A coupled sliding and rolling friction model for DEM calibration

The accuracy of dense Discrete Element Method (DEM) simulations is sensitive to initial density, contact orientation, particle size and shape, and interparticle interaction parameters including contact stiffness, cohesion, coefficients of friction, and coefficients of restitution. Although studies have characterized the effects of individual particle interaction parameters on mechanical responses of loaded granular material, research combining DEM parameters for calibration is scarce. Robust DEM calibration methodology combining sliding and rolling friction coefficients was developed and validated to predict bulk residual soil strength of initially dense DEM particle assemblies.     

耦合船体横摇的减摇水舱流体运动和减摇效果预测

减摇水舱用于减小船体的横摇运动。由于水舱内部结构复杂,导致流体晃荡呈非线性。为了降低预测水舱特性和减摇效果的难度,采用计算流体力学VOF模型来分析水舱中流体的晃荡,在时域内,运用数值方法完成船体非线性横摇运动的实时仿真,其中耦合了水舱中流体和船体的运动。船体随机横摇时,进行水舱流体流量和力矩的功率谱分析,得到减摇频率范围及减摇前后的效果。结果表明,在其减摇频率范围内,减摇水舱具有良好的减摇能力,验证了此方法的可行性。     

Equations of motion for mechanical systems: A unified approach

This paper presents a unified framework from which emerge the Lagrange equations, the Gibbs-Appell Equations and the Generalized Inverse Equations for describing the motion of constrained mechanical systems. The unified approach extends the applicability of the first two approaches to systems where the constraints are non-linear functions of the generalized velocities and are not necessarily independent. Furthermore, the approach leads to the Explicit Gibbs-Appell Equations.     

Regularization and stability of the constraints in the dynamics of multibody systems

In the analysis of multibody dynamics, we are often required to deal with singularity problems where the constraint Jacobian matrix may become less than full rank at some instantancous configurations. This creates numerical instability which will affect the performance of the mechanical system. A modification procedure of the constraints when they vanish or become linearly dependent is proposed to regularize the dynamics of the system. A distinction between the asymptotic stability due to the representation of the constraints (at the velocity and acceleration level), and the one due to the singularity is discussed in full in this paper. It is shown that Baumgarte technique could be extended to accommodate the representation of the constraints in the neighborhood of singularity. A two link planar manipulator undergoing large motion and passing through a singular configuration is used to illustrate the proposed stability technique.     

不锈钢/普碳钢爆炸焊接与轧制

以不锈钢/普碳钢为对象,对爆炸焊接+轧制联合技术进行了研究。爆炸焊接参数通过计算和优化设计,准确地预示了不锈钢/普碳钢大型厚板坯的爆炸焊接窗口;复合后的板坯在选定的轧制参数下进行热轧和冷轧;在保证复合质量的条件下,经过轧制可获得力学性能、尺寸精度完全合格的大面积薄复合板。     

The theory of relativistic analytical mechanics of the rotational systems

I'IntroductionThespinningmotionisintrinsicattributeofmicroscopicparticle.In1979,R.BengtssonandS.Frauendorfaccuratlymeasuredthemaximumvolumesofthespinningrotativevelocityof14kindsofnucleons,andtheresultsshowedthatthemaximumvolumesofthespinningrotativevelocityofeachnucleonaredifferent[ll.Withthede\'elopingofmodernscienceandtechnology,moreandmoreexperimentalfactsrelatedtothehighspeedrotationquestions,theEinstein'srelativitytheoryandtherotationaltheoryofclassicalmechanicsarenotsuitabletothesepro…     

A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids

A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipative solids, including finite elastic and plastic deformations, non-Newtonian viscosity, rate sensitivity, arbitrary flow and hardening rules, as well as heat conduction. We show that a joint potential function exists such that both the conservation of energy and the balance of linear momentum equations follow as Euler-Lagrange equations. The identification of the joint potential requires a careful distinction between equilibrium and external temperatures, which are equal at equilibrium. The variational framework predicts the fraction of dissipated energy that is converted to heat. A comparison of this prediction and experimental data suggests that α-titanium and Al2024-T conform to the variational framework.     

Generalization of a new parametric formulation of mechanics for systems with variable mass

In this paper a new parametric formulation of mechanics, formulated by the author himself and based on the separation of the double role of time (independent variable and a parameter) with the aid of a family of varied paths, is extended to the arbitrary rheonomic systems with variable mass. For such systems d'Alembert–Lagrange's principle, general Hamilton's principle, and the corresponding Hamiltonian formalism are formulated, as well as the energy relations with energy change law. The obtained results are illustrated by a simple, but characteristic example.     

Equations of motion for nonholonomic mechanical systems with unilateral constraints

IntroductionThemotionofamechanicalsystemwithunilateralconstraintsismoregeneralthanwithbilateralconstraints1andyetitsinvestigationismoredifficult[1,2].Thesystemswithunilateralconstraintsinvolvetheholonomicmechanicalsystemswithunilateralholonomicconstraints[3～6]andthenonholonondcmeChanicalsystemswithunilateralholonondcconstraintS[7]andthenonholonondcmechanicalsystemswithunilateralnonholonondcconstraintS[2]andsoon.ThispaperstUdiesatypeofmoregeneralsystemswithunilateralconstfaints:nonholonondcs…     

Weak formulation and first order form of the equations of motion for a class of constrained mechanical systems

Some new theoretical results are presented on modeling the dynamic response of a class of discrete mechanical systems subject to equality motion constraints. Both the development and presentation are facilitated by employing some fundamental concepts of differential geometry. At the beginning, the equations of motion of the corresponding unconstrained system are presented on a configuration manifold with general properties, first in strong and then in a primal weak form, using Newton׳s law of motion as a foundation. Next, the final weak form is obtained by performing a crucial integration by parts step, involving a covariant derivative. This step required the clarification and enhancement of some concepts related to the variations employed in generating the weak form. The second part of this work is devoted to systems involving holonomic and non-holonomic scleronomic constraints. The equations of motion derived in a recent study of the authors are utilized as a basis. The novel characteristic of these equations is that they form a set of second order ordinary differential equations (ODEs) in both the coordinates and the Lagrange multipliers associated to the constraint action. Based on these equations, the corresponding weak form is first obtained, leading eventually to a consistent first order ODE form of the equations of motion. These equations are found to appear in a form resembling the form obtained after application of the classical Hamilton׳s canonical equations. Finally, the new theoretical findings are illustrated by three representative examples.     

Asymmetric motion of a two-dimensional symmetric flapping model

A two-dimensional symmetric flapping model is studied in terms of the bifurcation using discrete vortex method. This model consists of two wings attached together at a hinge, and the flapping motion of the wings is symmetric with respect to the horizontal line. The center of mass of this model can move according to the hydrodynamic force generated by an interaction of the wing and vortices separated from boundary layer. The bifurcation parameter is a time scale of the dissipation, which is simplified to contrast the transition of the type of the motion. Bifurcation diagram shows that steady motion of zero-mean velocity (with symmetric flapping) is unstable in a parameter region, and that there is another region where two types of a steady stable flapping motion coexist. We illustrate these types of the motion.     

Equations of motion of a multibody system and Lie groups

Usually, the methods used for forming the equations relating to the motion of a complex system are based either on the use of general theorems or on the use of conventional techniques of analytical mechanics (Lagrange or Hamilton equations). In this case the formation of the equations of motion was made using a method allowing us to draft these equations in a more synthetic form. It uses the properties of the displacement group as a LIE group. Its main advantage is that it allows a totally intrinsic analytical calculation in the vector space of the wrenches or complex forces [8]. A symbolic calculus code has been designed in order to apply this approach. Initially, we have used and tested it in any open loop multibody system. The symbolic calculus code was applied, for instance, in the context of a study into the crash of a vehicle driven into a barrier.

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Sommario I metodi più comunemente usati per formulare le equazioni relative al moto di un sistema complesso si basano o su teoremi generali o su tecniche convenzionali della meccanica analitica (equazioni di Lagrange o di Hamilton). Nel presente studio, invece, le equazioni del moto vengono formulate usando una metologia che ne permette la scrittura in una forma più sintetica, sfruttando le proprietà del gruppo degli spostamenti come di un gruppo di Lie: il principale vantaggio del metodo è di permettere un calcolo analitico totalmente intrinseco nello spazio vettoriale delle forze complesse [8]. Per poter applicare questo approccio, è stato sviluppato un codice di calcolo simbolico. Per cominciare, l'approccio è stato usato e sperimentato per un generico sistema multicorpo a loop aperto: per esempio, nel contesto di uno studio sull'urto di un veicolo su di una barriera.

     

Stability for basic system of equations of atmospheric motion

The topological characteristics for the basic system of equations of atmospheric motion were analyzed with the help of method provided by stratification theory. It was proved that in the local rectangular coordinate system the basic system of equations of atmospheric motion is stable in infinitely differentiable function class. In the sense of local solution, the necessary and sufficient conditions by which the typical problem for determining solution is well posed were also given. Such problems as something about ＂speculating future from past＂ in atmospheric dynamics and how to amend the conditions for determining solution as well as the choice of underlying surface when involving the practical application were further discussed. It is also pointed out that under the usual conditions, three motion equations and continuity equation in the basic system of equations determine entirely the property of this system of equations.     

A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics

Growth (and resorption) of biological tissue is formulated in the continuum setting. The treatment is macroscopic, rather than cellular or sub-cellular. Certain assumptions that are central to classical continuum mechanics are revisited, the theory is reformulated, and consequences for balance laws and constitutive relations are deduced. The treatment incorporates multiple species. Sources and fluxes of mass, and terms for momentum and energy transfer between species are introduced to enhance the classical balance laws. The transported species include: (i) a fluid phase, and (ii) the precursors and byproducts of the reactions that create and break down tissue. A notable feature is that the full extent of coupling between mass transport and mechanics emerges from the thermodynamics. Contributions to fluxes from the concentration gradient, chemical potential gradient, stress gradient, body force and inertia have not emerged in a unified fashion from previous formulations of the problem. The present work demonstrates these effects via a physically consistent treatment. The presence of multiple, interacting species requires that the formulation be consistent with mixture theory. This requirement has far-reaching consequences. A preliminary numerical example is included to demonstrate some aspects of the coupled formulation.     

爆破地震地面运动的演变功率谱密度函数分析

按照Priestly提出的演变随机过程理论，对非平稳随机过程的演变功率谱密度函数进行了理论推导，并给出了定义。在此基础上，建立了基于均匀调制随机过程的爆破地震动演变功率谱密度函数。经对比发现，理论模型计算值与实验测试结果具有较好的一致性。     

Metamorphoses of resonance curves in systems of coupled oscillators:The case of degenerate singular points

We study dynamics of two coupled periodically driven oscillators. The internal motion is separated off exactly to yield a nonlinear fourth-order equation describing inner dynamics. Periodic steady-state solutions of the fourth-order equation are determined within the Krylov–Bogoliubov–Mitropolsky approach and we compute the corresponding amplitude profiles.Metamorphoses of these amplitude curves induced by changes of control parameters as well as the corresponding changes of dynamics are studied within the framework of theory of differential properties of algebraic curves. The major finding is that there is a very rich dynamics in neighborhoods of degenerate singular points.     

Dynamic flight stability of a hovering model insect: lateral motion

The lateral dynamic flight stability of a hovering model insect （dronefly） was studied using the method of computational fluid dynamics to compute the stability derivatives and the techniques of eigenvalue and eigenvector analysis for solving the equations of motion. The main results are as following. （i） Three natural modes of motion were identified： one unstable slow divergence mode （mode 1）, one stable slow oscillatory mode （mode 2）, and one stable fast subsidence mode （mode 3）. Modes 1 and 2 mainly consist of a rotation about the horizontal longitudinal axis （x-axis） and a side translation; mode 3 mainly consists of a rotation about the x-axis and a rotation about the vertical axis. （ii） Approximate analytical expressions of the eigenvalues are derived, which give physical insight into the genesis of the natural modes of motion. （iii） For the unstable divergence mode, td, the time for initial disturbances to double, is about 9 times the wingbeat period （the longitudinal motion of the model insect was shown to be also unstable and td of the longitudinal unstable mode is about 14 times the wingbeat period）. Thus, although the flight is not dynamically stable, the instability does not grow very fast and the insect has enough time to control its wing motion to suppress the disturbances.     

浅埋的圆柱形孔洞对SH波的散射与地震动

研究了浅埋的圆柱形孔洞对以任意方向入射的平面SH波的散射与地震动问题。利用复变函数和多极坐标方法构造了问题的位移解。当入射波的波长与圆孔的半径相比较小时,地震动将受到较大的影响。影响地震动有三个主要参数:(1)SH波的入射角0;(2)入射波波数,即圆柱形孔洞的半径与入射波半波长之比;(3)h/R,即圆柱形孔洞至表面的距离与圆孔半径之比。当较大时,地震动幅值变化激烈,位移幅值可出现跳动和放大的现象。当h/R增大至10～12时,位移幅值变化恢复至半空间的情况,表明圆柱形孔洞的影响可被忽略。     

A new derivation of the vectorial equation of motion for a test particle in the Schwarzchild field

A new derivation of the vectorial equation of motion for a test particle in the Schwarzchild field is given which greatly simplifies the procedure given by C.A.Murray.     

A numerical simulation of hydrodynamic forces of ground-effect problem using Lagrange's equation of motion

On the basis of the potential flow theory, Lagrange's equation of motion is used to study the unsteady ground-effect problem. The forces and moments acting on the moving body are solved in terms of the derivatives of added masses in which the generalized Taylor's formulae are applied. The singular integral equations used to solve the surface source intensities and their derivatives are regularized by the Gauss flux theorem and are therefore amenable to the direct use of the Gaussian quadrature formula. In illustration, the condition of a prolate spheroid moving in the fore-and-aft direction at constant speed past a flat ground with a protrusion is considered. The hydrodynamic forces and moments acting on the moving spheroid are investigated systematically by varying the size of the protrusion and the cruising height of the spheroid. © 1998 John Wiley & Sons, Ltd.