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2021年 第42卷 第7期    刊出日期：2021-07-01

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论文

The size-dependent elastohydrodynamic lubrication contact of a coated half-plane with non-Newtonian fluid

Jie SU, Hongxia SONG, Liaoliang KE, S. M. AIZIKOVICH

2021, 42(7):  915-930.  doi:10.1007/s10483-021-2744-7

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Based on the couple-stress theory, the elastohydrodynamic lubrication (EHL) contact is analyzed with a consideration of the size effect. The lubricant between the contact surface of a homogeneous coated half-plane and a rigid punch is supposed to be the non-Newtonian fluid. The density and viscosity of the lubricant are dependent on fluid pressure. Distributions of film thickness, in-plane stress, and fluid pressure are calculated by solving the nonlinear fluid-solid coupled equations with an iterative method. The effects of the punch radius, size parameter, coating thickness, slide/roll ratio, entraining velocity, resultant normal load, and stiffness ratio on lubricant film thickness, in-plane stress, and fluid pressure are investigated. The results demonstrate that fluid pressure and film thickness are obviously dependent on the size parameter, stiffness ratio, and coating thickness.



On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams

Pei ZHANG, Hai QING

2021, 42(7):  931-950.  doi:10.1007/s10483-021-2750-8

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Due to the conflict between equilibrium and constitutive requirements, Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest. As an alternative, the stress-driven model has been recently developed. In this paper, for higher-order shear deformation beams, the ill-posed issue (i.e., excessive mandatory boundary conditions (BCs) cannot be met simultaneously) exists not only in strain-driven nonlocal models but also in stress-driven ones. The well-posedness of both the strain- and stress-driven two-phase nonlocal (TPN-StrainD and TPN-StressD) models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded (FG) materials. The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions. By using the generalized differential quadrature method (GDQM), the coupling governing equations are solved numerically. The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.

Reflection and transmission of quasi-plane waves at the interface of piezoelectric semiconductors with initial stresses

S. A. SAHU, S. NIRWAL, S. MONDAL

2021, 42(7):  951-968.  doi:10.1007/s10483-021-2738-9

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We examine the reflection and transmission phenomena of quasi-longitudinal plane (QP) waves in an AlN-ZnO laminated composite structure. The structure is designed under the influence of the initial stresses in which one carrier piezoelectric semiconductor (PSC) half-space is in welded contact with another PSC half-space. The secular equations in the transversely isotropic PSC material are derived from the general dynamic equation, taking the initial stresses into consideration. It is shown that the incident quasi-longitudinal wave (QP-mode) at the interface generates four types of reflected and transmitted waves, namely, QP wave, quasi-transverse (QSV) wave, electric-acoustic (EA) wave, and carrier plane (CP) wave. The algebraic equations are obtained by imposing the boundary conditions on the common interface of the laminated structure. Reflection and transmission coefficients of waves are obtained by implementing Cramer’s rule. Profound impacts of the initial stresses and exterior electric biasing field on the reflection and transmission coefficients of waves are investigated and presented graphically.

Criteria for minimization of spectral abscissa of time-delay systems

Zaihua WANG

2021, 42(7):  969-980.  doi:10.1007/s10483-021-2751-9

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Spectral abscissa (SA) is defined as the real part of the rightmost characteristic root(s) of a dynamical system, and it can be regarded as the decaying rate of the system, the smaller the better from the viewpoint of fast stabilization. Based on the Puiseux series expansion of complex-valued functions, this paper shows that the SA can be minimized within a given delay interval at values where the characteristic equation has repeated roots with multiplicity 2 or 3. Four sufficient conditions in terms of the partial derivatives of the characteristic function are established for testing whether the SA is minimized or not, and they can be tested directly and easily.

Nonlinear vibration of functionally graded graphene plateletreinforced composite truncated conical shell using first-order shear deformation theory

Shaowu YANG, Yuxin HAO, Wei ZHANG, Li YANG, Lingtao LIU

2021, 42(7):  981-998.  doi:10.1007/s10483-021-2747-9

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In this study, the first-order shear deformation theory (FSDT) is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite (FG-GPLRC). The vibration analyses of the FG-GPLRC truncated conical shell are presented. Considering the graphene platelets (GPLs) of the FG-GPLRC truncated conical shell with three different distribution patterns, the modified Halpin-Tsai model is used to calculate the effective Young’s modulus. Hamilton’s principle, the FSDT, and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell. The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell. Then, the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method. The effects of the weight fraction and distribution pattern of the GPLs, the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed. This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.

Vibration analysis of two-dimensional structures using micropolar elements

M. KOHANSAL-VAJARGAH, R. ANSARI, M. FARAJI-OSKOUIE, M. BAZDID-VAHDATI

2021, 42(7):  999-1012.  doi:10.1007/s10483-021-2746-8

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Based on the micropolar theory (MPT), a two-dimensional (2D) element is proposed to describe the free vibration response of structures. In the context of the MPT, a 2D formulation is developed within the ABAQUS finite element software. The user-defined element (UEL) subroutine is used to implement a micropolar element. The micropolar effects on the vibration behavior of 2D structures with arbitrary shapes are studied. The effect of micro-inertia becomes dominant, and by considering the micropolar effects, the frequencies decrease. Also, there is a considerable discrepancy between the predicted micropolar and classical frequencies at small scales, and this difference decreases when the side length-to-length scale ratio becomes large.

Dual solutions of time-dependent magnetohydrodynamic stagnation point boundary layer micropolar nanofluid flow over shrinking/stretching surface

H. B. LANJWANI, M. S. CHANDIO, M. I. ANWAR, S. A. SHEHZAD, M. IZADI

2021, 42(7):  1013-1028.  doi:10.1007/s10483-021-2749-7

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Time-dependent, two-dimensional (2D) magnetohydrodynamic (MHD) micropolar nanomaterial flow over a shrinking/stretching surface near the stagnant point is considered. Mass and heat transfer characteristics are incorporated in the problem. A model of the partial differential expressions is altered into the forms of the ordinary differential equations via similarity transformations. The obtained equations are numerically solved by a shooting scheme in the MAPLE software. Dual solutions are observed at different values of the specified physical parameters. The stability of first and second solutions is examined through the stability analysis process. This analysis interprets that the first solution is stabilized and physically feasible while the second one is un-stable and not feasible. Furthermore, the natures of various physical factors on the drag force, skin-friction factor, and rate of mass and heat transfer are determined and interpreted. The micropolar nanofluid velocity declines with a rise in the suction and magnetic parameters, whereas it increases by increasing the unsteadiness parameter. The temperature of the micropolar nanofluid rises with increase in the Brownian motion, radiation, thermophoresis, unsteady and magnetic parameters, but it decreases against an increment in the thermal slip constraint and Prandtl number. The concentration of nanoparticles reduces against the augmented Schmidt number and Brownian movement values but rises for incremented thermophoresis parameter values.

Electrokinetic energy conversion of electro-magneto-hydro-dynamic nanofluids through a microannulus under the time-periodic excitation

Guangpu ZHAO, Jiali ZHANG, Zhiqiang WANG, Yongjun JIAN

2021, 42(7):  1029-1046.  doi:10.1007/s10483-021-2745-5

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In this work, the effects of externally applied axial pressure gradients and transverse magnetic fields on the electrokinetic energy conversion (EKEC) efficiency and the streaming potential of nanofluids through a microannulus are studied. The analytical solution for electro-magneto-hydro-dynamic (EMHD) flow is obtained under the condition of the Debye-Hückel linearization. Especially, Green’s function method is used to obtain the analytical solutions of the velocity field. The result shows that the velocity distribution is characterized by the dimensionless frequency ?, the Hartmann number Ha, the volume fraction of the nanoparticles φ, the geometric radius ratio a, and the wall ζ potential ratio b. Moreover, the effects of three kinds of periodic excitations are compared and discussed. The results also show that the periodic excitation of the square waveform is more effective in increasing the streaming potential and the EKEC efficiency. It is worth noting that adjusting the wall ζ potential ratio and the geometric radius ratio can affect the streaming potential and the EKEC efficiency.

Heat transfer analysis of MHD and electroosmotic flow of non-Newtonian fluid in a rotating microfluidic channel: an exact solution

T. SIVA, S. JANGILI, B. KUMBHAKAR

2021, 42(7):  1047-1062.  doi:10.1007/s10483-021-2752-6

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The heat transfer of the combined magnetohydrodynamic (MHD) and electroosmotic flow (EOF) of non-Newtonian fluid in a rotating microchannel is analyzed. A couple stress fluid model is scrutinized to simulate the rheological characteristics of the fluid. The exact solution for the energy transport equation is achieved. Subsequently, this solution is utilized to obtain the flow velocity and volume flow rates within the flow domain under appropriate boundary conditions. The obtained analytical solution results are compared with the previous data in the literature, and good agreement is obtained. A detailed parametric study of the effects of several factors, e.g., the rotational Reynolds number, the Joule heating parameter, the couple stress parameter, the Hartmann number, and the buoyancy parameter, on the flow velocities and temperature is explored. It is unveiled that the elevation in a couple stress parameter enhances the EOF velocity in the axial direction.

Numerical and statistical approach for Casson-Maxwell nanofluid flow with Cattaneo-Christov theory

T. MUSHTAQ, A. RAUF, S. A. SHEHZAD, F. MUSTAFA, M. HANIF, Z. ABBAS

2021, 42(7):  1063-1076.  doi:10.1007/s10483-021-2748-6

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The rheological features of an incompressible axi-symmetric Casson-Maxwell nanofluid flow between two stationary disks are examined. The lower permeable disk is located at z=-a, while the upper disk is placed at z=a. Both the disks are porous and subjected to uniform injection. The fluid properties such as thermal conductivity vary with temperature. The Cattaneo-Christov thermal expression is implemented along with the Buongiorno nanofluid theory. By operating the similarity functions, the reduced form of the fluid model in terms of ordinary differential equations is obtained and solved by the bvp4c numerical technique. The physical quantities are demonstrated graphically on the velocity and temperature fields. Three-dimensional flow arrangements and twodimensional contour patterns against several dimensionless variables are also sketched. The numerical values of the local Nusselt and Sherwood numbers for various quantities are presented in tabular set-up. The intensity of the linear relationship between the Nusselt and Sherwood numbers is assessed through Pearson’s product-moment correlation technique. The statistical implication of the linear association between variables is also examined by the t-test statistic approach.