A linear complementarity model for multibody systems with frictional unilateral and bilateral constraints

The Lagrange-I equations and measure differential equations for multibody systems with unilateral and bilateral constraints are constructed.For bilateral constraints,frictional forces and their impulses contain the products of the filled-in relay function induced by Coulomb friction and the absolute values of normal constraint reactions.With the time-stepping impulse-velocity scheme,the measure differential equations are discretized.The equations of horizontal linear complementarity problems(HLCPs),which are used to compute the impulses,are constructed by decomposing the absolute function and the filled-in relay function.These HLCP equations degenerate into equations of LCPs for frictional unilateral constraints,or HLCPs for frictional bilateral constraints.Finally,a numerical simulation for multibody systems with both unilateral and bilateral constraints is presented.     

Two-dimensional modeling of unilateral contact-induced shaft precessional motions in bladed-disk/casing systems

The present work targets shaft whirling motions induced by direct blade/casing unilateral contact occurrences in aircraft engine bladed-disk assemblies. These contact events are favored by increasingly reduced blade-tip clearances and potentially lead to harmful interactions that may threaten the engine structural integrity.A simplified 2D in-plane finite element model representative of the engine fan stage is built, accounting for the flexibility of the shaft through two linear springs attached to the disk center node and the structural coupling provided by the fan frame and the bearings, modeled by an array of linear springs. A linear stability analysis of the reduced-order coupled system reveals two unstable zones in a selected rotational speed range, emanating from the linearly predicted modal coincidence speeds.Through a time-marching strategy, two asymmetric contact initiation mechanisms are investigated: (1) a prescribed casing distortion and (2) a mass imbalance on the bladed-disk. It is shown how the 1-nodal diameter mode of the first modal family of the bladed-disk is dominant when a modal interaction arises from the transient casing distortion and leads to divergent regimes. The presence of the frame/bearings coupling induces a shift in the critical speeds detected, generally characterized by a backward traveling wave in the rotating frame and a forward traveling one in the fixed frame. Further, when a mass imbalance is the excitation source, the suspension modes appear to have a major role and a stable limit cycle is reached regardless of the coupling stiffness with much lower energy levels than in divergent regimes.     

Dynamics of finite element structural models with multiple unilateral constraints

Fast and accurate simulation of mechanical structures with complex geometry requires application of the finite element method. This leads frequently to models with a relatively large number of degrees of freedom, which may also possess non-linear properties. Things become more complicated for systems involving unilateral contact and friction. In classical structural dynamics approaches, such constraints are usually modeled by special contact elements. The characteristics of these elements must be selected in a delicate way, but even so the success of these methods cannot be guaranteed. This study presents a numerical methodology, which is suitable for determining dynamic response of large scale finite element models of mechanical systems with multiple unilateral constraints. The method developed is based on a proper combination of results from two classes of direct integration methodologies. The first one includes standard methods employed in determining dynamic response of structural models possessing smooth non-linearities. The second class of methods includes specialized methodologies that simulate the response of dynamical systems with unilateral constraints. The validity and effectiveness of the methodology developed is illustrated by numerical results.     

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 .     

Equations of motion for nonholonomic mechanical systems with unilateral constraints

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

Unilateral Multibody Dynamics

Contact processes may be represented by local discretization, by a rigid body approach or by a mixed method using both ideas. For the dynamics of mechanical systems a rigid body approach is described achieving good results also for multiple contact problems. This paper considers mainly contacts in multi-body systems where the corresponding contact constraints vary with time thus generating structure-variant systems. The equations of motion for dynamical systems with such an unilateral behavior are discussed, solution methods and applications are presented.     

General results for complete contacts subject to oscillatory shear

In this paper, we consider the general interfacial characteristics of a square elastic block, pressed onto an elastically similar half-plane by a constant normal force, and subjected to oscillatory shear. It is found that there is a critical coefficient of friction, 0.543, above which the contact is permanently stuck along its entire length for a shearing force below about 55% of that needed to cause sliding. For shearing forces above this, the contact interface will either shakedown to a fully adhered state (depending on the degree of reversal of the shear loading) or will exhibit cyclic slip at an interior point. If the coefficient of friction is below 0.543, the application of normal load alone will produce equal and opposite slip zones attached to the contact edges. The subsequent imposition of a shear force causes the leading edge slip zone to increase in length while the presence of residual slipping tractions at the trailing edge causes the trailing edge to lift off. Under oscillatory loading, the contact edges cycle between slip and separation over a minute region while an interior point may exhibit cyclic slip if the loading history is sufficiently demanding. The results found are of practical relevance to the study of fretting fatigue of complete contacts, such as some types of spline joint.     

An isotropic unilateral damage model coupled with frictional sliding for quasi-brittle materials

In this paper, we present an original extension of an isotropic damage model for quasi-brittle materials and assess its predictive capabilities. The proposed model accounts not only for unilateral behavior related to the opening and closure of microcracks but also for inelastic strains reflecting the frictional sliding along closed microcracks. More importantly, owing to its careful mathematical formulation with a particular attention paid to the continuous differentiability of the underlined thermodynamic potential, the model ensures the continuity of the inelastic stress–strain response. First applications show that it is able to predict the asymmetric behavior and hysteretic response of microcracked materials such as concrete and some rocks     

On models of dynamic systems with dry friction

An approach to the design of models of dynamical systems with high dry friction in the kinematic pair is developed. The members of the kinematic pair are represented by parts of rigid bodies. The system as a whole is considered to have a variable structure. According to this assumption, two modes of motion with different dissipative characteristics are possible. The states in which the modes exchange and the motion switches over into critical modes with dynamic self-locking are established. A system with a variable transfer function between members that form a nonideal constraint is described __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 97–105, May 2007.     

微/纳尺度粘着滑动接触的多尺度分析

采用分子动力学与有限元耦合的多尺度方法,求解二维刚性圆柱表面压头与弹性平面的微/纳尺度粘着滑动接触问题,通过与全分子动力学模拟结果的比较验证了多尺度方法的有效性。对压头半径、滑动速度、下压深度以及是否考虑粘着效应等对滑动接触性能的影响进行了全面研究,通过不同条件下摩擦力及接触力分布的比较,揭示了上述各参数对粘着滑动接触...     

Stability of a cylindrical shell with constraint of deflections and unilateral contacts

Yuzhone Design Bureau, Dnepropetrovsk, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 31, No. 9, pp. 46–50, September 1995.     

Simulation of spatial multibody systems with friction

A formulation for modeling and simulation of friction effects in spatial multibody systems is presented. Constraint reaction forces on rigid bodies that are connected by joints that support friction are derived as functions of Lagrange multipliers, using D’Alembert’s principle. Friction forces acting on bodies are calculated as a function of joint geometry, constraint reaction forces that are functions of Lagrange multipliers, and relative velocities at constraint contact points that are determined by system kinematics. Friction forces are implemented in index 0 differential-algebraic equations of motion that are solved numerically using explicit and implicit numerical integration methods. Spatial examples are presented, yielding accurate results and demonstrating that the systems are not stiff, even in the presence of friction and stiction.     

Part 1: Dynamical Characterization of a Frictionally Excited Beam

The dynamics of an experimental frictionally excited beam areinvestigated. The friction is characterized and shown to involve contactcompliance. Beam displacements are approximated from strain gagesignals. The system dynamics are rich, including a variety of periodic,quasi-periodic and chaotic responses. Proper orthogonal decomposition isapplied to chaotic data to obtain information about the spatialcoherence of the beam dynamics. Responses for different parameter valuesresult in a different set of proper orthogonal modes. The number ofproper orthogonal modes that account for 99.99% of the signalpower is compared to the corresponding number of linear normal modes,and it is verified that the proper orthogonal modes are more efficientin capturing the dynamics.     

Noether's theory of mechanical systems with unilateral constraints

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A constitutive theory for creep behavior of initially isotropic materials sustaining unilateral damage

The goal of the present work is to modify structure of the creep constitutive equations existing in the literature, and simultaneously to incorporate both damage induced anisotropy and unilateral damage into the constitutive model. The proposed nonlinear-tensor constitutive equation for creep together with the damage evolution equation take into account the secondary and tertiary creep of the initially isotropic materials. The material parameters of the model are determined using basic experiments. It is shown that the creep model is capable of describing available experimental data for the lateral creep responses under uniaxial compression.