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Elastic response of Carbon Black reinforced polyester based composites using micromechanical models: Role of interphase 基于微力学模型的炭黑增强聚酯基复合材料弹性响应:界面相的作用
M. Karevan
Carbon-based reinforcements have been widely reported in improving mechanical properties of polymers. However, still few studies exist on the incorporation of the interphase as a result of the interfacial interactions into analytical prediction tools. To better understand the effect of interfacial interphase, this study compares and correlates the experimental mechanical response of polyester based composites filled with carbon black (CB) with the elastic behavior obtained from the micromechanical models. Mold cast composites of polyester reinforced with 0 wt%–10 wt% of CB were fabricated. To determine the length of cooperative rearranging region (CRR) as a measure of the interphase, thermal studies focusing on the variations in the specific heat capacity or the relaxation strength of the composites around the glass transition temperature (Tg) range were performed using a thermodynamical model. Micromechanical models such as the Halpin-Tsai and Tandon-Weng were used to determine the Young’s modulus with respect to the CB wt% and diameter as well as the interphase thickness and modulus. The results exhibited the sensitivity of the models to the existence of the interphase as a secondary mechanism, which was correlated to the cross-link density and interfacial bonding. The impact results showed the decrease in the impact resistance upon the addition of higher filler loadings ascribed to the destroyed bonding at the interface and CBs agglomeration confirmed by morphological studies. The research results can be further utilized in the explanation of the changes in the elastic response of carbon-based reinforced thermosetting composites emphasizing the key role of interphase.
碳基增强材料在改善聚合物力学性能方面得到了广泛的报道。然而,将界面相互作用导致的界面相纳入分析预测工具的研究仍然很少。为了更好地理解界面相的影响,本研究将炭黑填充聚酯基复合材料的实验力学响应与微观力学模型得到的弹性行为进行了比较和关联。制备了含0 wt% ~ 10 wt% CB的聚酯增强模铸复合材料。为了确定协同重排区(CRR)的长度作为间相的度量,使用热力学模型对复合材料在玻璃化转变温度(Tg)范围内比热容或弛豫强度的变化进行了热研究。采用Halpin-Tsai和Tandon-Weng等微力学模型确定了相对于CB wt%和直径的杨氏模量以及相间厚度和模量。结果表明,该模型对界面相作为次级机制的存在具有敏感性,这与交联密度和界面键合有关。冲击结果表明,添加较高的填料时,由于界面键结破坏和形态研究证实的CBs团聚,抗冲击性降低。研究结果可以进一步用于解释碳基增强热固性复合材料弹性响应的变化,强调界面相的关键作用。
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引用次数: 0
Peristaltic flow of electrically conducting nanofluid under the action of Joule and radiative heat within an asymmetric microchannel 非对称微通道中焦耳热和辐射热作用下导电纳米流体的蠕动流动
S. Mohanty, B. Mohanty, Satyaranjan Mishra
The proposed mathematical model is based upon the peristaltic flow of an electrical conducting nanofluid within an asymmetric microchannel. The flow takes place under the action of dissipative heat energy due to the occurrence of the magnetic field that is basically known as Joule heating and radiative heat proposed as thermal radiation along with the additional heat source. Moreover, the impact of upper/lower wall zeta potential and the expression for the electric potential is presented using the Poisson Boltzmann equation and Debey length approximation. The well-known numerical practice is used for distorted governing equations with appropriate boundary conditions. Further, computation of the pressure gradient is obtained for the associated physical parameters. The graphical illustration shows the characteristics of the pertinent parameters on the flow problem and the tabular result represents the simulated values for the rate coefficients. In the significant examination, the study reveals that the mobility parameter due to the occurrence of the electric field vis-à-vis time parameter encourages the velocity distribution within the center of the channel furthermore significant retardation occurs near the wall region.
所提出的数学模型是基于导电纳米流体在不对称微通道内的蠕动流动。流动是在耗散热能的作用下发生的,由于磁场的存在,基本上被称为焦耳加热和辐射热,即热辐射,伴随着额外的热源。此外,利用泊松-玻尔兹曼方程和Debey长度近似给出了上下壁zeta电位的影响和电势的表达式。对于具有适当边界条件的扭曲控制方程,采用了众所周知的数值方法。此外,还计算了相关物理参数的压力梯度。图表显示了流动问题中相关参数的特征,表格结果表示速率系数的模拟值。在显著性检验中,研究发现,由于电场的发生而引起的迁移率参数vis-à-vis时间参数促进了通道中心内的速度分布,并且在靠近壁面区域出现了明显的延迟。
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引用次数: 1
Wave propagation and directionality in two-dimensional periodic lattices considering shear deformations 考虑剪切变形的二维周期晶格中的波传播和方向性
Soroush Sepehri, M. Mosavi Mashhadi, Mir Masoud Seyyed Fakhrabadi
The effects of shear deformation on analysis of the wave propagation in periodic lattices are often assumed negligible. However, this assumption is not always true, especially for the lattices made of beams with smaller aspect ratios. Therefore, in the present paper, the effect of shear deformation on wave propagation in periodic lattices with different topologies is studied and their wave attenuation and directionality performances are compared. Current experimental limitations make the researchers focus more on the wave propagation in the direction perpendicular to the plane of periodicity in micro/nanoscale lattice materials while for their macro/mesoscale counterparts, in-plane modes can also be analyzed as well as the out-of-plane ones. Four well-known topologies of hexagonal, triangular, square, and Kagomé are considered in the current paper and their wave propagation is investigated both in the plane of periodicity and in the out-of-plane direction. The finite element method is used to formulate the governing equations and Bloch’s theorem is used to solve the dispersion relations. To investigate the effect of shear deformation, both the Timoshenko and Euler-Bernoulli beam theories are implemented. The results indicate that including shear deformation in wave propagation has a softening effect on the band diagrams of wave propagation and moves the dispersion branches to lower frequencies. It can also reveal some bandgaps that are not predicted without considering the shear deformation.
剪切变形对周期性晶格波传播分析的影响通常被认为可以忽略不计。然而,这种假设并不总是正确的,特别是对于由较小宽高比的梁构成的晶格。因此,本文研究了剪切变形对波在不同拓扑结构的周期晶格中的传播的影响,并比较了它们的波衰减和定向性能。目前的实验限制使得研究人员更多地关注于微/纳米尺度晶格材料中垂直于周期平面方向的波传播,而对于宏观/中尺度晶格材料,既可以分析面内模式,也可以分析面外模式。本文考虑了六角形、三角形、正方形和菱形四种著名的拓扑结构,并研究了它们在周期平面和面外方向上的波传播。采用有限元法建立控制方程,采用布洛赫定理求解色散关系。为了研究剪切变形的影响,采用了Timoshenko和Euler-Bernoulli梁理论。结果表明,在波传播中加入剪切变形对波传播带图有软化作用,使频散分支向低频移动。它还可以揭示一些不考虑剪切变形而无法预测的带隙。
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引用次数: 1
Simulation of time-dependent radiative heat motion over a stretching/shrinking sheet of hybrid Nanofluid: Stability analysis for dual solutions 混合纳米流体拉伸/收缩薄片上随时间的辐射热运动的模拟:对偶溶液的稳定性分析
S. Tinker, S. Mishra, P. Pattnaik, R. Sharma
The heat transfer characteristics for the flow of a time-dependent hybrid nanofluid with thermal radiation and source/sink over a stretching/shrinking sheet are examined in the current investigation. We have transformed the governing equations of the presented study into the similarity equations utilizing similarity variables. However, a numerical solution is obtained by using in-build MATLAB code bvp5c. The mass and energy profiles for diverse values of thermophysical parameters are studied together with their physical quantities. It is observed that dual solutions exist, that is, one is upper, and the other is lower branch solution for a definite choice of the unsteadiness parameter. Also, stability analysis is executed to determine the long-term stability of dual solutions, indicating that out of the two, only one is stable and the other is unstable. It is revealed that comparatively, the first solution shows stability, while the second solution shows instability. There is a considerable influence of second-order slip on the problem’s respective flow and heat transfer characteristics. Further, major outcomes also show the dimensionless frictional stress and the magnitude of conventional heat transfer enhancement with growing suction parameter values.
在当前的研究中,研究了具有热辐射和源/汇的时变混合纳米流体在拉伸/收缩片上的传热特性。我们将本研究的控制方程转化为利用相似变量的相似方程。然而,通过内置的MATLAB代码bvp5c获得了数值解。研究了不同热物性参数值的质量和能量分布及其物理量。观察到,对于非定常参数的选择,存在对偶解,即一个是上分支解,另一个是下分支解。同时进行稳定性分析,确定对偶解的长期稳定性,表明两者中只有一个是稳定的,另一个是不稳定的。结果表明,相对而言,第一种解是稳定的,而第二种解是不稳定的。二阶滑移对问题各自的流动和传热特性有相当大的影响。此外,主要结果还表明,随着吸力参数值的增加,无量纲摩擦应力和常规传热的增强幅度。
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引用次数: 7
On the buckling and bending analysis of FG straight-sided quadrilateral nanoplates using a continuum mechanics-based surface elastic model 基于连续介质力学表面弹性模型的FG直边四边形纳米板屈曲和弯曲分析
A. Shahabodini, B. Ahmadi
In this research, an elastic model based on the continuum mechanics is developed to study the static behaviors of functionally graded (FG) arbitrary straight-sided quadrilateral nanoplates. The model is constructed in the framework of Gurtin-Murdoch’s surface and Mindlin’s plate theories to account for the surface energy and shear deformation effects, simultaneously. The variational differential quadrature (VDQ) method is used along with a mapping technique to do the discretization process in a variational framework by means of differential and integral operators. Consequently, a weak form of governing equations is obtained from the energy quadratic representation of the problem. The solution method is of a distinguished feature as it involves just the first-order derivative of the field components in the mapping and discretization. After assuring the effectiveness of presented model by doing comparative studies, the critical buckling load and static deflection of the FG nanoplates with different shapes in geometry are investigated considering the surface effects. It is found that the surface energies effect on the static behavior of the rectangular nanoplates is more significant as compared to the non-rectangular nanoplates.
本文建立了基于连续介质力学的弹性模型,研究了功能梯度(FG)任意直边四边形纳米片的静态行为。该模型是在Gurtin-Murdoch表面理论和Mindlin板理论的框架下构建的,同时考虑了表面能和剪切变形效应。采用变分微分求积(VDQ)方法和映射技术,利用微分和积分算子在变分框架内进行离散化处理。因此,从问题的能量二次表示得到了控制方程的弱形式。求解方法的一个显著特点是它只涉及映射和离散过程中场分量的一阶导数。在通过对比研究确定模型有效性的基础上,考虑表面效应,研究了不同几何形状FG纳米板的临界屈曲载荷和静挠度。结果表明,与非矩形纳米片相比,表面能对矩形纳米片静态性能的影响更为显著。
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引用次数: 0
Chaotic vibrations of carbon nanotubes subjected to a traversing force considering nonlocal elasticity theory 考虑非局部弹性理论的碳纳米管在横移力作用下的混沌振动
R. Ebrahimi
The existence of chaos in the lateral vibration of the carbon nanotube (CNT) can contribute to source of instability and inaccuracy within the nano mechanical systems. So, chaotic vibrations of a simply supported CNT which is subjected to a traversing harmonic force are studied in this paper. The model of the system is formulated by using nonlocal Euler–Bernoulli beam theory. The equation of motion is solved using the Rung–Kutta method. The effects of the nonlocal parameter, velocity and amplitude of the traversing harmonic force on the nonlinear dynamic response of the system are analyzed by the bifurcation diagrams, phase plane portrait, power spectra analysis, Poincaré map and the maximum Lyapunov exponent. The results indicate that the nonlocal parameter, velocity and amplitude of the traversing harmonic force have considerable effects on the bifurcation behavior and can be used as effective control parameters for avoiding chaos.
碳纳米管(CNT)横向振动中混沌的存在是造成纳米机械系统不稳定和不精确的原因之一。因此,本文研究了简支碳纳米管在简谐力作用下的混沌振动。采用非局部欧拉-伯努利梁理论建立了系统的模型。运动方程用龙库塔法求解。通过分岔图、相平面肖像、功率谱分析、庞加莱图和最大李雅普诺夫指数分析了非局部参数、遍历谐波力的速度和幅值对系统非线性动态响应的影响。结果表明,非局部参数、遍历谐力的速度和幅值对分岔行为有较大影响,可以作为有效的控制参数来避免混沌。
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引用次数: 1
Unsteady squeezing flow of a magnetized nano-lubricant between parallel disks with Robin boundary conditions 具有Robin边界条件的磁化纳米润滑剂在平行圆盘间的非定常挤压流动
J. Umavathi, Sapnali Limbaraj Patil, B. Mahanthesh, O. A. Bég
The aim of the present work is to examine the impact of magnetized nanoparticles (NPs) in enhancement of heat transport in a tribological system subjected to convective type heating (Robin) boundary conditions. The regime examined comprises the squeezing transition of a magnetic (smart) Newtonian nano-lubricant between two analogous disks under an axial magnetism. The lower disk is permeable whereas the upper disk is solid. The mechanisms of haphazard motion of NPs and thermophoresis are simulated. The non-dimensional problem is solved numerically using a finite difference method in the MATLAB bvp4c solver based on Lobotto quadrature, to scrutinize the significance of thermophoresis parameter, squeezing number, Hartmann number, Prandtl number, and Brownian motion parameter on velocity, temperature, nanoparticle concentration, Nusselt number, factor of friction, and Sherwood number distributions. The obtained results for the friction factor are validated against previously published results. It is found that friction factor at the disk increases with intensity in applied magnetic field. The haphazard (Brownian) motion of nanoparticles causes an enhancement in thermal field. Suction and injection are found to induce different effects on transport characteristics depending on the specification of equal or unequal Biot numbers at the disks. The main quantitative outcome is that, unequal Biot numbers produce significant cooling of the regime for both cases of disk suction or injection, indicating that Robin boundary conditions yield substantial deviation from conventional thermal boundary conditions. Higher thermophoretic parameter also elevates temperatures in the regime. The nanoparticles concentration at the disk is boosted with higher values of Brownian motion parameter. The response of temperature is similar in both suction and injection cases; however, this tendency is quite opposite for nanoparticle concentrations. In the core zone, the resistive magnetic body force dominates and this manifests in a significant reduction in velocity, that is damping. The heat build-up in squeeze films (which can lead to corrosion and degradation of surfaces) can be successfully removed with magnetic nanoparticles leading to prolonged serviceability of lubrication systems and the need for less maintenance.
本研究的目的是研究磁化纳米颗粒(NPs)在摩擦系统中对流加热(Robin)边界条件下增强热传递的影响。所研究的体制包括磁性(智能)牛顿纳米润滑剂在两个类似圆盘之间的轴向磁性的挤压跃迁。下盘是可渗透的,而上盘是固体的。模拟了NPs随机运动和热泳的机制。在基于Lobotto正交的MATLAB bvp4c求解器中,采用有限差分法对无量纲问题进行了数值求解,考察了热涌参数、挤压数、哈特曼数、普朗特尔数和布朗运动参数对速度、温度、纳米颗粒浓度、努selt数、摩擦因数和舍伍德数分布的影响。得到的摩擦系数的结果与先前发表的结果进行了验证。结果表明,在外加磁场作用下,摩擦系数随磁场强度的增大而增大。纳米颗粒的随机(布朗)运动引起热场增强。发现吸入和注入对输运特性的影响不同,这取决于磁盘上的Biot数相等或不相等的规格。主要的定量结果是,不相等的Biot数对盘吸或盘注两种情况都会产生显著的冷却,这表明Robin边界条件与传统的热边界条件有很大的偏差。较高的热泳参数也会使体系中的温度升高。随着布朗运动参数的增大,圆盘上纳米颗粒的浓度增加。吸力和注入情况下的温度响应相似;然而,这种趋势与纳米颗粒浓度完全相反。在核心区,磁阻体力占主导地位,这表现为速度的显著降低,即阻尼。磁性纳米颗粒可以成功地消除挤压膜中的热量积聚(可能导致表面腐蚀和降解),从而延长润滑系统的使用寿命,减少维护需求。
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引用次数: 17
The nonlocal parameter for three-dimensional nonlocal elasticity analyses of square graphene sheets: An exact buckling analysis 方形石墨烯片三维非局部弹性分析的非局部参数:精确屈曲分析
A. Naderi
This paper studies buckling problem of square nano-plates under uniform biaxial pressure through using three-dimensional nonlocal elasticity theory. Equations of stability are solved analytically for square nano-plates with simple supports using a Navier-type method. Critical buckling stress is presented for nano square plates with different thickness-length and nonlocal parameter-length ratios. The critical buckling stress is also reported using different local (classical) and nonlocal two-dimensional plate theories constructed essentially based on some simplifying assumptions. Comparison of the results of two-dimensional and three-dimensional theories for both local and nonlocal cases shows that the nonlocal two-dimensional plate theories are not as accurate as the local two-dimensional ones. This issue however reveals importance of the nonlocal three-dimensional solutions. Finally, through comparison of the numerical results with those obtained from molecular dynamic simulations, the value of the nonlocal parameter is calibrated for square graphene sheets. This parameter can be also used for the other nonlocal three-dimensional mechanical analyses of square graphene sheets to find accurate solutions.
本文利用三维非局部弹性理论研究了方形纳米板在双轴均匀压力下的屈曲问题。采用navier型方法解析求解了具有简单支撑的方形纳米板的稳定性方程。给出了不同厚度-长度和非局部参数-长度比的纳米方形板的临界屈曲应力。用不同的局部(经典)和非局部二维板理论也报道了临界屈曲应力,这些理论基本上是基于一些简化的假设。将二维和三维理论在局部和非局部情况下的计算结果进行比较,结果表明非局部二维板理论的计算精度不如局部二维板理论。然而,这个问题揭示了非局部三维解的重要性。最后,通过与分子动力学模拟结果的比较,对方形石墨烯片的非局部参数进行了标定。该参数也可用于方形石墨烯片的其他非局部三维力学分析,以找到准确的解。
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引用次数: 1
Theoretical analysis of SWCNT- MWCNT/ H 2 O hybrid flow over an upward/downward moving rotating disk SWCNT- MWCNT/ h2o在上下旋转圆盘上混合流动的理论分析
R. J. P. Gowda, R. Naveenkumar, J. Madhukesh, B. Prasannakumara, R. Gorla
The flow-through various disk movement has wide range of applications in manufacturing processes like, computer storage equipment’s, rotating machines, electronic and various types of medical equipment’s. Inspired from these applications, here we scrutinised the consequences of homogeneous-heterogeneous reactions and uniform heat source/sink on the three-dimensional (3D) hybrid SWCNT-MWCNT’s flow on time dependent moving upward/downward rotating disk. The renowned innovation of this paper is the application of the hybrid nanofluid made up of SWCNT and MWCNT’s. Heat generation/absorption effect for the disk that does not move up or down creates a dual flow on the disk. Alternatively, the rotation and upright motion of the disk creates a 3D flow on the surface which has not been considered in the open literature. The modelled PDE’s are reduced in to ODE’s by opting suitable similarity variables and boundary constraints. Here, we used RKF-45 method to obtain the numerical approximations by adopting shooting technique. The analysis of rate of heat transfer is done through graphs. Further, change in velocity, thermal and concentration profiles for various non-dimensional parameters are deliberated briefly and illustrated with the help of suitable plots. The results reveal that, the, rise in values of homogeneous and heterogeneous reaction parameters improve the rate of reaction which results in reduction of the distribution rate and diminishes the concentration gradient. An increase in expansion/contraction parameter enhances the velocity and thermal gradients.
通过各种磁盘运动的流动在制造过程中有广泛的应用,如计算机存储设备,旋转机械,电子和各种类型的医疗设备。受这些应用的启发,我们仔细研究了均相-非均相反应和均匀热源/汇对三维(3D)混合swcnts - mwcnt随时间向上/向下旋转圆盘流动的影响。本文最著名的创新之处在于将单壁碳纳米管与多壁碳纳米管混合制成纳米流体。不上下移动的磁盘产生热量/吸收效应在磁盘上产生双重流动。另外,磁盘的旋转和垂直运动在表面上产生3D流,这在公开文献中尚未考虑。通过选择合适的相似性变量和边界约束,将模型的偏微分方程简化为偏微分方程。在这里,我们使用RKF-45方法,采用射击技术获得数值近似。用图表分析了传热速率。此外,还简要讨论了各种无量纲参数的速度、温度和浓度变化曲线,并用合适的图加以说明。结果表明,均相和非均相反应参数值的增大使反应速率加快,从而使分布速率降低,浓度梯度减小。膨胀/收缩参数的增大增大了速度梯度和热梯度。
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引用次数: 17
Magneto convective flow of casson nanofluid due to Stefan blowing in the presence of bio-active mixers 生物活性混合剂存在下,Stefan吹入卡森纳米流体的磁控对流
V. Puneeth, S. Manjunatha, B. J. Gireesha, R. Gorla
The induced magnetic field for three-dimensional bio-convective flow of Casson nanofluid containing gyrotactic microorganisms along a vertical stretching sheet is investigated. The movement of these microorganisms cause bioconvection and they act as bio-active mixers that help in stabilising the nanoparticles in the suspension. The two forces, Thermophoresis and Brownian motion are incorporated in the Mathematical model along with Stefan blowing. The resulting model is transformed to ordinary differential equations using similarity transformations and are solved using RKF − 45 method. The Velocity, Induced Magnetic field, Temperature, Concentration of Nanoparticles, and Motile density profiles are interpreted graphically. It is observed that the Casson parameter decreases the flow velocity and enhances the temperature, concentration, and motile density profiles and also it is noticed that the blowing enhances the nanofluid profiles whereas, suction diminishes the nanofluid profiles. On the other hand, it is perceived that the rate of heat conduction is enhanced with Thermophoresis and Brownian motion.
研究了含陀螺定向微生物的卡森纳米流体沿垂直拉伸片的三维生物对流的感应磁场。这些微生物的运动引起生物对流,它们作为生物活性混合器,有助于稳定悬浮液中的纳米颗粒。热泳动和布朗运动两种力与斯蒂芬吹气一起被纳入数学模型。使用相似变换将所得模型转换为常微分方程,并使用RKF−45方法求解。速度、感应磁场、温度、纳米粒子浓度和运动密度曲线用图形解释。观察到,卡森参数降低了流速,增强了温度、浓度和运动密度分布,还注意到吹气增强了纳米流体分布,而吸力减弱了纳米流体分布。另一方面,热泳动和布朗运动使热传导率提高。
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引用次数: 12
期刊
Proceedings of the Institution of Mechanical Engineers Part N-Journal of Nanomaterials Nanoengineering and Nanosystems
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