhe Cheng; Chenghui Xu; Zhenhuan Zhou Abstract: A Hamiltonian-based analytical method is used to study the mode III interface cracks in magnetoelectroelastic bimaterials with an imperfect interface. By introducing an unknown vector, the governing equations are reformulated in sets of first-order ordinary differential equations. Using separation of variables, eigensolutions in the symplectic space are obtained. An exact solution of the unknown vector is obtained and expressed in terms of symplectic eigensolutions. Singularities of mechanical, electric, and magnetic fields are evaluated with the generalized intensity factors. Comparisons are made to verify accuracy and stability of the proposed method. Numerical examples including mixed boundary conditions are given. PubDate: 2017-05-06 DOI: 10.1007/s10483-017-2222-9

Authors:Lei Wang; De’an Sun; Aifang Qin Abstract: This paper presents general semi-analytical solutions to Fredlund and Hasan’s one-dimensional (1D) consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations (PDEs), which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domain. The Crump’s method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature. PubDate: 2017-05-04 DOI: 10.1007/s10483-017-2209-8

Authors:Weibin Wen; Hongshuai Lei; Kai Wei; Baosheng Xu; Shengyu Duan; Daining Fang Abstract: A time integration algorithm for structural dynamic analysis is proposed by uniform cubic B-spline functions. The proposed algorithm is successfully used to solve the dynamic response of a single degree of freedom (SDOF) system, and then is generalized for a multiple-degree of freedom (MDOF) system. Stability analysis shows that, with an adjustable algorithmic parameter, the proposed method can achieve both conditional and unconditional stabilities. Validity of the method is shown with four numerical simulations. Comparison between the proposed method and other methods shows that the proposed method possesses high computation accuracy and desirable computation efficiency. PubDate: 2017-05-04 DOI: 10.1007/s10483-017-2207-8

Authors:Yiqiang Chen; Wenjuan Yao; Shaofeng Liu 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: 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: 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: 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: 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