Size-dependent effects on critical flow velocity of fluid-conveying microtubes via nonlocal strain gradient theory

Size-dependent Timoshenko and Euler–Bernoulli models are derived for fluid-conveying microtubes in the framework of the nonlocal strain gradient theory. The equations of motion and boundary conditions are deduced by employing the Hamilton principle. A flow-profile-modification factor, which is related to the flow velocity profile, is introduced to consider the size-dependent effects of flow. The analytical solutions of predicting the critical flow velocity of the microtubes with simply supported ends are derived. By choosing different values of the nonlocal parameter and the material length scale parameter, the critical flow velocity of the nonlocal strain gradient theory can be reduced to that of the nonlocal elasticity theory, the strain gradient theory, or the classical elasticity theory. It is shown that the critical flow velocity can be increased by increasing the flexural rigidity, decreasing the length of tube, decreasing the mass density of internal flow, or increasing the shear rigidity. The critical flow velocity can generally increase with the increasing material length scale parameter or the decreasing nonlocal parameter. The flow-profile-modification factor can decrease the critical flow velocity. The critical flow velocity predicted by classical elasticity theory is generally larger than that of nonlocal strain gradient theory when considering the size-dependent effect of flow.     

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.     

Wave propagation in double-walled carbon nanotube conveying fluid considering slip boundary condition and shell model based on nonlocal strain gradient theory

In this paper, wave propagation in fluid-conveying double-walled carbon nanotube (DWCNT) was investigated by using the nonlocal strain gradient theory. In so doing, the shear deformable shell theory was used, taking into consideration nonlocal and material length scale parameters. The effect of van der Waals force between the two intended walls and the DWCNT surroundings was modeled as Winkler foundation. The classical governing equations were derived from Hamilton’s principle. Results were validated by comparing them to the results of the references obtained through molecular dynamic method, and a remarkable consistency was found between the results. According to the findings, the effects of nonlocal and material length scale parameters, wave number, fluid velocity and stiffness of elastic foundation are more considerable in the nonlocal strain gradient theory than in classical theory.     

Cylindrical functionally graded shell model based on the first order shear deformation nonlocal strain gradient elasticity theory

Microsystem Technologies - In this article, a cylindrical functionally graded shell model is developed in the framework of nonlocal strain gradient theory for the first time. For this purpose, the...     

Size dependency in nonlinear instability of smart magneto-electro-elastic cylindrical composite nanopanels based upon nonlocal strain gradient elasticity

In the present article, a new size-dependent panel model is established incorporating the both hardening-stiffness and softening-stiffness small scale effects jointly with electrostatics and magnetostatics to study analytically the buckling and postbuckling behavior of smart magneto-electro-elastic (MEE) composite nanopanels under combination of axial compression, external electric and magnetic potentials. To this end, the nonlocal strain gradient elasticity theory in conjunction with the Maxwell equations is applied to the classical panel theory to develop a more comprehensive size-dependent panel model including simultaneously the both nonlocality and strain gradient size dependency. With the aid of the virtual work’s principle, the size-dependent differential equations of the problem are derived. The attained non-classical governing differential equations are solved analytically by means an improved perturbation technique within the framework of the boundary layer theory of shell buckling. Explicit analytical expressions associated with the nonlinear axial stability equilibrium paths of the electromagnetic actuated smart MEE composite nanopanels including nonlocality and strain gradient micro-size dependency are proposed. It is displayed that the nonlocal size effect leads to reduce the buckling stiffness, while the strain gradient size dependency causes to enhance it. Moreover, it is found that by applying a negative electric field as well as positive magnetic field, the influences of the nonlocal and strain gradient size effects on the critical buckling load of an axially loaded MEE composite nanopanel are more significant.

     

Size-dependent nonlinear bending behavior of porous FGM quasi-3D microplates with a central cutout based on nonlocal strain gradient isogeometric finite element modelling

Engineering with Computers - With the aid of the non-uniform rational B-spline (NURBS)-based isogeometric technique, for the first time, the size-dependent geometrically nonlinear bending...     

Random vibrations of functionally graded nanobeams based on unified nonlocal strain gradient theory

Microsystem Technologies - In present study the dynamic response of a functionally graded nanobeam supported by visco-elastic foundation to a stationary random excitation, based on non-local strain...     

Adaptive registration of magnetic resonance images based on a viscous fluid model

This paper develops a new viscous fluid registration algorithm that makes use of a closed incompressible viscous fluid model associated with mutual information. In our approach, we treat the image pixels as the fluid elements of a viscous fluid governed by the nonlinear Navier–Stokes partial differential equation (PDE) that varies in both temporal and spatial domains. We replace the pressure term with an image-based body force to guide the transformation that is weighted by the mutual information between the template and reference images. A computationally efficient algorithm with staggered grids is introduced to obtain stable solutions of this modified PDE for transformation. The registration process of updating the body force, the velocity and deformation fields is repeated until the mutual information reaches a prescribed threshold. We have evaluated this new algorithm in a number of synthetic and medical images. As consistent with the theory of the viscous fluid model, we found that our method faithfully transformed the template images into the reference images based on the intensity flow. Experimental results indicated that the proposed scheme achieved stable registrations and accurate transformations, which is of potential in large-scale medical image deformation applications.     

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.     

Frequency analysis of nanoporous mass sensors based on a vibrating heterogeneous nanoplate and nonlocal strain gradient theory

Microsystem Technologies - A new modeling of nano-mechanical mass sensors constructed from porous nanomaterials is presented based on generalized nonlocal strain gradient theory (NSGT). In this...     

Damping vibration behavior of visco-elastically coupled double-layered graphene sheets based on nonlocal strain gradient theory

Microsystem Technologies - This paper develops a nonlocal strain gradient plate model for damping vibration analysis of visco-elastically coupled double-layered graphene sheets. For more accurate...     

基于GVF的骨架snake模型

提出了一种基于梯度矢量流(GVF)的快速收敛骨架snake算法。首先利用GVF变换后凹腔内外力的特点检测出物体的骨架,然后以骨架作为指引修改其外力的方向和大小,以达到快速收敛。该算法不但能解决GVF不能解决的深凹腔问题,而且在速度上也远远超过GVF。     

Nonlinear analysis of size-dependent frequencies in porous FG curved nanotubes based on nonlocal strain gradient theory

A nonlocal strain gradient model is developed in this research to analyse the nonlinear frequencies of functionally graded porous curved nanotubes. It is assumed that the curved nanotube is in contact with a two-parameter nonlinear elastic foundation and is also subjected to the uniform temperature rise. The non-classical theory presented for curved nanotubes contains a nonlocal parameter and a material length scale parameter which can capture the size effect. A power law distribution function is used to describe the graded properties through the thickness direction of curved nanotubes. The even dispersion pattern is used to model the porosities distribution. The high-order shear deformation theory and the von Kármán type of geometric non-linearity are utilized to obtain the nonlinear governing equations of the structure. The size-dependent equations of motion for the large amplitude vibrations of curved nanotubes are obtained by employing Hamilton’s principle. The analytical solutions are extracted for the curved nanotube with immovable hinged-hinged boundary conditions. Size-dependent frequencies of the curved nanotube exposed to thermal field are obtained using the two-step perturbation technique and Galerkin procedure. The effects of important parameters such as nonlocal and length scale parameters, temperature field, elastic foundation, porosity, power law index and geometrical parameters are studied in detail.

     

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.

     

Numerical fluid loading coefficients for the modal velocities of a cylindrical shell

The generalized fluid loading coefficients for the modal velocities of a simply-supported shell section are defined and formulated. The simplified nature of infinite cylindrical coordinates is employed in the geometry of interaction by assuming the predominance radial effects in a baffled extension of the finite shell. An efficient numerical procedure for the computational evaluation of the integrals which define the direct and cross mode components of the fluid impedance is presented and applied. The approach and illustrated results are directly applicable in the combined solution of shell and fluid interaction problems.     

A thin cylindrical shell finite element based on a mixed formulation

A specialized functional for thin cylindrical shells derived from the Washizu-Hu variational principle using considerations of relaxed continuity requirements is presented. A mixed formulation for a cylindrical thin shell finite element is developed from this functional. The assumed fields for displacements and stress resultants are bilinear functions in the longitudinal and circunferential directions.The agreement between the present results and those obtained in previous formulations is good if the comparison is based on the precision related to the number of variables involved in the problem.     

Dynamic transverse vibration characteristics and vibro-buckling analyses of axially moving and rotating nanobeams based on nonlocal strain gradient theory

Microsystem Technologies - Dynamic transverse vibration characteristics and vibro-buckling analyses of axially moving nanobeam and rotating nanobeam based on nonlocal strain gradient theory are...     

微型Mindlin板非线性动力学模型的建立

随着MEMS技术工艺的发展,微型结构在工程领域的应用越来越广泛.对于微型结构,经典连续介质力学理论的本构关系中不包含任何特征长度尺度,不能反映结构在微米尺度下的尺寸效应.本文基于Von Karman大变形理论和一阶剪切变形理论,把考虑尺寸效应的应变梯度理论推广至微型Mindlin板的非线性问题.分别计算微结构的应变能,包括宏观变形应变能和微观变形应变能两部分,结合微型Mindlin板结构的动能及外力功,代入Hamilton原理,得到了微型Mindlin板在大变形情况下的非线性动力学方程及边界条件.     

Analysis of nonlinear vibration and instability of electrostatic functionally graded micro-actuator based on nonlocal strain gradient theory considering thickness effect

Microsystem Technologies - In this work, we develop a model of an electrostatic functionally graded (FG) micro-actuator based on the nonlocal strain gradient theory (NSGT) incorporated the...