Size-dependent effects on critical flow velocity of a SWCNT conveying viscous fluid based on nonlocal strain gradient cylindrical shell model

This article investigates vibration and instability analysis of a single-walled carbon nanotube (SWCNT) conveying viscous fluid flow. For this purpose, the first-order shear deformation shell model is developed in the framework of nonlocal strain gradient theory (NSGT) for the first time. The proposed model is a conveying viscous fluid in which the external force of fluid flow is applied by the modified Navier–Stokes relation and considering slip boundary condition and Knudsen number. The NSGT can be reduced to the nonlocal elasticity theory, strain gradient theory or the classical elasticity theory by inserting their specific nonlocal parameters and material length scale parameters into the governing equations. Comparison of above-mentioned theories suggests that the NSGT predicts the greatest critical fluid flow velocity and stability region. The governing equations of motion and corresponding boundary conditions are discretized using the generalized differential quadrature method. Furthermore, the effects of the material length scale, nonlocal parameter, Winkler elastic foundation and Pasternak elastic foundation on vibration behavior and instability of a SWCNT conveying viscous fluid flow with simply supported and clamped–clamped boundary conditions are investigated.     

CFD analysis of viscous non-Newtonian flow under the influence of a superimposed rotational vibration

The effects of a superimposed sinusoidal rotational vibration on the flow of non-Newtonian fluids in a tube are studied numerically by computational fluid dynamics (CFD). Inelastic time-independent fluids of the power law, Herschel-Bulkley, Bingham plastic, and Newtonian types are investigated. Newtonian flow is unchanged by any superimposed oscillations but the flow of non-Newtonian fluids is greatly affected. The flow of shear-thinning fluids and viscoplastic fluids is enhanced, whilst the flow of shear-thickening fluids is retarded. The effects of the various rheological as well as vibration parameters are studied in detail. Flow is affected by both vibration frequency and amplitude, but different amplitude-frequency combinations which correspond to the same peak acceleration result in the same effect. Mechanical vibration in the sonic range generates substantial flow enhancements in low to moderately viscous fluids, but has limited scope for highly viscous fluids. Mechanical vibration in the ultrasound range, however, has a good potential for the processing of highly viscous materials, being able to generate orders of magnitude enhancement in flow. The extent of flow enhancement achieved is also dependent on the nature of the superimposed vibration: a rotational oscillation produces more flow enhancement than a transversal oscillation, but less than a longitudinal oscillation.     

Dynamic stiffness formulation and free vibration analysis of a spinning composite beam

The dynamic stiffness matrix of a spinning composite beam is developed and then used to investigate its free vibration characteristics. Of particular interest in this study is the inclusion of the bending–torsion coupling effect that arises from the ply orientation and stacking sequence in laminated fibrous composites. The theory is particularly intended for thin-walled composite beams and does not include the effects of shear deformation and rotatory inertia. Hamilton’s principle is used to derive the governing differential equations, which are solved for harmonic oscillation. Exact expressions for the bending displacement, bending rotation, twist, bending moment, shear force and torque at any cross-section of the beam, are also obtained in explicit analytical form. The dynamic stiffness matrix, which relates the amplitudes of loads to those of responses at the end of the spinning beam in free vibration is then derived by imposing the boundary conditions. This enables natural frequency calculation of a spinning composite beam at various spinning speeds to be made by applying the Wittrick–Williams algorithm to the resulting dynamic stiffness matrix. The spinning speed at which the fundamental natural frequency tends to zero is the critical speed, which is established for a composite shaft that has been taken from the literature as an example. The results are discussed and some are compared with published ones. The paper concludes with some remarks.     

Nonlocal vibration and instability analysis of carbon nanotubes conveying fluid considering the influences of nanoflow and non-uniform velocity profile

In this article, the influences of non-uniform velocity profile attributable to slip boundary condition and viscosity of fluid on the dynamic instability of carbon nanotubes (CNTs) conveying fluid are investigated. The nonlocal elasticity theory and the Euler–Bernoulli beam theory are employed to derive partial differential equation of nanotubes conveying fluid. Furthermore, a dimensionless momentum correction factor (MCF) is obtained as a function of Knudsen number (Kn) so as to insert the effects of non-uniform velocity profile into the equation of motion. In continuation, complex eigen-frequencies of the system are attained with respect to different boundary conditions, the momentum correction factor, slip boundary condition and nonlocal parameter. The results delineate that considering the effects of non-uniform velocity profile could diminish predicted critical velocity of flow. Therefore, the divergence instability occurs in the lower values of flow velocity. In addition, the MCF decreases through enhancement of Kn; hence, the effects of non-uniform velocity profile are more noticeable for liquid fluid than gas fluid.     

Finite element analysis of viscous fluid flow

A finite element model for the analysis of two dimensional viscous flows is formulated using the virtual work method. The model is in part based on a finite element shell model, using the same reduced integration of quadratic interpolations for all variables[1]. Differences from preceding formulations are that integration by parts is applied to the continuity equation, yielding different loading terms which are more easily defined in some problems, and a new approach is used for the convective inertia terms, giving a clearer interpretation of their effects which are distributed to both sides of the nonlinear recurrence relation. In the case of compressible flow, for which comparatively few formulations have been proposed to date, the thermal energy equation is used to form a two stage solution and here this seems the most natural and economical approach.     

Size-dependent vibration analysis of multi-span functionally graded material micropipes conveying fluid using a hybrid method

Microscale fluid-conveying pipes and functionally graded materials (FGMs) have many potential applications in engineering fields. In this paper, the free vibration and stability of multi-span FGM micropipes conveying fluid are investigated. The material properties of FGM micropipes are assumed to change continuously through thickness direction according to a power law. Based on modified couple stress theory, the governing equation and boundary conditions are derived by applying Hamilton’s principle. Subsequently, a hybrid method which combines reverberation-ray matrix method and wave propagation method is developed to determine the natural frequencies, and the results determined by present method are compared with those in the existing literature. Then, the effects of material length scale parameter, volume fraction exponent, location and number of supports on dynamic characteristics of multi-span FGM micropipes conveying fluid are discussed. The results show that the size effect is significant when the diameter of micropipe is comparable to the length scale parameter, and the natural frequencies determined by modified couple stress theory are larger than those obtained by classical beam theory. It is also found that natural frequencies and critical velocities increase rapidly with the increase of volume fraction exponent when it is less than 10, and the intermediate supports could improve the stability of pipes conveying fluid significantly.     

Finite element analysis of viscous,incompressible fluid flow: Part 2: Applications

The first part of this paper described a general numerical procedure for the analysis of two-dimensional flows of viscous, incompressible fluids, using the finite element method. A number of special computational procedures were also discussed that allowed significant reductions to be made in the computational effort required in the solution of problems. The present paper is devoted to demonstrating the utility of the methods described by the solution of several example problems. The illustrative examples consist of flow in a plane 90° T, flow in a cavity and flow around a circular cylinder.     

考虑内流压力时输流曲管的混沌运动及其抑制模型

考虑内部流体压力因素的影响,研究了具有非线性运动约束输流曲管的混沌运动及其抑制模型.首先,在输流曲管的运动微分方程中计入流体压力作用项,并采用微分求积法对此方程进行离散化处理.然后,通过数值迭代计算,分析了在流体压力这一参数区域内曲管的多种运动形态(包括混沌运动).研究表明,流体压力因素对曲管的动力响应有较大的影响,在实际工程中应给予充分考虑.在此基础之上,提出了一种曲管的混沌抑制模型,有效的消除了系统的混沌运动.     

Finite element analysis of viscous,incompressible fluid flow: Part 1 : Basic methodology

A numerical procedure is developed for the analysis of general two-dimensional flows of viscous, incompressible fluids using the finite element method. The partial differential equations describing the continuum motion of the fluid are discretized by using an integral energy balance approach in conjunction with the finite element approximation. The nonlinear algebraic equations resulting from the discretization process are solved using a Picard iteration technique.A number of computational procedures are developed that allow significant reductions to be made in the computational effort required for the analysis of many flow problems. These techniques include a coarse-to-fine-mesh rezone procedure for the detailed study of regions of particular interest in a flow field and a special finite element to model far-field regions in external flow problems.     

圆管绕流旋涡脱落诱导振动的数值模拟

利用计算流体力学软件Ansys／Flotran CFD,首先对粘性不可压缩流体的固定圆管绕流进行了数值模拟,然后结合逐步积分法完成了同时考虑纵横两向弹性支撑圆管绕流旋涡脱落诱导振动的数值模拟,并通过快速傅立叶变换,得到了弹性支撑圆管和固定圆管的升力及弹性支承圆管横向位移响应的功率谱．通过计算结果分析,得出了一些有价值的结论,可供从事具有圆管绕流构件设备设计的工程技术人员参考．     

Stability analysis of a pipe conveying fluid with a nonlinear energy sink

This paper considers the global stability problem of the system comprising a pipe conveying fluid and a nonlinear energy sink (PCF-NES) system.First,a quadratic...     

Parametric excitation analysis of a piezoelectric-nanotube conveying fluid under multi-physics field

Microsystem Technologies - In this study, nonlinear vibration of a carbon nanotube conveying fluid is investigated. The nanotube is covered by a piezoelectric layer and is subjected to a magnetic...     

Free vibration and critical angular velocity of a rotating variable thickness two-directional FG circular microplate

Microsystem Technologies - In this paper, the free vibration of a rotating variable thickness two-directional FG circular microplate is studied. The governing equations of motion for the microplate...     

Non-coaxial rotating flow of viscous fluid with heat and mass transfer

Heat and mass transfer in unsteady non-coaxial rotating flow of viscous fluid over an infinite vertical disk is investigated. The motion in the fluid is induced due to two sources. Firstly, due to the buoyancy force which is caused because of temperature and concentration gradients. Secondly, because of non-coaxial rotation of a disk such that the disk executes cosine or since oscillation in its plane and the fluid is at infinity. The problem is modeled in terms of coupled partial differential equations with some physical boundary and initial conditions. The dimensionless form of the problem is solved via Laplace transform method for exact solutions. Expressions for velocity field, temperature and concentration distributions are obtained, satisfying all the initial and boundary conditions. Skin friction, Nusselt number and Sherwood number are also evaluated. The physical significance of the mathematical results is shown in various plots and is discussed for several embedded parameters. It is found that magnitude of primary velocity is less than secondary velocity. In limiting sense, the present solutions are found identical with published results.

     

旋转Timoshenko输流管道的固有频率和稳定性分析

基于Timoshenko梁模型,本文研究了旋转输流管道在自由振动状态下的流固耦合振动特性.考虑流体压力、重力、初始轴应力作用,基于Hamilton原理和欧拉角转换,推导得到了旋转Timoshenko输流管道的偏微分方程.根据Galerkin截断法将运动方程进行离散,通过求解系统的特征方程即可得到输流管一阶复频率的实部和虚部,实部代表固有频率,虚部代表能量变化.在流速较高时,研究发现必须考虑4阶及以上Galerkin截断,才能得到稳定的结果.通过与EulerBernoulli梁模型对比,验证了本文的结果正确性.研究发现针对短粗型管道,Timoshenko梁模型更加精确.此外研究了多种参数对旋转Timoshenko输流管道固有频率和振动稳定性的影响.研究结果表明质量比、流速、剪切系数对Timoshenko输流管道流固耦合振动的稳定性影响显著,而转动惯量、重力、流体压力和初始轴应力在一定程度上也会影响管道振动的频率和稳定性.转速的出现将管道频率分为两个量值,但转速并不影响系统能量变化.     

Finding leading modes of a viscous free surface flow: An asymmetric generalized eigenproblem

Stability of steady, two-dimensional, slide coating flow of Newtonian liquid to small, two-dimensional disturbances is analyzed by means of Galerkin's method and finite element basis functions. The resulting sequence of computational problems consists of large, sparse, asymmetric generalized eigenproblemsJx= Mx in whichJ andM depend on system parameters andM is singular. These are solved for the leading modes—eigenvalues of algebraically largest real part, and their eigenvectors—by a flexible method assembled from the iterative Arnoldi algorithm with Schur-Wielandt deflation developed by Saad for the asymmetric eigenproblem; initialization that takes advantage of continuation and can incorporate rational acceleration; complex or real shift of eigenvalue, as appropriate; and—a key ingredient-approximately exponential preconditioning by rational transformation suitable to the singular behavior. The results include leading modes of complicated structure, examples of mode overtaking, turning points beyond which the steady flows do not exist, and Hopf points that mark onset of deleterious, spontaneous oscillations of the flow.     

转子通过临界转速时碰摩热效应对振动特性的影响

转子-定子之间的碰撞与摩擦是一个危害性很大的现象,也是十分复杂的物理过程．这一过程消耗的机械能,绝大部分生成热能．尽管每次碰撞与摩擦的热效应对转子影响很小,但是由于热量的散失相对于转子的振动来说是一个较慢的过程,一旦出现较频繁的碰摩,热载荷的累积效应是不容忽视的．转子通过临界转速时,如果振动幅度过大就会导致碰摩．碰撞引起转子振动相位的变化,而碰摩产生的热挠曲将会延长碰摩过程．在建立了转子与定子之间的弹性碰撞接触、摩擦和热传导的简化模型的基础上,应用数值方法分析了转子通过临界转速时上述碰摩过程的一个简单例子．     

On a finite dynamic element method for free vibration analysis of structures

This paper explores the concept of finite dynamic elements involving higher order dynamic correction terms in the associated stiffness and mass matrices. Such matrices are then developed for a rectangular prestressed membrane element. Next, efficient analysis techniques for the eigenproblem solution of the resulting quadratic matrix equations are described in detail. These are followed by suitable numerical examples which indicate that employment of such dynamic elements in conjunction with an efficient quadratic matric solution technique will result in a most significant economy in the free vibration analysis of structures.