On the non-persistence of irrotational motion in a viscous heat-conducting fluid

We consider the possibility of irrotational flow in a fluid exterior to a moving rigid obstacle, or interior to a moving rigid shell. Observations show that when a rigid body is impulsively set into motion an irrotational flow may exist initially but does not persist. The breakup of this irrotational flow and the associated phenomenon of generation of vorticity at the wall are generally attributed to the condition of adherence at the fluid-solid interface. Since this condition itself is derived from observation, one can ask whether there is another explanation for the phenomenon. The purpose of this paper is to show that a persistent irrotational flow is incompatible with the second law of thermodynamics.     

P波对界面部分脱胶的刚性圆柱夹杂物的散射

本文求解了弹性Ｐ波对界面部分脱胶的可动刚性圆柱夹杂物的散射问题。将脱胶区看作表面不相接触的弧形界面裂纹，借助波函数展开法并利用边界条件将问题转化为一组对偶级数方程。然后通过引入裂纹面的位错密度函数，将其化为一组具有Ｈｉｌｂｅｒｔ核的第二类奇异积分方程，并进一步化为Ｃａｕｃｈｙ型奇异积分方程组，数值求解方程组可获得动应力强度因子，夹杂物刚体振动位移和散射截面等重要参量。结果显示该类结构在较低的频率上发生共振，此低频共振特性与脱胶区大小，入射波方向、材料组合等多种参数有关。与已有方法相比，本文的方法更具一般性，适用于任意材料组合。     

On certain bounds for the in-plane translational stiffness of a disc inclusion at a bi-material elastic interface

This paper presents a set of bounds that can be used to estimate the in-plane translational stiffness of a rigid circular disc inclusion that is embedded at the interface between two dissimilar elastic half-space regions.     

Dynamics of a spacecraft with large flexible appendage constrained by multi-strut passive damper

This paper is concerned with the dynamics of a spacecraft with multi-strut passive damper for large flexible appendage.The damper platform is connected to the spacecraft by a spheric hinge,multiple damping struts and a rigid strut.The damping struts provide damping forces while the rigid strut produces a motion constraint of the multibody system.The exact nonlinear dynamical equations in reducedorder form are firstly derived by using Kane’s equation in matrix form.Based on the assumptions of small velocity and small displacement,the nonlinear equations are reduced to a set of linear second-order differential equations in terms of independent generalized displacements with constant stiffness matrix and damping matrix related to the damping strut parameters.Numerical simulation results demonstrate the damping effectiveness of the damper for both the motion of the spacecraft and the vibration of the flexible appendage,and verify the accuracy of the linear equations against the exact nonlinear ones.     

THE AXISYMMETRIC MIXED BOUNDARY-VALUE PROBLEM OF THE VERTICAL VIBRATION OF A RIGID FOUNDATIONON SATURATED LAYERED SOIL SUBGRADE

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Bubble collapse in compressible fluids using a spectral element marker particle method. Part 1. Newtonian fluids

This paper is concerned with the development of a high‐order numerical scheme for the modelling of two‐phase Newtonian flows. The companion paper, herein referred to as Part 2, extends the scheme to two‐phase viscoelastic flows. The particular problem of the collapse of a two‐dimensional bubble in the vicinity of a rigid boundary is considered. The governing equations are discretized using the spectral element method, and the two phases are modelled using a marker particle method. The marker particle scheme is validated using the Zalesak slotted disk rotation test problem. A comprehensive set of results is presented for the problem of bubble collapse near a rigid wall, and qualitative agreement is obtained with other numerical studies and experimental observations. Viscous effects are shown to inhibit bubble collapse and prevent jet formation and are therefore likely to have a mitigating effect on cavitation damage.Copyright © 2011 John Wiley & Sons, Ltd.     

Global Weak Solutions¶for the Two-Dimensional Motion¶of Several Rigid Bodies¶in an Incompressible Viscous Fluid

We consider the two-dimensional motion of several non-homogeneous rigid bodies immersed in an incompressible non-homogeneous viscous fluid. The fluid, and the rigid bodies are contained in a fixed open bounded set of ?². The motion of the fluid is governed by the Navier-Stokes equations for incompressible fluids and the standard conservation laws of linear and angular momentum rule the dynamics of the rigid bodies. The time variation of the fluid domain (due to the motion of the rigid bodies) is not known a priori, so we deal with a free boundary value problem. The main novelty here is thedemonstration of the global existence of weak solutions for this problem. More precisely, the global character of the solutions we obtain is due to the fact that we do not need any assumption concerning the lack of collisions between several rigid bodies or between a rigid body and the boundary. We give estimates of the velocity of the bodies when their mutual distance or the distance to the boundary tends to zero.     

Off-center impact of an elastic column by a rigid mass

Based on the Timoshenko beam model the equations of motion are obtained for large deflection of off-center impact of a column by a rigid mass via Hamilton's principle. These are a set of coupled nonlinear partial differential equations. The Newmark time integration scheme and differential quadrature method are employed to convert the equations into a set of nonlinear algebraic equations for displacement components. The equations are solved numerically and the effects of weight and velocity of the rigid mass and also off-center distance on deformation of the column are studied.     

含半无限裂纹正交各向异性板插入刚性楔块应力强度因子的计算

本文通过对半无限正交各向异性平面Fourier变换,建立了一种特殊位移模式的应力场计算公式.解决了一外形轮廓曲线为f(χ)的刚性楔块插入半无限长裂纹问题,建立了求解分离坐标和应力强度因子的方程式.其特例均与各向同性体相应问题的解一致.     

Scattering far field solution of SH-wave by movable rigid cylindrical interface inclusion

The Green's function is used to solve the scattering far field solution of SH-wave by a movable rigid cylindrical interface inclusion in a linear elastic body. First, a suitable Green's function is developed, which is the fundamental displacement solution of an elastic half space with a movable rigid half-cylindrical inclusion impacted by out-of-plane harmonic line source loaded at any point of its horizontal surface. By using the Green's function, a series of Fredholm integral equations of the first kind which determine the scattering far field can be set up. Then the paper gives the expressions on the far field including the displacement mode of scattering wave and the solution of scattering cross-section. Finally, some examples and numerical results are discussed to analyze the influence of the combination of different media parameters on the answer of far field.     

Slope-deflection method for elastic-plastic multistory frames

Slope-Deflection Method for elastic rigid frames is generalized for elastic-plastic analysis of rigid frames of work-hardening materials. The plastic strain is here treated as an additional set of externally applied moments. The end moments of the component members of the frame are obtained from the solution of a set of linear algebraic equations. No iteration is required. Numerical results of the analysis of a portal frame and a two-story plane frame subject to side loads beyond the elastic range are shown.     

Demonstration of a coupled floating offshore wind turbine analysis with high-fidelity methods

This paper presents results of numerical computations for floating off-shore wind turbines using, as an example, a machine of 10-MW rated power. The aerodynamic loads on the rotor are computed using the Helicopter Multi-Block flow solver developed at the University of Liverpool. The method solves the Navier–Stokes equations in integral form using the arbitrary Lagrangian–Eulerian formulation for time-dependent domains with moving boundaries. Hydrodynamic loads on the support platform are computed using the Smoothed Particle Hydrodynamics method, which is mesh-free and represents the water and floating structures by a set of discrete elements, referred to as particles. The motion of the floating offshore wind turbine is computed using a Multi-Body Dynamic Model of rigid bodies and frictionless joints. Mooring cables are modelled as a set of springs and dampers. All solvers were validated separately before coupling, and the results are presented in this paper. The importance of coupling is assessed and the loosely coupled algorithm used is described in detail alongside the obtained results.     

On the dynamical symmetry points and the orientations of the principal axes of inertia of a rigid body

For an arbitrary rigid body, all dynamical symmetry points are found, and the directions of the axes of dynamical symmetry are determined for these points. We obtain conditions on the principal central moments of inertia under which the Lagrange and Kovalevskaya cases can be realized for the rigid body. We also analyze the set of orientations of the bases formed by the principal axes of inertia for various points of the rigid body.     

The axisymmetric mixed boundary-value problem of the vertical vibration of a rigid foundation on saturated layered soil subgrade

Based on the theory of elastic wave propagation in saturated soil subgrade established by the author of this paper, the axisymmetric vertical vibration of a rigid circular foundation resting on partially saturated soil subgrade which is composed of a dry elastic layer and a saturated substratum is studied. The analysis relied on the use of integral transform techniques and a pair of dual integral equations governing the vertical vibration of the rigid foundation is listed under the consideration of mixed boundary-value condition. The results are reduced to the case for saturated half-space. The set of dual integral equations are reduced to a Fredholm integral equation of the second kind and solved by numerical procedures. Numerical examples are given at the end of the paper and plots of the dynamic compliance coefficient C_v versus the dimensionless frequency a₀ are presented. Foundation item: the National Natural Science Foundation of China (59579018) Biography: CHEN Sheng-li (1974-)     

Bubble collapse in compressible fluids using a spectral element marker particle method. Part 2. Viscoelastic fluids

This paper is concerned with the development of a high‐order numerical scheme for two‐phase viscoelastic flows. In the companion paper, herein referred to as Part 1, the scheme is applied to the modelling of two‐phase Newtonian flows. The particular problem of the collapse of a 2D bubble in the vicinity of a rigid boundary is considered. Attention is given to the construction of the most general form of the compressible Oldroyd B model that is consistent with the compressible Newtonian and upper‐convected Maxwell models in the appropriate limits. The governing equations are discretized using the spectral element method, and the two phases are modelled using a marker particle method. A comprehensive set of results is presented for the problem of bubble collapse near a rigid wall, and qualitative agreement is obtained with other numerical studies and experimental observations. Viscoelastic effects that are predicted include increased bubble oscillation with increasing Weissenberg number and considerable bubble deformation and cusping near the wall. Most importantly, it has been shown that viscoelasticity has the ability to prevent jet formation and therefore is likely to have a mitigating effect on cavitation damage. Copyright © 2012 John Wiley & Sons, Ltd.     

人体上肢运动学动力学建模与仿真技术的研究

根据多体动力学原理,以人体解剖学为基础,对人体上肢进行建模,推导了其动力学和运动学方程,建立了人体上肢四刚体四自由度动力学模型,运用多系统动力学软件ADAMS,结合UG建模功能,对人体上肢动力学和运动学特性进行了分析计算,对人体上肢收臂翻掌过程的运动进行了仿真,并将计算结果与实测数据进行了对比,验证了模型的正确性和有效性。     

Stability of an elastic arch in a rigid cavity

A thin, elastic circular arch, clamped at its ends and constrained in a rigid cavity, is subjected to a uniformly distributed parallel loading. Stability of equilibrium in the large “snap-through” is investigated both analytically and experimentally and good agreement is found to exist between the two modes of investigation. It is concluded that the set of simplifying assumptions introduced in the analysis is justified. Simple analytical results obtained in the paper allow the design of underground shelters under this type of loading.     

Analysis of bifurcation bending modes of arches and panels

This paper reports the results of numerical analysis of the bifurcation solutions of nonlinear boundary-value problems of plane bending of elastic arches and panels. Problems are formulated for a system of six nonlinear ordinary differential equations of the first order with independent fields of finite displacements and rotations. Two loading versions (by follower and conservative pressures) and two versions of boundary conditions (rigid clamping and pinning) are considered. In the case of clamped arches and panels, the set of solutions consists of symmetric and asymmetric bending modes which exist only for positive values of the load parameter. In the case of pinning, the set of solutions includes symmetric and asymmetrical modes which correspond to positive, negative, and zero values of the parameter. In both problems, the phase relations between the state parameter and the load parameter are bifurcated, ambiguous, have isolated branches, and admit a catastrophe — a finite jump from the fundamental equilibrium mode to a buckled mode.     

勒让德伪谱法求解三维刚体摆姿态运动最优控制问题

研究伪谱法求解三维刚体摆姿态运动最优控制问题. 针对三维刚体摆这类含有约束的力学模型,提出了基于勒让德伪谱法的三维刚体摆姿态最优控制方法. 利用插值逼近设计了三维刚体摆姿态运动最优控制算法,得到了三维刚体摆的姿态最优控制轨迹,并结合松弛参数来控制插值点的取值,寻找满足的可行解. 仿真结果表明,基于勒让德伪谱法的最优控制算法使得三维刚体摆能以较小的误差运动到期望的末端姿态,且计算速度快,能够获得精度较高的控制输入量.