Forced vibrations of fluid-conveyed double piezoelectric functionally graded micropipes subjected to moving load

This article is aimed to study the forced vibrations of double piezoelectric functionally graded material micropipes conveying fluid carrying a moving load based on the flexoelectricity theory and modified couple stress theory. The two micropipes are identical and are connected with each other continuously by visco-Pasternak medium. The top micropipe is traversed by a load and is labeled as the primary micropipe. The bottom micropipe is labeled as the secondary micropipe. Non-classical governing equations together with corresponding boundary conditions based on the Hamilton’s principle are obtained and then solved by differential quadrature and Runge–Kutta methods. The influences of the material gradient index, length scale parameter, potential electrical, visco-Pasternak foundation, fluid velocity, various boundary conditions, velocity of the moving load and flexoelectric effect on the dimensionless dynamic deflections of system are discussed. The results show that the flexoelectric and piezoelectric effects tend to increase/decrease the dimensionless dynamic deflections of the primary/secondary pipe, respectively. In addition, the effects of spring constant, shear constant and damping coefficient of the visco-Pasternak medium on the dynamic displacement of the primary and secondary micropipes are vice versa.     

Critical rotational speed,critical velocity of fluid flow and free vibration analysis of a spinning SWCNT conveying viscous fluid

In this article, the influences of rotational speed and velocity of viscous fluid flow on free vibration behavior of spinning single-walled carbon nanotubes (SWCNTs) are investigated using the modified couple stress theory (MCST). Taking attention to the first-order shear deformation theory, the modeled rotating SWCNT and its equations of motion are derived using Hamilton’s principle. The formulations include Coriolis, centrifugal and initial hoop tension effects due to rotation of the SWCNT. This system is conveying viscous fluid, and the related force is calculated by modified Navier–Stokes relation considering slip boundary condition and Knudsen number. The accuracy of the presented model is validated with some cases in the literatures. Novelty of this study is considering the effects of spinning, conveying viscous flow and MCST in addition to considering the various boundary conditions of the SWCNT. Generalized differential quadrature method is used to approximately discretize the model and to approximate the equations of motion. Then, influence of material length scale parameter, velocity of viscous fluid flow, angular velocity, length, length-to-radius ratio, radius-to-thickness ratio and boundary conditions on critical speed, critical velocity and natural frequency of the rotating SWCNT conveying viscous fluid flow are investigated.     

GDQR法用于输流曲管的流致振动研究

将广义微分求积法(GDQR)用于分析输流曲管的流致振动问题,这是一个新的尝试．基于输流曲管的面内振动微分方程,利用GDQR法使曲管系统在空间域上得以离散化,从而获得了输流曲管的动力学方程组．数值算例中,计算得到了输流曲管在几种典型边界条件下的固有频率以及曲管发生失稳的临界流速等,这些计算结果与前人的解析解结果吻合较好．此外,还给出了两端固定输流曲管典型的动力响应行为．研究表明,GDQR法极易处理输流曲管这一类动力学模型,精度令人满意,进一步的研究可望推广到输流管道的非线性振动分析中．     

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.     

微尺度悬臂管颤振的研究

本文基于修正的偶应力理论并考虑Lagrange应变张量所给出的几何非线性,运用Hamilton原理建立了微悬臂管的平面振动微分方程.通过对线性方程的特征值分析,得到了微管的前四阶复频率及临界流速—质量比曲线(临界流速曲线)对材料长度尺寸参数的依赖关系;并且发现宏观管和微尺度管(或者具有不同材料长度尺寸参数的微管)的临界流速曲线可能会相交.运用基于中心流形—范式理论的投影法,计算了临界流速处系统的第一李雅普诺夫系数和退化特征值关于流速的变化率,以此为基础论证了分岔的超临界性质;并对临界流速曲线上的滞后部分及不同尺度管的该曲线的交点处的动力学性质作了探讨,发现了不同的分岔方向.     

A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate

The static bending behavior of porous functionally graded (PFG) micro-plate under the geometrically nonlinear analysis is studied in this article. A small-scale nonlinear solution is established using the Von-Kármán hypothesis and the modified couple stress theory (MCST). To obtain the deflection of the plate, the Reddy higher-order plate theory coupled with isogeometric analysis (IGA) is utilized. The distribution of porosities is assumed to be even and uneven across the plate’s thickness and the effective material properties of porous functionally graded micro-plate are calculated using the refined rule-of-mixture hypothesis. The influence of power index, porosity parameter and material length scale parameter on the nonlinear behaviors of static bending of porous FGM micro-plates are also investigated using several numerical examples.

     

分析两端扭转弹簧约束下简支输流管道的动力特性

研究了两端受扭转弹簧约束的简支输流管道的固有频率特性和静态失稳临界流速.根据梁模型横向弯曲振动模态函数,由端部支承和约束边界条件得到了其模态函数的一般表达式.根据动力方程的特征方程,具体分析了约束弹性刚度、流体压强、流速和管截面轴向力等参数对管道固有频率特性和静态失稳临界流速的影响.数值分析表明,约束弹性刚度的增大使管道的固有频率和失稳临界流速明显提高;流体流速、压强和管截面受到的轴向压力的增加使管道的固有频率和失稳临界流速降低.当管道的固有频率和失稳临界流速较低时,可以通过增加端部约束的方法来提高.     

两端固定输流管振动实验研究

通过实验的方法对简谐激励和脉动流作用下的两端固定输流管的动力学行为进行振动测试分析.设计并制作了两端固定输流管的振动实验装置,为确保实验结果翔实可靠,选取三种不同材料的管分别进行了三次实验,研究了管内流体流速、激振力振幅和脉动流频率对两端固定输流管振动特性的影响.结果表明,流体流速和激振力幅值对两端固定输流管的一阶共振特性和振动幅值有着显著影响,在脉动流作用下,两端固定输流管存在混沌运动,并且随着脉动频率的增大,管道平均振幅减小.     

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.     

Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell

In this research, thermal buckling and forced vibration characteristics of the imperfect composite cylindrical nanoshell reinforced with graphene nanoplatelets (GNP) in thermal environments are presented. Halpin–Tsai nanomechanical model is used to determine the material properties of each layer. The size-dependent effects of GNPRC nanoshell is analyzed using modified couple stress theory. For the first time, in the present study, porous functionally graded multilayer couple stress (FMCS) parameter which changes along the thickness is considered. The novelty of the current study is to consider the effects of porosity, GNPRC, FMCS and thermal environment on the resonance frequencies, thermal buckling and dynamic deflections of a nanoshell using FMCS parameter. The governing equations and boundary conditions are developed using Hamilton’s principle and solved by an analytical method. The results show that, porosity, GNP distribution pattern, modified couple stress parameter, length to radius ratio, mode number and the effect of thermal environment have an important role on the resonance frequencies, relative frequency change, thermal buckling, and dynamic deflections of the porous GNPRC cylindrical nanoshell using FMCS parameter. The results of current study can be useful in the field of materials science, micro-electro-mechanical systems and nano electromechanical systems such as microactuators and microsensors.

     

Experimental investigation on size-dependent higher-mode vibration of cantilever microbeams

A new perspective is presented to study size-dependent elasticity experimentally within micron scale utilizing dynamic approach. The size-dependent vibration of cantilever microbeams made of nickel is studied for the first three transverse modes. The normalized natural frequency of the first mode manifests strong size effect as reported. Remarkably, the normalized natural frequencies of the second and third mode also increase to 1.9 times as the thickness of microbeams decreases from 15 to 2.1 μm. Similarly the normalized bending rigidity increases to about 3.5 times. It is the first time that elastic size effect is observed in vibration of higher modes. Moreover, the size-dependent vibration of the first mode is interpreted in light of the modified couple stress theory, and the theoretical prediction also fit the experimental results of high modes very well. Hence it is confirmed that modified couple stress theory is valid for vibration of higher modes too.

     

变流速输液管的周期和混沌振动

研究了参数激励和外激励联合作用下输流管道的非线性振动问题．只考虑管道变形的几何非线性因素,利用Hamilton原理得到单侧受简谐均布载荷作用下输液管的非线性动力学方程,对系统运动偏微分方程综合运用多尺度法和Galerkin离散方法,得到了主参数共振-1／2亚谐共振和1：2内共振情况下的平均方程．数值模拟结果表明参数激励和外激励联合作用下的悬臂输液管呈现周期运动、多倍周期运动和混沌运动的变化规律．     

输流管道动力学与控制的最新进展

管道系统在航空航天, 石油输送, 深海探测, 核能工程等工程领域发挥着输送流体的作用.由于复杂结构功能设计、支承条件、内部流体和外部环境等因素引起输流管道中的流体和管道发生强烈地耦合,导致的动力学问题严重限制了输流管道在各种领域中的工程应用.因此,输流管道的复杂动力学行为引起了工程和科学领域学者们的广泛关注, 本文综述和讨论了最新的输流管道振动与控制的研究和进展.     

Eigenvalue branches and modes for flutter of cantilevered pipes conveying fluid

This paper describes the relationship between the eigenvalue branches and the corresponding unstable modes associated with flutter of cantilevered pipes conveying fluid. The order of branches in root locus diagrams is clearly defined. The flutter configuration of the pipes at the critical flow velocities are drawn graphically at every 12th period to define the order of quasi-mode of flutter configuration. The transferences of flutter-type instability from one eigenvalue branch to another are thoroughly investigated and discussed in case of continuous pipes conveying fluid. The critical mass ratios, at which the transference of the eigenvalue branches related to flutter take place, are definitely determined.     

输流管道弯曲和振动的有限元分析

基于Timoshenko梁理论,利用虚功原理严格地建立了输流管道弯曲和振动的有限元方程.利用加速度合成定理推导了流体横向加速度的表达式,计算了两端简支和悬臂两种边界条件下管道受到重力和流体作用时的挠度和转角,分析了流体流速对其影响.两端简支条件下将预应力效应整合到管道应变能中,并讨论了轴向预应力与弯曲挠度的关系.给出了两种边界条件下管道自由振动的前三阶固有频率与流体流速的关系,分析了两端简支条件下管道轴向预应力对振动固有频率的影响.结果表明：两端简支边界条件下,流体速度增大则挠度和转角相应增大,预应力使得挠度和转角减小;前三阶固有频率随流速增大而减小,预应力增大则导致各阶固有频率增大.悬臂边界条件下,流体速度增大则挠度和转角减小,前三阶固有频率随流速增大而减小.     

Pulsatile vibrations of viscoelastic microtubes conveying fluid

In this paper, the pulsatile coupled vibrations of a viscoelastic microtube conveying pulsatile fluid is examined for the first time. The problem is grouped into the class of parametrically excited, internally damped, gyroscopic where both Coriolis and parametric forces are present in the presence of viscosity. The Kelvin–Voigt approach of the viscosity, the Euler–Bernoulli for the deformation, the modified couple stress theory for the small size, and Hamilton’s principle for deriving differential equations are used. Parametric frequency–response curves are obtained in the vicinity of the parametric resonance near the critical speed for both subcritical and supercritical regimes. The effect of the flow pulsation on the oscillations is investigated.

     

Nonlinear resonance responses of size-dependent functionally graded cylindrical microshells with thermal effect and elastic medium

The nonlinear resonance responses of functionally graded (FG) cylindrical microshells with the elastic medium is investigated by considering thermal and scale effects. First, using the modified couple stress theory, the nonlinear dynamics model for FG microshell are established. Then the reduced nonlinear differential equations are derived by Galerkin’s method and static condensation. Finally, subharmonic, superharmonic and primary resonances of FG cylindrical microshells are analyzed by a perturbation method. In addition, the bifurcation characteristics of the nonlinear dynamic responses are investigated by some numerical examples. The effects of key parameters (modal damping, excitation frequency, foundation medium, scale parameter and thermal effect) on the nonlinear resonance responses are also discussed by numerical simulation.

     

Parametric studies of coupled vibration of cylindrical pipes conveying fluid with the wave propagation approach

The wave propagation approach is extended to the coupled frequency analysis of finite cylindrical pipes conveying dense fluid. The downstream, upstream and mixed frequencies of the pipe are defined and discussed. The effects of fluid and shell parameters on the coupled frequencies are investigated. The difference between the coupled and uncoupled frequencies decreases with the circumferential mode n, but increases with the mode n after the number n where the fundamental frequency is obtained. The fundamental frequency can change from one circumferential mode to another circumferential mode with the h/R ratios. However for a shorter shell the fundamental frequency may keep with the same mode n in the interested h/R ratios. For different boundary conditions the transition of fundamental frequency between circumferential modes occurs at different h/R ratios. The downstream frequency increases with increasing fluid velocity, whereas the upstream frequency decreases as the fluid velocity increases. However, the mixed frequency of the pipe decreases with the increase of the fluid velocity. For a given flow velocity all the three frequencies decrease with decreasing h/R ratios. However the mixed frequency drops more with increasing fluid velocity at small h/R ratios than at large h/R ratios. Therefore negative frequencies may occur for small h/R ratios if the fluid velocity is large enough, which means that instability occurs first for thinner pipes.     

基础激励作用下悬臂输流管的振动实验研究

通过实验的方法对基础激励作用下悬臂输流管的动力学行为进行振动测试分析.设计并搭建了悬臂输流管振动测试的实验平台,深入研究了悬臂输流管在不同流速及不同参数情况下的振动行为,分析了在基础激励作用下,悬臂输流管振幅的变化规律.结果表明,悬臂输流管的物理参数对悬臂输流管发生颤振失稳的临界流速有着极其显著的影响,在基础激励作用下,悬臂输流管的振幅明显增大,并且当激振力频率接近悬臂输流管的固有频率时,输流管的振幅达到最大.     

Postbuckling analysis of hydrostatic pressurized FGM microsized shells including strain gradient and stress-driven nonlocal effects

Herein, with the aid of the newly proposed theory of nonlocal strain gradient elasticity, the size-dependent nonlinear buckling and postbuckling behavior of microsized shells made of functionally graded material (FGM) and subjected to hydrostatic pressure is examined. As a consequence, the both nonlocality and strain gradient micro-size dependency are incorporated to an exponential shear deformation shell theory to construct a more comprehensive size-dependent shell model with a refined distribution of shear deformation. The Mori–Tanaka homogenization scheme is utilized to estimate the effective material properties of FGM nanoshells. After deduction of the non-classical governing differential equations via boundary layer theory of shell buckling, a perturbation-based solving process is employed to extract explicit expressions for nonlocal strain gradient stability paths of hydrostatic pressurized FGM microsized shells. It is observed that the nonlocality size effect causes to decrease the critical hydrostatic pressure and associated end-shortening of microsized shells, while the strain gradient size dependency leads to increase them. In addition, it is found that the influence of the internal strain gradient length scale parameter on the nonlinear instability characteristics of hydrostatic pressurized FGM microsized shells is a bit more than that of the nonlocal one.