Table of Content

01 January 2020, Volume 41 Issue 1

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Articles

Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation

Jiren XUE, Yewei ZHANG, Hu DING, Liqun CHEN

2020, 41(1):  1-14.  doi:10.1007/s10483-020-2560-6

Abstract ( 632 )   HTML ( 32)   PDF (1148KB) ( 579 )  

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The nonlinear behaviors and vibration reduction of a linear system with a nonlinear energy sink (NES) are investigated. The linear system is excited by a harmonic and random base excitation, consisting of a mass block, a linear spring, and a linear viscous damper. The NES is composed of a mass block, a linear viscous damper, and a spring with ideal cubic nonlinear stiffness. Based on the generalized harmonic function method, the steady-state Fokker-Planck-Kolmogorov equation is presented to reveal the response of the system. The path integral method based on the Gauss-Legendre polynomial is used to achieve the numerical solutions. The performance of vibration reduction is evaluated by the displacement and velocity transition probability densities, the transmissibility transition probability density, and the percentage of the energy absorption transition probability density of the linear oscillator. The sensitivity of the parameters is analyzed for varying the nonlinear stiffness coefficient and the damper ratio. The investigation illustrates that a linear system with NES can also realize great vibration reduction under harmonic and random base excitations and random bifurcation may appear under different parameters, which will affect the stability of the system.

Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end

Tianli JIANG, Huliang DAI, Kun ZHOU, Lin WANG

2020, 41(1):  15-32.  doi:10.1007/s10483-020-2557-9

Abstract ( 563 )   HTML ( 12)   PDF (1075KB) ( 99 )  

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In this study, the nonplanar post-buckling behavior of a simply supported fluid-conveying pipe with an axially sliding downstream end is investigated within the framework of a three-dimensional (3D) theoretical model. The complete nonlinear governing equations are discretized via Galerkin's method and then numerically solved by the use of a fourth-order Runge-Kutta integration algorithm. Different initial conditions are chosen for calculations to show the nonplanar buckling characteristics of the pipe in two perpendicular lateral directions. A detailed parametric analysis is performed in order to study the influence of several key system parameters such as the mass ratio, the flow velocity, and the gravity parameter on the post-buckling behavior of the pipe. Typical results are presented in the form of bifurcation diagrams when the flow velocity is selected as the variable parameter. It is found that the pipe will stay at its original straight equilibrium position until the critical flow velocity is reached. Just beyond the critical flow velocity, the pipe would lose stability by static divergence via a pitchfork bifurcation, and two possible nonzero equilibrium positions are generated. It is shown that the buckling and post-buckling behaviors of the pipe cannot be influenced by the mass ratio parameter. Unlike a pipe with two immovable ends, however, the pinned-pinned pipe with an axially sliding downstream end shows some different features regarding post-buckling behaviors. The most important feature is that the buckling amplitude of the pipe with an axially sliding downstream end would increase first and then decrease with the increase in the flow velocity. In addition, the buckled shapes of the pipe varying with the flow velocity are displayed in order to further show the new post-buckling features of the pipe with an axially sliding downstream end.

Large eddy simulation of high-Reynolds-number atmospheric boundary layer flow with improved near-wall correction

Shengjun FENG, Xiaojing ZHENG, Ruifeng HU, Ping WANG

2020, 41(1):  33-50.  doi:10.1007/s10483-020-2559-7

Abstract ( 698 )   HTML ( 11)   PDF (2101KB) ( 181 )  

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It is highly attractive to develop an efficient and flexible large eddy simulation (LES) technique for high-Reynolds-number atmospheric boundary layer (ABL) simulation using the low-order numerical scheme on a relatively coarse grid, that could reproduce the logarithmic profile of the mean velocity and some key features of large-scale coherent structures in the outer layer. In this study, an improved near-wall correction scheme for the vertical gradient of the resolved streamwise velocity in the strain-rate tensor is proposed to calculate the eddy viscosity coefficient in the subgrid-scale (SGS) model. The LES code is realized with a second-order finite-difference scheme, the scale-dependent dynamic SGS stress model, the equilibrium wall stress model, and the proposed correction scheme. Very-high-Reynolds-number ABL flow simulation under the neutral stratification condition is conducted to assess the performance of the method in predicting the mean and fluctuating characteristics of the rough-wall turbulence. It is found that the logarithmic profile of the mean streamwise velocity and some key features of large-scale coherent structures can be reasonably predicted by adopting the proposed correction method and the low-order numerical scheme.

Momentum and heat transfer of a special case of the unsteady stagnation-point flow

T. G. FANG, F. J. WANG

2020, 41(1):  51-82.  doi:10.1007/s10483-020-2556-9

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This paper investigates the unsteady stagnation-point flow and heat transfer over a moving plate with mass transfer, which is also an exact solution to the unsteady Navier-Stokes (NS) equations. The boundary layer energy equation is solved with the closed form solutions for prescribed wall temperature and prescribed wall heat flux conditions. The wall temperature and heat flux have power dependence on both time and spatial distance. The solution domain, the velocity distribution, the flow field, and the temperature distribution in the fluids are studied for different controlling parameters. These parameters include the Prandtl number, the mass transfer parameter at the wall, the wall moving parameter, the time power index, and the spatial power index. It is found that two solution branches exist for certain combinations of the controlling parameters for the flow and heat transfer problems. The heat transfer solutions are given by the confluent hypergeometric function of the first kind, which can be simplified into the incomplete gamma functions for special conditions. The wall heat flux and temperature profiles show very complicated variation behaviors. The wall heat flux can have multiple poles under certain given controlling parameters, and the temperature can have significant oscillations with overshoot and negative values in the boundary layers. The relationship between the number of poles in the wall heat flux and the number of zero-crossing points is identified. The difference in the results of the prescribed wall temperature case and the prescribed wall heat flux case is analyzed. Results given in this paper provide a rare closed form analytical solution to the entire unsteady NS equations, which can be used as a benchmark problem for numerical code validation.

Modelling two-layer nanofluid flow in a micro-channel with electro-osmotic effects by means of Buongiorno's model

M. D. K. NIAZI, Hang XU

2020, 41(1):  83-104.  doi:10.1007/s10483-020-2558-7

Abstract ( 555 )   HTML ( 9)   PDF (1050KB) ( 536 )  

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A fully developed steady immiscible flow of nanofluid in a two-layer microchannel is studied in the presence of electro-kinetic effects. Buongiorno's model is employed for describing the behavior of nanofluids. Different from the previous studies on two-layer channel flow of a nanofluid, the present paper introduces the flux conservation conditions for the nanoparticle volume fraction field, which makes this work new and unique, and it is in coincidence with practical observations. The governing equations are reduced into a group of ordinary differential equations via appropriate similarity transformations. The highly accurate analytical approximations are obtained. Important physical quantities and total entropy generation are analyzed and discussed. A comparison is made to determine the significance of electrical double layer (EDL) effects in the presence of an external electric field. It is found that the Brownian diffusion, the thermophoresis diffusion, and the viscosity have significant effects on altering the flow behaviors.

Analysis on nonlinear effect of unsteady percolation in the inhomogeneous shale gas reservoir

Xinchun SHANG, Jiaxuan LIU, Xuhua GAO, Weiyao ZHU

2020, 41(1):  105-122.  doi:10.1007/s10483-020-2553-5

Abstract ( 629 )   HTML ( 6)   PDF (1160KB) ( 94 )  

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The nonlinear effects of unsteady multi-scale shale gas percolation, such as desorption, slippage, diffusion, pressure-dependent viscosity, and compressibility, are investigated by numerical simulation. A new general mathematical model of the problem is built, in which the Gaussian distribution is used to describe the inhomogeneous intrinsic permeability. Based on the Boltzmann transformation, an efficient semi-analytical method is proposed. The problem is then converted into a nonlinear equation in an integral form for the pressure field, and a related explicit iteration scheme is constructed by numerical discretization. The validation examples show that the proposed method has good convergence, and the simulation results also agree well with the results obtained from both numerical and actual data of two vertical fractured test wells in the literature. Desorption, slippage, and diffusion have significant influence on shale gas flows. The accuracy of the usual technique that the product of viscosity and compressibility is approximated as its value at the average formation pressure is examined.

Surface wave transference in a piezoelectric cylinder coated with reinforced material

K. K. PANKAJ, S. A. SAHU, S. KUMARI

2020, 41(1):  123-138.  doi:10.1007/s10483-020-2555-8

Abstract ( 633 )   HTML ( 8)   PDF (951KB) ( 625 )  

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The present study deals with the propagation of a polarized shear horizontal (SH) wave in a pre-stressed piezoelectric cylinder circumscribed by a self-reinforced cylinder. The interface of the two media is assumed mechanically imperfect. For obtaining the dispersion relation, the mathematical formulation has been developed and solved by an analytical treatment. The effects of various parameters, i.e., the thickness ratio, the imperfect interface, the initial stress, the reinforcement, and the piezoelectric and dielectric constants, on the dispersion curve are observed prominently. The dispersion curves for different modes have been also plotted. The consequences of the study may be used for achieving optimum efficiency of acoustic wave devices.

Effects of electric/magnetic impact on the transient fracture of interface crack in piezoelectric-piezomagnetic sandwich structure: anti-plane case

Xing ZHAO, Zhenghua QIAN, Jinxi LIU, Cunfa GAO

2020, 41(1):  139-156.  doi:10.1007/s10483-020-2552-5

Abstract ( 650 )   HTML ( 10)   PDF (605KB) ( 95 )  

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Due to the incompatibility of the interlaminar deformations, the interface debonding or cracking usually happens in a layered magnetoelectric (ME) structure under an applied load. In this paper, the transient responses of the anti-plane interface cracks in piezoelectric (PE)-piezomagnetic (PM) sandwich structures are studied by the standard methods of the integral transform and singular integral equation. Discussion on the numerical examples indicates that the PE-PM-PE structure under electric impact is more likely to fracture than the PM-PE-PM structure under a magnetic impact. The dynamic stress intensity factors (DSIFs) are more sensitive to the variation of the active layer thickness. The effects of the material constants on the DSIFs are dependent on the roles played by PE and PM media during the deformation process.

New regularization method and iteratively reweighted algorithm for sparse vector recovery

Wei ZHU, Hui ZHANG, Lizhi CHENG

2020, 41(1):  157-172.  doi:10.1007/s10483-020-2561-6

Abstract ( 665 )   HTML ( 8)   PDF (194KB) ( 114 )  

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Motivated by the study of regularization for sparse problems, we propose a new regularization method for sparse vector recovery. We derive sufficient conditions on the well-posedness of the new regularization, and design an iterative algorithm, namely the iteratively reweighted algorithm (IR-algorithm), for efficiently computing the sparse solutions to the proposed regularization model. The convergence of the IR-algorithm and the setting of the regularization parameters are analyzed at length. Finally, we present numerical examples to illustrate the features of the new regularization and algorithm.

High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws

Lingyan TANG, Songhe SONG, Hong ZHANG

2020, 41(1):  173-192.  doi:10.1007/s10483-020-2554-8

Abstract ( 671 )   HTML ( 9)   PDF (1977KB) ( 110 )  

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In this paper, the maximum-principle-preserving (MPP) and positivitypreserving (PP) flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes (WCNSs) for scalar conservation laws and the compressible Euler systems in both one and two dimensions. The main idea of the present method is to rewrite the scheme in a conservative form, and then define the local limiting parameters via case-by-case discussion. Smooth test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of accuracy. Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes.