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1.
The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions. The project supported by the National Natural Science Foundation of China (10272067), the Doctoral Program Foundation of the Education Ministry of China (20030422046), the Natural Science Foundation of Shandong Province, China (Y2006A14) and the Research Foundation of Shandong University at Weihai. The English text was polished by Keren Wang.  相似文献   

2.
The fractional calculus is used in the constitutive relationship model of viscoelastic fluid. A generalized Maxwell model with fractional calculus is considered. Based on the flow conditions described, two flow cases are solved and the exact solutions are obtained by using the Weber transform and the Laplace transform for fractional calculus.The project supported by the National Natural Science Foundation of China (10272067, 10426024), the Doctoral Program Foundation of the Education Ministry of China (20030422046) and the Natural Science Foundation of Shandong University at Weihai. The English text was polished by Keren Wang.  相似文献   

3.
广义Maxwell黏弹性流体在两平板间的非定常流动   总被引:2,自引:0,他引:2  
将分数阶微积分运算引入Maxwell黏弹性流体的本构方程,研究了黏弹性流体在两平板问的非定常流动.对于广义Maxwell黏弹性流体的分数阶导数模型,导出了对时间具有分数阶导数的特殊运动方程,利用分数阶微积分的Laplace变换理论,得到了流动的解析解.  相似文献   

4.
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid was introduced. The velocity and temperature fields of the vortex flow of a generalized second fluid with fractional derivative model were described by fractional partial differential equations. Exact analytical solutions of these differential equations were obtained by using the discrete Laplace transform of the sequential fractional derivatives and generalized Mittag-Leffier function. The influence of fractional coefficient on the decay of vortex velocity and diffusion of temperature was also analyzed.  相似文献   

5.
丙烯酸弹性体的率相关分数阶黏弹性模型研究   总被引:1,自引:0,他引:1  
丙烯酸弹性体VHB 4910作为一种重要的介电弹性体, 在软体机器人、致动器、俘能器和智能隔振器等领域有很好的应用前景. 但材料的非线性黏弹性对其力学行为有显著影响. 近来分数阶模型在复杂材料的建模中取得了成功. 本文基于分数阶有限变形Kelvin-Voigt流变学模型建立弹性体的三维张量本构, 并进一步推导单向拉伸情况下的本构关系. 随后对VHB 4910完成一系列不同拉伸速率下的单向拉伸实验. 基于本构方程的可加性, 首先分别利用Neo-Hookean, Mooney-Rivlin和Gent模型完成超弹性弹簧单元的参数识别, 随后完成可变阶数和固定阶数的分数阶模型的参数识别, 以探究弹性体材料分数阶本构关系的率相关性. 结果发现: Mooney-Rivlin模型弹簧模型的拟合精度最高; 两种拟合方式的分数阶模型均可以很好地模拟黏弹性弹性体的率相关黏弹性行为; 固定分数阶的阶数对模型拟合结果影响不大; 分数阶元件的黏性系数与伸长速率呈明显的非线性关系, 表明其具有非牛顿流体特性, 在此基础上, 发展一种修正的幂律定律来定量描述这种非线性关系, 该模型较Cross流体模型有更高的拟合精度.   相似文献   

6.
7.
The fractional calculus approach in the constitutive relationship model of a generalized second grade fluid is introduced. Exact analytical solutions are obtained for a class of unsteady flows for the generalized second grade fluid with the fractional derivative model between two parallel plates by using the Laplace transform and Fourier transform for fractional calculus. The unsteady flows are generated by the impulsive motion or periodic oscillation of one of the plates. In addition, the solutions of the shear stresses at the plates are also determined. The project supported by the National Natural Science Foundation of China (10372007, 10002003) and CNPC Innovation Fund  相似文献   

8.
分数阶黏弹性土层中分数阶三维轴对称桩的竖向振动   总被引:1,自引:0,他引:1  
将桩基和土体视为三维连续介质,桩基和土体的应力一应变关系采用分数阶黏弹性模型描述。在三维轴对称情况下,利用三维弹性理论和连续介质力学理论,运用分离变量法和分数阶导数的性质,得到了分数阶黏弹性土层中分数阶黏弹性桩基的三维轴对称解;并分析了相关参数对桩顸动态刚度和等效阻尼的影响。研究结果表明:与土体相比,桩基的相关参量对桩顶复刚度的影响较大;桩基和土体的密度比、模量比对桩顶复刚度都有较大的影响。  相似文献   

9.
The article describes the unsteady motion of viscoelastic fluid for a Maxwell model with fractional derivatives. The flow is produced by cylinder, considering time dependent quadratic shear stress ft2 on Maxwell fluid with fractional derivatives. The fractional calculus approach is used in the constitutive relationship of Maxwell model. By applying Laplace transform with respect to time t and modified Bessel functions, semianalytical solutions for velocity function and tangential shear stress are obtained. The obtained semianalytical results are presented in transform domain, satisfy both initial and boundary conditions. Our solutions particularized to Newtonian and Maxwell fluids having typical derivatives. The inverse Laplace transform has been calculated numerically. The numerical results for velocity function are shown in Table by using MATLAB program and compared them with two other algorithms in order to provide validation of obtained results. The influence of fractional parameters and material constants on the velocity field and tangential stress is analyzed by graphs.  相似文献   

10.
The fractional calculus approach in the constitutive relationship model of viscoelastic fluid is introduced. A generalized Maxwell model with the fractional calculus was considered. Exact solutions of some unsteady flows of a viscoelastic fluid between two parallel plates are obtained by using the theory of Laplace transform and Fourier transform for fractional calculus. The flows generated by impulsively started motions of one of the plates are examined. The flows generated by periodic oscillations of one of the plates are also studied.  相似文献   

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