A parametric study on nonlinear flow-induced dynamics of a fluid-conveying cantilevered pipe in post-flutter region from macro to micro scale

A mathematical formulation is proposed to investigate the nonlinear flow-induced dynamic characteristics of a cantilevered pipe conveying fluid from macro to micro scale. The model is developed by using the extended Hamilton's principle in conjunction with the inextensibility condition and laminar and turbulent flow profiles as well as modified couple stress theory. The current model is capable of recovering the classical model of cantilevered pipe conveying fluid by neglecting the couple stress effect. The governing equation of motion is presented in dimensionless form in a convenient and usable manner. To solve the problem at hand, the integro-partial-differential equation of motion is discretized into a set of ordinary differential equations via Galerkin method. Afterward, a Runge–Kutta's finite difference scheme is employed to evaluate the nonlinear dynamic response of the cantilevered pipe conveying fluid. A parametric study is carried out to examine the influences of mass parameter and dimensionless mean flow velocity on the nonlinear dynamic characteristics of the cantilevered pipe conveying fluid in post-flutter region. The role of size-dependency in the nonlinear behavior of pipe is explored by converting the new set of dimensionless parameters into the conventional one. Eventually, some convergence studies are performed to indicate the reliability of present results.     

Modal interactions in the vibrations of a heated annular plate

We investigate the non-linear forced vibrations of a thermally loaded annular plate with clamped–clamped immovable boundary conditions in the presence of a three-to-one internal resonance between the first and second axisymmetric modes. We consider the in-plane thermal load to be axisymmetric and excite the plate externally by a harmonic force near primary resonance of the second mode. We then use the non-linear von Kármán plate equations to model the behavior of the system and apply the method of multiple scales to investigate its responses. We found that the response can be periodic oscillations consisting of both modes, with a large component from the first mode. Moreover, the periodic solutions may undergo Hopf bifurcations, which lead to aperiodic oscillations of the plate.     

Pull-in voltage analysis of electrostatically actuated MEMS with piezoelectric layers: A size-dependent model

A size-dependent model for electrostatically actuated microbeam-based MEMS (micro-electro-mechanical systems) with piezoelectric layers attached is developed based on a modified couple stress theory. By using Hamilton's principle, the nonlinear differential governing equation and boundary conditions of the MEM structure are derived. In the newly developed model, the residual stresses, fringing-field and axial stress effects are considered for the fixed–fixed microbeam with piezoelectric layers. The results of the present model are compared with those from the classical model. The results show the size effect becomes prominent if the beam dimension is comparable to the material length scale parameter (MLSP). The effects of MLSP, the residual stresses and axial stress on the pull-in voltage are also studied. The study may be helpful to characterize the mechanical and electrostatic properties of small size MEMS, or guide the design of microbeam-based devices for a wide range of potential applications.     

Non-classic modeling of three-dimensional manipulation with different geometry of atomic force microscopy components: Multi-scale approach

The size effect must be considered for dynamic modeling of an AFM since the dimensions of the AFM, are in micro-scale. In this study, a three-dimensional multi-scale method based on a non-classical continuum mechanic theory is developed in order to include material length scale parameter (MLSP) in the dynamic behavior of manipulation carried out by AFM. First, the governing equations of Macro Field (MF) are derived using the modified coupled stress theory and the Kirchhoff plate model. Moreover, Nano Field (NF) is modeled using the molecular dynamics equations. The MF and the NF are then combined employing the multi-scale algorithm. Rectangular and dagger cantilevers are taken into account to obtain manipulation results. The influence of two types of tip on the manipulation results is also investigated. The obtained results show that the deformations of the AFM components in non-classic models are less than the one in the classical model. Furthermore, Root Mean Square (RMS) results for a nano-particle demonstrates that damage and deformation of the nano-particle are underestimated by the classical model. The investigations carried out in the present study show the significance of employing the non-classical theory for analyzing AFM performance, particularly for estimation of separation time span.     

Non-linear theories of beams and plates accounting for moderate rotations and material length scales

The primary objective of this paper is to formulate the governing equations of shear deformable beams and plates that account for moderate rotations and microstructural material length scales. This is done using two different approaches: (1) a modified von Kármán non-linear theory with modified couple stress model and (2) a gradient elasticity theory of fully constrained finitely deforming hyperelastic cosserat continuum where the directors are constrained to rotate with the body rotation. Such theories would be useful in determining the response of elastic continua, for example, consisting of embedded stiff short fibers or inclusions and that accounts for certain longer range interactions. Unlike a conventional approach based on postulating additional balance laws or ad hoc addition of terms to the strain energy functional, the approaches presented here extend existing ideas to thermodynamically consistent models. Two major ideas introduced are: (1) inclusion of the same order terms in the strain–displacement relations as those in the conventional von Kármán non-linear strains and (2) the use of the polar decomposition theorem as a constraint and a representation for finite rotations in terms of displacement gradients for large deformation beam and plate theories. Classical couple stress theory is recovered for small strains from the ideas expressed in (1) and (2). As a part of this development, an overview of Eringen׳s non-local, Mindlin׳s modified couple stress theory, and the gradient elasticity theory of Srinivasa–Reddy is presented.     

Bubble dynamics and interactions with a pair of micro pillars in tandem

This study investigates flow patterns and bubble dynamics of two-phase flow around two 100 μm diameter circular pillars in tandem, which were entrenched inside a horizontal micro channel. Bubble velocity, trajectory, size, and void fraction were measured using a high speed camera and analyzed using a particle tracking velocimetry method. A range of gas and liquid superficial velocities were tested, resulting in different bubbly flow patterns, which were consistent with previous studies. These flow patterns were altered as they interacted with the pillars. Depending on the relative transverse location of bubbles to the pillars, and through bubble–bubble interaction, the flow sometimes returned to its original state. It was also determined that the pillars altered both the bubble trajectory and void fraction, especially in the pillars region.     

Structural dynamics and stability analysis of 2D-FG microbeams with two-directional porosity distribution and variable material length scale parameter

Abstract

Since the two-directional functionally graded (2D-FG) materials can satisfy the new requirements raised based on the elimination of the stress concentration, delamination and cracking problems accompanying with the low cost and lightweight on the structures without sacrificing the stiffness and strength, the structural analyses of these structures become more important than ever. Moreover, the usage of the micro-electromechanical systems composed of 2D-FG materials has been increasing in automotive, military, space, biomedical, and nuclear energy industries. Within this study, the free vibration and buckling behaviors of 2D-FG porous microbeams are investigated based on the modified couple stress theory by employing a transverse shear-normal deformation beam theory and using finite element method. The effects of the thickness to material length scale parameter (MLSP) accompanying with the micro-porosity volume fraction ratio, boundary condition, aspect ratio, and gradient index on the dimensionless fundamental frequencies and dimensionless critical buckling loads of the 2D-FG porous microbeams are investigated. Moreover, with assumption of the variable material length scale parameters (VMLSP), the computed results are compared with ones obtained by employing constant MLSP. It is found that VMLSP increases the stiffness of the 2D-FG porous microbeams and effects the free vibration and buckling responses of these structures.     

Uncertainty quantification for dynamics of geometrically nonlinear structures coupled with internal acoustic fluids in presence of sloshing and capillarity

In this paper, we propose an uncertainty quantification analysis, which is the continuation of a recent work performed in a deterministic framework. The fluid–structure system under consideration is the one experimentally studied in the sixties by Abramson, Kana, and Lindholm from the Southwest Research Institute under NASA contract. This coupled system is constituted of a linear acoustic liquid contained in an elastic tank that undergoes finite dynamical displacements, inducing geometrical nonlinear effects in the structure. The liquid has a free surface on which sloshing and capillarity effects are taken into account. The problem is expressed in terms of the acoustic pressure field in the fluid, of the displacement field of the elastic structure, and of the normal elevation field of the free surface. The nonlinear reduced-order model constructed in the recent work evoked above is reused for implementing the nonparametric probabilistic approach of uncertainties. The objective of this paper is to present a sensitivity analysis of this coupled fluid–structure system with respect to uncertainties and to use a classical statistical inverse problem for carrying out the experimental identification of the hyperparameter of the stochastic model. The analysis show a significant sensitivity of the displacement of the structure, of the acoustic pressure in the liquid, and of the free-surface elevation to uncertainties in both linear and geometrically nonlinear simulations.     

Nonlinear normal modes and their superposition in a two degrees of freedom asymmetric system with cubic nonlinearities

This paper investigates nonlinear normal modes and their superposition in a two degrees of freedom asymmetric system with cubic nonlinearities for all nonsingular conditions, based on the invariant subspace in nonlinear normal modes for the nonlinear equations of motion. The focus of attention is to consider relation between the validity of superposition and the static bifurcation of modal dynamics. The numerical results show that the validity has something to do not only with its local restriction, but also with the static bifurcation of modal dynamics. Project Supported by the National Natural Science Foundation and PSF of China     

分子动力学模拟含不同初始缺陷单晶镍的断裂行为与应力演化

断裂是一个跨尺度复杂的物理过程,对宏观尺度的断裂行为已有深入的研究和发展,然而对微观尺度的断裂行为及断裂过程中应力场的变化缺乏深入的理解。本文通过分子动力学模拟,研究了具有不同初始缺陷(尖锐裂纹、钝裂纹和孔洞)的单晶镍的断裂行为和应力分布特征。结果表明,不同的初始缺陷导致了不同的断裂机制、断裂强度和抗断裂性能。含初始孔洞的单晶镍样品有最高的断裂强度和最强的抗断裂性能,这与孔洞扩展过程中堆积层错的形成密切相关。其次是含初始钝裂纹的样品,在裂纹扩展过程中出现由[100]超位错发射引起的裂尖钝化;含尖锐裂纹的样品表现为脆性断裂,裂尖原子没有出现微结构的变化,其强度和抗断裂性能最低。此外,不同的初始缺陷也会导致断裂过程中应力分布的变化,对含有尖锐裂纹的脆性断裂试样,高应力(拉伸应力、平均应力和米塞斯应力)总是出现在扩展裂纹的裂尖。而对于含有钝裂纹或孔洞的韧性断裂试样,高应力不仅分布在裂尖,也分布在位错发射和堆积层错形成的区域,在裂纹/孔洞扩展之前,应力随着加载时间的增加而迅速增加,而一旦裂纹或孔洞开始扩展,应力增加非常缓慢或几乎不增加,但拉伸应力值始终大于平均应力和米塞斯应力值。这表明,在I型...     

The key role of dislocation dissociation in the plastic behaviour of single crystal nickel-based superalloy with low stacking fault energy: Three-dimensional discrete dislocation dynamics modelling

To model the deformation of single crystal nickel based superalloys (SCNBS) with low stacking fault energy (SFE), three-dimensional discrete dislocation dynamics (3D-DDD) is extended by incorporating dislocation dissociation mechanism. The present 3D-DDD simulations show that, consistent with the existing TEM observation, the leading partial can enter the matrix channel efficiently while the trailing partial can hardly glide into it when the dislocation dissociation is taken into account. To determine whether the dislocation dissociation can occur or not, a critical percolation stress (CPS) based criterion is suggested. According to this CPS criterion, for SCNBS there exists a critical matrix channel width. When the channel width is lower than this critical value, the dislocation tends to dissociate into an extended configuration and vice versa. To clarify the influence of dislocation dissociation on CPS, the classical Orowan formula is improved by incorporating the SFE. Moreover, the present 3D-DDD simulations also show that the yielding stress of SCNBSs with low SFE may be overestimated up to 30% if the dislocation dissociation is ignored. With dislocation dissociation being considered, the size effect due to the width of γ matrix channel and the length of γ′ precipitates on the stress–strain responses of SCNBS can be enhanced remarkably. In addition, due to the strong constraint effect by the two-phase microstructure in SCNBS, the configuration of formed junctions is quite different from that in single phase crystals such as Cu. The present results not only provide clear understanding of the two-phase microstructure levelled microplastic mechanisms in SCNBSs with low SFE, but also help to develop new continuum-levelled constitutive laws for SCNBSs.     

Stability of equilibrium states in a simple system with unilateral contact and Coulomb friction

The aim of this paper is to study the stability of equilibrium states in a mechanical system involving unilateral contact with Coulomb friction. Since the assumptions made in classical stability theorems are not satisfied with this class of systems, we return to the basic definitions of stability by studying the time evolution of the distance between a given equilibrium and the solution of a Cauchy problem where the initial conditions are in a neighborhood of the equilibrium. It was recently established that the dynamics is well posed in the case of analytical data. In the present study, we focus in particular on the stability of the equilibrium states under a constant force and deal only with a simple mass-spring system in .     

拉压异性材料含受压圆孔大平板的极限分析

探讨了广义双剪应力强度理论在平面应力状态下的屈服轨迹及其方程式,并用于拉压异性材料圆孔受内压的极限分析,得到了与拉压比有关的弹性极限内压力,弹塑性区的应力、塑性内压力与弹塑性分界半径之间的关系、塑性区的最大半径和最大内压力,所得极值均高于用莫尔强度理论分析的结果。     

Conserving and decaying energy for finite-strain three-dimensional solids with rotational degrees of freedom in nonlinear dynamics

In this work, we design a time-stepping scheme, which can ensure either conservation of energy or dissipation of energy of high (unresolved) modes for nonlinear dynamic analysis. The latter is needed to improve the performance in stress computation and long-term numerical stability. Finite element implementation details are given for finite-strain three-dimensional solid model with independent rotational degrees of freedom. The addition of a rotation field requires a particular choice of large strain measures, allowing one to separate large rotation and large displacement. Several numerical simulations illustrate a very satisfying performance of the proposed time-stepping scheme.     

New Transforms for the Resolving Equations in Elastic Theory and New Integral Transforms, with Applications to Boundary-Value Problems of Mechanics

This paper reviews results from an analysis of exact boundary-value solutions of static and dynamic elasticity obtained by the method of integral transforms. Consideration is given to the solutions of problems for a half-space and a blunted hollow cone, the heat conduction problem for a cone, and the diffraction problem for a cone with a hole along the generatrix. Solutions of mechanics problems are analyzed and the method of integral transforms is generalized     

拉压不同弹性模量薄板上圆孔的应力分析

采用弹性理论研究了拉压不同弹性模量薄板上圆孔的孔边应力集中问题．采用广义虎克定律推导出了拉压不同弹性模量薄板上圆孔边的应力平衡方程,并联合利用应力函数及边界条件得到了拉压不同弹性模量薄板上圆孔边的应力表达式．算例分析表明,当薄板材料的拉压弹性模量相差较大时,采用经典弹性理论研究薄板上圆孔的孔边应力是不合适的,当经典弹性理论与拉压不同弹性模量弹性理论的计算结果间的差别超过工程允许误差5%时,应该采用拉压不同弹性模量弹性理论进行计算．