Table of Content

01 November 2017, Volume 38 Issue 11

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Articles

Equivalent inclusions in micromechanics with interface energy effect

Zhenguo ZHANG, Yongqiang CHEN, Zhuping HUANG

2017, 38(11):  1497-1516.  doi:10.1007/s10483-017-2276-9

Abstract ( 443 )   HTML   PDF (335KB) ( 114 )  

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In order to apply classical micromechanics in predicting the effective properties of nanocomposites incorporating interface energy, a concept of equivalent inclusion (EI) is usually adopted. The properties of EI are obtained by embedding a single inclusion with the interface into an infinite matrix. However, whether such an EI is universal for different micromechanics-based methods is rarely discussed in the literature. In this paper, the interface energy theory is used to study the applicability of the above mentioned EI. It is found that some elastic properties of the EI are related only to the properties of the inclusion and the interface, whereas others are also related to the properties of the matrix. The former properties of the EI can be applied to both the classical Mori-Tanaka method (MTM) and the generalized self-consistent method (GSCM). However, the latter can be applied only to the MTM. Two kinds of new EIs are proposed for the GSCM and used to estimate the effective mechanical properties of nanocomposites.

Complex variable approach in studying modified polarization saturation model in two-dimensional semipermeable piezoelectric media

S. SINGH, K. SHARMA, R. R. BHARGAVA

2017, 38(11):  1517-1532.  doi:10.1007/s10483-017-2281-9

Abstract ( 334 )   HTML   PDF (406KB) ( 90 )  

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A modified polarization saturation model is proposed and addressed mathematically using a complex variable approach in two-dimensional (2D) semipermeable piezoelectric media. In this model, an existing polarization saturation (PS) model in 2D piezoelectric media is modified by considering a linearly varying saturated normal electric displacement load in place of a constant normal electric displacement load, applied on a saturated electric zone. A centre cracked infinite 2D piezoelectric domain subject to an arbitrary poling direction and in-plane electromechanical loadings is considered for the analytical and numerical studies. Here, the problem is mathematically modeled as a non-homogeneous Riemann-Hilbert problem in terms of unknown complex potential functions representing electric displacement and stress components. Having solved the Hilbert problem, the solutions to the saturated zone length, the crack opening displacement (COD), the crack opening potential (COP), and the local stress intensity factors (SIFs) are obtained in explicit forms. A numerical study is also presented for the proposed modified model, showing the effects of the saturation condition on the applied electrical loading, the saturation zone length, and the COP. The results of fracture parameters obtained from the proposed model are compared with the existing PS model subject to electrical loading, crack face conditions, and polarization angles.

Nonlinear oscillations of sigmoid functionally graded material plates moving in longitudinal direction

Yanqing WANG, J. W. ZU

2017, 38(11):  1533-1550.  doi:10.1007/s10483-017-2277-9

Abstract ( 439 )   HTML   PDF (471KB) ( 19 )  

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Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material (S-FGM) plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D'Alembert's principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von Kármán nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic balance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the excitation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates.

Model predictive control of rigid spacecraft with two variable speed control moment gyroscopes

Pengcheng WU, Hao WEN, Ti CHEN, Dongping JIN

2017, 38(11):  1551-1564.  doi:10.1007/s10483-017-2278-9

Abstract ( 379 )   HTML   PDF (570KB) ( 354 )  

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In this paper, an attitude maneuver control problem is investigated for a rigid spacecraft using an array of two variable speed control moment gyroscopes (VSCMGs) with gimbal axes skewed to each other. A mathematical model is constructed by taking the spacecraft and the gyroscopes together as an integrated system, with the coupling interaction between them considered. To overcome the singular issues of the VSCMGs due to the conventional torque-based method, the first-order derivative of gimbal rates and the second-order derivative of the rotor spinning velocity, instead of the gyroscope torques, are taken as input variables. Moreover, taking external disturbances into account, a feedback control law is designed for the system based on a method of nonlinear model predictive control (NMPC). The attitude maneuver can be realized fast and smoothly by using the proposed controller in this paper.

Comprehensive investigation of stress intensity factors in rotating disks containing three-dimensional semi-elliptical cracks

M. FAKOOR, S. M. N. GHOREISHI

2017, 38(11):  1565-1578.  doi:10.1007/s10483-017-2273-9

Abstract ( 341 )   HTML   PDF (1811KB) ( 18 )  

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Initiation and propagation of cracks in rotating disks may cause catastrophic failures. Therefore, determination of fracture parameters under different working conditions is an essential issue. In this paper, a comprehensive study of stress intensity factors (SIFs) in rotating disks containing three-dimensional (3D) semi-elliptical cracks subjected to different working conditions is carried out. The effects of mechanical properties, rotational velocity, and orientation of cracks on SIFs in rotating disks under centrifugal loading are investigated. Also, the effects of using composite patches to reduce SIFs in rotating disks are studied. The effects of patching design variables such as mechanical properties, thickness, and ply angle are investigated separately. The modeling and analytical procedure are verified in comparison with previously reported results in the literature.

Effects of second diffusing component and cross diffusion on primary and secondary thermoconvective instabilities in couple stress liquids

R. RAVI, C. KANCHANA, P. G. SIDDHESHWAR

2017, 38(11):  1579-1600.  doi:10.1007/s10483-017-2280-9

Abstract ( 263 )   HTML   PDF (463KB) ( 25 )  

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Linear and weakly nonlinear analyses are made for the Rayleigh-Bénard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The Lorenz model is used to study the inverted bifurcation. Positive values of the Soret coefficient favor a pitchfork bifurcation, whereas negative values favor a Hopf bifurcation. Takens-Bogdanov and codimension-two bifurcations are not as much influenced by the Soret coefficient as pitchfork and Hopf bifurcations. The influence of the Soret coefficient on the inverted bifurcation is similar to the influence on the pitchfork bifurcation. The influence of other parameters on the aforementioned bifurcations is also similar as reported earlier in the literature. Using the Newell-Whitehead-Segel equation, the condition for occurrence of Eckhaus and zigzag secondary instabilities is obtained. The domain of appearance of Eckhaus and zigzag instabilities expands due to the presence of the Soret coefficient for positive values. The Soret coefficient with negative values enhances heat transport, while positive values diminish it in comparison with heat transport for the case without the Soret effect. The dual nature of other parameters in influencing heat and mass transport is shown by considering positive and negative values of the Soret coefficient.

Interaction of weak free-stream disturbance with an oblique shock:validation of the shock-capturing method

Caihong SU, Jinlei GENG

2017, 38(11):  1601-1612.  doi:10.1007/s10483-017-2279-9

Abstract ( 349 )   HTML   PDF (467KB) ( 183 )  

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Transition prediction is of great importance for the design of long distance flying vehicles. It starts from the problem of receptivity, i.e., how external disturbances trigger instability waves in the boundary layer. For super/hypersonic boundary layers, the external disturbances first interact with the shock ahead of the flying vehicles before entering the boundary layer. Since direct numerical simulation (DNS) is the only available tool for its comprehensive and detailed investigation, an important problem arises whether the numerical scheme, especially the shock-capturing method, can faithfully reproduce the interaction of the external disturbances with the shock, which is so far unknown. This paper is aimed to provide the answer. The interaction of weak disturbances with an oblique shock is investigated, which has a known theoretical solution. Numerical simulation using the shock-capturing method is conducted, and results are compared with those given by theoretical analysis, which shows that the adopted numerical method can faithfully reproduce the interaction of weak external disturbances with the shock.

Hydromagnetic thin film flow of Casson fluid in non-Darcy porous medium with Joule dissipation and Navier's partial slip

G. S. SETH, R. TRIPATHI, M. K. MISHRA

2017, 38(11):  1613-1626.  doi:10.1007/s10483-017-2272-7

Abstract ( 401 )   HTML   PDF (1580KB) ( 164 )  

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In this paper, the effects of viscous and Ohmic heating and heat generation/absorption on magnetohydrodynamic flow of an electrically conducting Casson thin film fluid over an unsteady horizontal stretching sheet in a non-Darcy porous medium are investigated. The fluid is assumed to slip along the boundary of the sheet. Similarity transformation is used to translate the governing partial differential equations into ordinary differential equations. A shooting technique in conjunction with the 4th order Runge-Kutta method is used to solve the transformed equations. Computations are carried out for velocity and temperature of the fluid thin film along with local skin friction coefficient and local Nusselt number for a range of values of pertinent flow parameters. It is observed that the Casson parameter has the ability to enhance free surface velocity and film thickness, whereas the Forchheimer parameter, which is responsible for the inertial drag has an adverse effect on the fluid velocity inside the film. The velocity slip along the boundary tends to decrease the fluid velocity. This investigation has various applications in engineering and in practical problems such as very large scale integration (VLSI) of electronic chips and film coating.

A closure model on velocity structure functions in homogeneous isotropic turbulence

Le FANG, Feng GAO

2017, 38(11):  1627-1634.  doi:10.1007/s10483-017-2274-9

Abstract ( 425 )   HTML   PDF (453KB) ( 34 )  

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Closure models started from Chou's work have been developed for more than 70 years, aiming at providing analytical tools to describe turbulent flows in the spectral space. In this study, a preliminary attempt is presented to introduce a closure model in the physical space, using the velocity structure functions as key parameters. The present closure model appears to qualitatively reproduce the asymptotic scaling behaviors at small and large scales, despite some inappropriate behaviors such as oscillations. Therefore, further improvements of the present model are expected to provide appropriate descriptions of turbulent flows in the physical space.

Algorithm for transient growth of perturbations in channel Poiseuille flow

Jianlei ZHANG, Gang DONG, Yi LI

2017, 38(11):  1635-1650.  doi:10.1007/s10483-017-2275-9

Abstract ( 290 )   HTML   PDF (1084KB) ( 33 )  

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This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-modal methods based on the Orr-Sommerfeld and Squire (OSS) equations that assume simple base flows, this algorithm can be applied to arbitrarily complex base flows. In the proposed algorithm, a reorthogonalization Arnoldi method is used to improve orthogonality of the orthogonal basis of the Krylov subspace generated by solving the linearized forward and adjoint Navier-Stokes (N-S) equations. The linearized adjoint N-S equations with the specific boundary conditions for the channel are derived, and a new convergence criterion is proposed. The algorithm is then applied to a one-dimensional base flow (the plane Poiseuille flow) and a two-dimensional base flow (the plane Poiseuille flow with a low-speed streak) in a channel. For one-dimensional cases, the effects of the spanwise width of the channel and the Reynolds number on the transient growth of perturbations are studied. For two-dimensional cases, the effect of strength of initial low-speed streak is discussed. The presence of the streak in the plane Poiseuille flow leads to a larger and quicker growth of the perturbations than that in the one-dimensional case. For both cases, the results show that an optimal flow field leading to the largest growth of perturbations is characterized by high- and low-speed streaks and the corresponding streamwise vortical structures. The lift-up mechanism that induces the transient growth of perturbations is discussed. The performance of the re-orthogonalization Arnoldi technique in the algorithm for both one- and two-dimensional base flows is demonstrated, and the algorithm is validated by comparing the results with those obtained from the OSS equations method and the crosscheck method.