树木在风中摇曳的流固耦合数值模拟方法探索

树木在风中摇曳是一个流固耦合问题,但树的结构复杂,无法直接用已有的流固耦合数值方法来模拟.本文提出一种基于虚拟耦合面的流固耦合方法,该方法用一个虚拟的连续曲面把树冠包裹起来,在这个曲面上建立流固耦合关系,并将虚拟曲面上计算得到的风荷载作为树木结构的外力进行加载.虚拟耦合面本身不妨碍树木枝条的运动,且能避免在每个枝条、树...     

An improved HSFR method for natural vibration analysis of an immersed cylinder pile with a tip mass

Immersed cylinder piles are usually modelled as immersed cantilever cylinder columns carrying a tip mass and rotary moment of inertia. In this paper, the equations of motion of an immersed cylinder pile along transversal modes of vibration are developed. Compressibility of water and structural damping are included in the formulation. Natural frequencies of the immersed pile are obtained from the developed equations using harmonic sweep frequency response analyses. The proposed method is applied to numerical examples, and the results obtained are shown satisfactory when compared to other numerical solutions in the literature, or to finite element solutions and experimental data.     

Nonlinear analysis of the forced response of a beam with three mode interaction

An analysis is presented for the primary resonance of a clamped-hinged beam, which occurs when the frequency of excitation is near one of the natural frequencies,_n . Three mode interaction (₂ 3₁ and _{3 1} + 2₂) is considered and its influence on the response is studied. The case of two mode interaction (₂ 3₁) is also considered to compare it with the case of three mode interaction. The straight beam experiencing mid-plane stretching is governed by a nonlinear partial differential equation. By using Galerkin's method the governing equation is reduced to a system of nonautonomous ordinary differential equations. The method of multiple scales is applied to solve the system. Steady-state responses and their stability are examined. Results of numerical investigations show that there exists no significant difference between both modal interactions' influences on the responses.     

Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory

Abstract

This article contains the nonlocal elasticity theory to capture size effects in functionally graded (FG) nano-rod under magnetic field supported by a torsional foundation. Torque effect of an axial magnetic field on an FG nano-rod has been defined using Maxwell’s relation. The material properties were assumed to vary according to the power law in radial direction. The Navier equation and boundary conditions of the size-dependent FG nano-rod were derived by the Hamilton’s principle. These equations were solved by employing the generalized differential quadrature method (GDQM). Presented model has the ability to turn into the classical model if the material length scale parameter is taken to be zero. The effects of some parameters, such as inhomogeneity constant, magnetic field and small-scale parameter, were studied. As an important result of this study can be stated that an FG nano-rod model based on the nonlocal elasticity theory behaves softer and has smaller natural frequency.     

地磁场作用半平面铁磁结构广义Flamant问题的弹性变形扰动静磁场解

采用Fourier变换方法对广义Flamant载荷作用半平面铁磁结构弹性变形诱导的静磁场分布进行求解,得到的表达式经退化与集中力作用情形的扰动静磁场分布表达式相同.数值结果表明,载荷分布形式通过影响结构的弹性变形进而影响扰动磁场分布的形貌和大小,扰动静磁场分布的形貌与载荷极大值的分布区域有直接关联,扰动静磁场分布的最值与作用力的大小正相关;扰动静磁场强度的法向分量的最值随着与结构表面的距离的减小而增大,随载荷分布尺寸的增大而增大.     

FEM solution to natural convection flow of a micropolar nanofluid in the presence of a magnetic field

The two-dimensional, laminar, unsteady natural convection flow in a square enclosure filled with aluminum oxide (\(\hbox {Al}_{2} \hbox {O}_{3}\))–water nanofluid under the influence of a magnetic field, is considered numerically. The nanofluid is considered as Newtonian and incompressible, the nanoparticles and water are assumed to be in thermal equilibrium. The mathematical modelling results in a coupled nonlinear system of partial differential equations. The equations are solved using finite element method (FEM) in space, whereas, the implicit backward difference scheme is used in time direction. The results are obtained for Rayleigh (Ra), Hartmann (Ha) numbers, and nanoparticles volume fractions (\(\phi\)), in the ranges of \(10^3 \le Ra \le 10^7\), \(0\le Ha \le 500\) and \(0 \le \phi \le 0.2\), respectively. The streamlines and microrotation contours are observed to show similar behaviors with altering magnitudes. For low Ra values, when \(Ha=0\), symmetric vortices near the walls and a central vortex in opposite direction are observed in vorticity. As Ra increases, the central vortex splits into two due to the circulation in the effect of the buoyant flow. Boundary layer formation is observed when Ha increases for almost all Rayleigh numbers in both streamlines and vorticity. The isotherms have horizontal profiles for high Ra values owing to convective dominance over conduction. As Ha is increased, the convection effect is reduced, and isotherms tend to have vertical profiles. This study presents the first FEM application for solving highly nonlinear PDEs defining micropolar nanofluid flow especially for large values of Rayleigh and Hartmann numbers.     

Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field

In this paper, flow and heat transfer of a nanofluid over a stretching cylinder in the presence of magnetic field has been investigated. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved numerically by the fourth order Runge–Kutta integration scheme featuring a shooting technique. Different types of nanoparticles as copper (Cu), silver (Ag), alumina (Al₂O₃) and titanium oxide (TiO₂) with water as their base fluid has been considered. The influence of significant parameters such as nanoparticle volume fraction, nanofluids type, magnetic parameter and Reynolds number on the flow and heat transfer characteristics is discussed. It was found that the Nusselt number increases as each of Reynolds number or nanoparticles volume fraction increase, but it decreases as magnetic parameter increase. Also it can be found that choosing copper (for small of magnetic parameter) and alumina (for large values of magnetic parameter) leads to the highest cooling performance for this problem.     

Treatment of the small time instability in the finite element analysis of fluid structure interaction problems

In this paper, the fluid–structure interaction problem in mechanical systems in which a high frequency vibrating solid structure interacts with the surrounding fluid flow is considered. Such a situation normally appears in many microelectromechanical systems like a wide variety of microfluidic devices. A different implementation of the residual‐based variational multiscale flow method is employed within the arbitrary Lagrangian–Eulerian formulation. The combination of the variational multiscale method with appropriate stabilization parameters is used to handle the so‐called small time step instability in the finite element analysis of the fluid part in the coupled fluid–structure interaction problem. The capability of the employed approach has been demonstrated through finite element study of a benchmark example and FEM simulation of two different mechanical micropumping devices. High frequency vibrations of the solid membrane are used to derive the fluid flow in these micropumps. Results of FEM simulations are shown to be in good agreement with available experimental data.Copyright © 2012 John Wiley & Sons, Ltd.     

Stability of Poiseuille flow in the presence of a longitudinal magnetic field

The stability of the plane flow of an electrically conducting fluid with respect to small perturbations was studied at large Reynolds numbers in the presence of a longitudinal magnetic field. The dependence of the critical Reynolds number on the electrical conductivity is investigated. At large Reynolds numbers, a new branch of instability and a sudden change in the critical Reynolds numbers is found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 45–53, May–June, 2008.     

Numerical study of single bubble motion in liquid metal exposed to a longitudinal magnetic field

The paper presents numerical simulations modeling the ascent of an argon bubble in liquid metal with and without an external magnetic field. The governing equations for the fluid and the electric potential are discretized on a uniform Cartesian grid and the bubble is represented with a highly efficient immersed boundary method. The simulations performed were conducted matching experiments under the same conditions so that sound validation is possible. The three-dimensional trajectory of the bubble is analyzed quantitatively and related to the flow structures in the wake. Indeed, the substantial impact of the magnetic field in the bubble trajectory results from its influence on the wake. Quantitative data describing the selective damping of vortex structures are provided and discussed. As a result of applying a longitudinal field, the time-averaged bubble rise velocity increases for large bubbles, it reaches a maximum and then decreases when further increasing the magnetic interaction parameter. For small bubbles, the time-averaged bubble rise velocity decreases when increasing the magnetic field. The bubble Strouhal number as a dimensionless frequency is reduced with the application of a magnetic field for all bubbles considered and the zig–zag trajectory of the bubble becomes more rectilinear.     

A new system of equations which predicts the evolution of a wave packet due to a fluid-fluid interaction under a narrow bandwidth assumption

The problem of the capillary-gravity waves which may arise at an interface between two stratified fluids of different densities is investigated. Particular attention is paid to the case when two different wave modes move at the same speed and to the wave train produced by the ensuing interaction. In contrast to most previous studies, the wave steepness and the wave bandwidth are not taken to be of the same order of magnitude, but the latter is of one order smaller. This leads to a system of nonlinear evolution equations which can be used to predict the subsequent progression of the wave field. These equations may be compared with the more usual nonlinear Schrödinger set which are valid under the equal bandwidth assumption and also a recently derived set which describe broader bandwidth waves. A large class of solutions to the equations is found and the corresponding wave profiles are presented.     

High frequency scattering due to a pair of time-harmonic antiplane forces on the faces of a finite interface crack between dissimilar anisotropic materials

The high-frequency elastodynamic problem involving the excitation of an interface crack of finite width lying between two dissimilar anisotropic elastic half-planes has been analyzed. The crack surface is excited by a pair of time-harmonic antiplane line sources situated at the middle of the cracked surface. The problem has first been reduced to one with the interface crack lying between two dissimilar isotropic elastic half-planes by a transformation of relevant co-ordinates and parameters. The problem has then been formulated as an extended Wiener–Hopf equation (cf. Noble, 1958) and the asymptotic solution for high-frequency has been derived. The expression for the stress intensity factor at the crack tips has been derived and the numerical results for different pairs of materials have been presented graphically.     

Investigation of the onset of bioconvection in a suspension of oxytactic microorganisms subjected to high-frequency vertical vibration

This paper investigates the effect of vertical vibration on the stability of a dilute suspension of oxytactic microorganisms in a shallow horizontal fluid layer. For the case of high-frequency vibration, an averaging method is utilized to derive the equations describing the mean flow by decomposing the solutions of governing equations into two components: one that varies slowly with time, and a second that varies rapidly with time. Linear stability analysis is used to investigate the stability of the obtained averaged equations. It is predicted that high-frequency, low-amplitude vertical vibration has a stabilizing effect on a suspension of oxytactic microorganisms confined in a shallow horizontal layer. PACS 47.27 Te; 68.60 Dv     

Slip effects on the peristaltic flow of a Jeffrey fluid in an asymmetric channel under the effect of induced magnetic field

In the present study, we investigated the effects of slip and induced magnetic field on the peristaltic flow of a Jeffrey fluid in an asymmetric channel. The governing two‐dimensional equations for momentum, magnetic force function and energy are simplified by using the assumptions of long wavelength and low but finite Reynolds number. The reduced problem has been solved by Adomian decomposition method (ADM) and closed form solutions have been presented. Further, the exact solution of the proposed problem has also been computed and the mathematical comparison shows that both solutions are almost similar. The effects of pertinent parameters on the pressure rise per wavelength are investigated using numerical integration. The expressions for pressure rise, friction force, velocity, temperature, magnetic force function and the stream lines against various physical parameters of interest are shown graphically. Moreover, the behavior of different kinds of wave shape are also discussed. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonlinear Vibrations of a Simply Supported Rectangular Metallic Plate Subjected to Transverse Harmonic Excitation in the Presence of a One-to-One Internal Resonance

The nonlinear response of rectangular and square metallic plates subjectto transverse harmonic excitations is studied. The nonlinearitiesoriginate from the use of Von Kármán strains. The method of multiplescales is used to solve the system of differential equationsapproximately. Frequency response curves are presented for both squareand rectangular plates for primary resonance of either mode in thepresence of a one-to-one internal resonance. Stability of steady statesolutions is investigated. Bifurcation points and their types arediscussed.     

Perturbation solution to unsteady flow in a porous channel with expanding or contracting walls in the presence of a transverse magnetic field

An incompressible flow in a porous channel with expanding or contacting walls in the presence of a transverse magnetic field is considered. Using similarity transformations, the governing equations are reduced to the nonlinear ordinary differential equations. The exact similar solutions for the different cases of the expansion ratio and the Hartmann number are obtained with a singular perturbation method, and the associated behavior is discussed in detail.