Dynamic Analysis of Spatial Linkages: A Recursive Approach

In this paper, recursive equations of motion of spatial linkages are presented. The method uses the concepts of linear and angular momentums to generate the rigid body equations of motion in terms of the Cartesian coordinates of a dynamically equivalent constrained system of particles, without introducing any rotational coordinates and the corresponding rotational transformation matrix. For the open-chain system, the equations of motion are generated recursively along the serial chains. Closed-chain system is transformed to open-chain by cutting suitable kinematic joints and introducing cut–joint constraints. An example is chosen to demonstrate the generality and simplicity of the developed formulation.     

Modèles discrets de structures tissées : Analyse de stabilité et de drapéDiscrete models of woven structures: stability and draping analysis

A discrete model of a woven fabric structure is established, whereby nodes endowed with a mass and a rotational rigidity are connected by rigid bars to form a two-dimensional truss. The set of four bars that delineate a quadrilateral area is further endowed with a torsion deformation mode. The kinematics of the truss reproduces the large rotations and displacements encountered for real tissues. The equilibrium shape of such a structure is obtained as the minimum of its total potential energy versus the whole set of kinematic translational and rotational variables, accounting for eventual kinematic constraints due to contact with a rigid surface by the Lagrange multipliers method. A stability analysis is conducted, and the potentiality of the model is illustrated by fabric draping simulations. To cite this article: B. Ben Boubaker et al., C. R. Mecanique 330 (2002) 871–877.     

A 2D+t SPH model to study the breaking wave pattern generated by fast ships

A 2D+t approach is applied to study the wave pattern generated by high speed slender ships with a sharp stem. This allows approximating the ship motion through a set of equations which are mathematically equivalent to those governing the unsteady 2D free-surface flow generated by a deformable body in the vertical plane transverse to the ship. To describe the body deformation, a proper modeling of the solid boundaries is needed. To this purpose the fixed ghost particle technique recently developed by the authors for 2D SPH schemes is adopted. Then, an in-depth analysis of the bow breaking wave evolution is provided focusing on the different features of the plunging jet as function of the ship forward velocity. The comparison with experimental data proves the proposed SPH scheme to be robust and accurate.     

Direct measurement of static yield properties of cohesive suspensions

A technique of yield stress investigation based upon the combined use of two devices (an applied stress rheometer and an instrument for measuring the propagation velocity of small amplitude, torsional shear waves) is described. Investigations into the low shear rate rheological properties of illitic suspensions are reported for shear rates, typically, in the range 10^–4— 10^–1 s^–1 under applied stresses in the range 0.01 — 10 Nm^–2 and involving shear strains between 10^–1 and 10^–4. Results are presented which demonstrate that the technique does not invoke the excessive structural disruption of material associated with applied shear rate based methods (direct and otherwise) and the widely encountered problem of wall slip at the surface of rotational measuring devices is avoided using miniature vane geometries. Results are compared with those obtained using smooth-walled cyclindrical measuring devices in both applied stress and applied shear rate instruments.Yield measurements are considered in relation to the structural properties of the undisturbed material state and shear moduli obtained by studying the propagation of small amplitude (10^–5 rad), high frequency (~ 300 Hz) torsional shear waves through the test materials are reported. Experimental techniques and instrument modifications to permit these measurements are described.     

A Model for the Determination of the Resisting Torque of the Rolling Bearing Cage Motion of Slow-Speed Kinematic Pairs

A simplified, plane model for determination of resisting torques of the rolling bearing cage motion of low speed kinematic pairs is presented. The considerations are devoted to an arbitrary character of the point contact of a rolling element–cage pairs lying in a plane which is crossing the rolling elements in their geometrical centre. The model has been developed on the basis of the analysis of motion kinematics of a bearing track and rolling elements. The proposed algorithm allows for continuous tracking the resisting torque of the cage and its components during the kinematic pair motion.     

Parametric study of the Hartmann–Sprenger tube

Experiments were conducted with a Hartmann–Sprenger tube (H–S) to study the effect of different parameters on the frequency and amplitude of acoustic fluctuations excited when the H–S underexpanded jet impinges on an in-line cavity. Time averaged shadowgraphs were acquired to study the flow field between the underexpanded jet and the cavity for varying parameters of the H–S tube. It was observed that the H–S tube primarily excited two different modes. The first mode corresponds to the jet regurgitant mode (JRG) where the frequency of oscillations scales as a function of the cavity depth. The other mode is screech where an oscillating shock is formed in front of the cavity. The screech mode excites a higher acoustic frequency than the JRG and it is observed to be a strong function of the pressure ratio R, and distance between the jet and the cavity X. At a fixed cavity length, varying standoff distance X could excite either the JRG or screech. At very low standoff distances (X/D_j<0.8), the current study indicates that there is a mode switch from screech to JRG. A cavity to jet diameter, D_c/D_j>1 was found to sustain JRG over a wide range of X. Diameter ratios D_c/D_j<1 sustained high frequency screech modes in a wide range of H–S tube parameters.     

Nontangential Limit of the Weyl m-Functions for the Ergodic Schrödinger Equation

This paper deals with the spectral and qualitative problems associated with the one-dimensional ergodic Schrödinger equation. Let A ₂ be the set of those energies for which the real projective flow admits an invariant linear measure with square integrable density function. On this set we calculate the directional derivative of the Floquet coefficient and prove the existence of a nontangential limit of the Weyl m-functions in the L ¹-topology. In particular, we verify that the known Dieft–Simon inequality for the derivative of the rotation number obtained from Kotani's theory is in fact an equality. In the bounded orbit case we deduce the uniform boundedness of the Weyl m-functions and obtain necessary and sufficient conditions to assure their uniform convergence.     

Effect of temperature on the fracture modes of BHW-35 steel under mode-II loading

Finite element method (FEM) has been used to analyze the stress and strain fields and the stress tri-axial levels around the tip of the crack under mode- II loading. The results show that: under mode- II loading, the direction of the maximum tensile stress and that of the maximum tri-axial levels (R _o ) exist at an angle of –75. 3° from the original crack plane; the maximum shear stress andR _o = 0 exist along the original crack plane.Mode- II loading experiment using BHW-35 steel at different temperatures show that there are two kinds of fracture mode, opening mode (or tensile mode) and sliding mode (or shear mode). A decrease in temperature causes the fracture mode to change from shear mode to tensile mode. For BHW-35 steel, this critical temperature is about –90 C. Actually, under any kind of loading mode (mode I . mode II , mode III or mixed mode), there always exist several kinds of potenital fracture modes (for example, opening mode, sliding mode, tearing mode or mixed mode). The effect of temperature under mode- II loading is actually related to the change of the elastic-plastic properties of the material.     

The effect of T-stress on crack–inclusion interaction under mode I loading

A closed-form solution has been developed to predict the effect of T-stress on the crack–inclusion interaction. As validated by several numerical examples, the approximate solution has satisfactory accuracy for different inclusion shapes and modulus ratios between inclusion and matrix under different T-stress levels. Thus the role of T-stress in crack–inclusion interaction can be predicted quantitatively.     

Anisotropic plasticity for sheet metals using the concept of combined isotropic-kinematic hardening

Hill's 1948 anisotropic theory of plasticity (Hill, R., 1948. A theory of yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. London A193, 281–297) is extended to include the concept of combined isotropic-kinematic hardening, and the objective of this paper is to validate the model so that it may be useful for analyses of sheet metal forming. Isotropic hardening and kinematic hardening may be experimentally observed in sheet metals, if yielding is defined by the proportional limit or by a small proof strain. In this paper, a single exponential term is used to describe isotropic hardening and Prager's linear kinematic hardening rule is applied for simplicity. It is shown that this model can satisfactorily describe both the yield stress and the plastic strain ratio, the R-ratio, observed in tension test of specimens cut at various angles measured from the rolling direction of the sheet. Kinematic hardening leads to a gradual change in the direction of the plastic strain increment, as the axial strain increases in the tension test; while in the traditional approach for sheet metal, this direction does not change due to the use of isotropic hardening.     

Three-dimensional studies on bicomponent extrusion

The present work is concerned with the mathematical modelling and numerical simulation of three-dimensional (3-D) bicomponent extrusion. The objective is to provide an understanding of the flow phenomena involved and to investigate their impact on the free surface shape and interface configuration of the extruded article. A finite element algorithm for the 3-D numerical simulation of bicomponent stratified free surface flows is described. The presence of multiple free surfaces (layer interface and external free surfaces) requires special free surface update schemes. The pressure and viscous stress discontinuity due to viscosity mismatch at the interface between the two stratified components is handled with both a double node (u–v–w–P ₁ –P ₂ –h ₁ –h ₂) formulation and a penalty function (u–v–w–P–h ₁ –h ₂) formulation.The experimentally observed tendency of the less viscous layer to encapsulate the more viscous layer in stratified bicomponent flows of side-by-side configuration is established with the aid of a fully 3-D analysis in agreement with experimental evidence. The direction and degree of encapsulation depend directly on the viscosity ratio of the two melts. For shear thinning melts exhibiting a viscosity crossover point, it is demonstrated that interface curvature reversal may occur if the shearing level is such that the crossover point is exceeded. Extrudate bending and distortion of the bicomponent system because of the viscosity mismatch is shown. For flows in a sheath-core configuration it is shown that the viscosity ratio may have a severe effect on the swelling ratio of the bicomponent system.Modelling of the die section showed that the boundary condition imposed at the fluid/fluid/wall contact point is critical to the accuracy of the overall solution.     

Invertibility and dichotomy of differential operators on a half-line

A linear ordinary differential operator with bounded coefficients satisfying certain homogeneous initial conditions is shown to be invertible onL _n ² (0, ) if and only if the underlying system of differential equations has a dichotomy. Moreover, in that case the operator is proved to be a direct sum of two infinitesimal generators ofC ₀-semigroups, one of which has support on the negative half-line and the other on the positive half-line. The effect of perturbations of the initial values on the dichotomy is also described.     

Bifurcations and equilibria in the extended N-body ring problem

We consider the motion of an infinitesimal particle under the gravitational field of (n+1) bodies in ring configuration, that consist of n primaries of equal mass m placed at the vertices of a regular polygon, plus another primary of mass m₀=βm located at the geometric center of the polygon. We analyze the phase flow, determine the equilibria of the system, their linear stability and the bifurcations depending on the mass of the central primary (parameter β).This study is extended to the case when the central body is an ellipsoid or a radiation source. In this case, the topology of the problem is modified.     

Spreading of inkjet droplet of non-Newtonian fluid on solid surface with controlled contact angle at low Weber and Reynolds numbers

The dynamics of inkjet droplet of non-Newtonian fluid on glass substrates was investigated experimentally and compared with that of Newtonian fluid. The non-Newtonian fluids used here were 100 ppm solutions of polyethylene oxide (300k, 600k and 900k) dissolved in the 1:1 mixture of water and glycerin. Weber number (We) was 2–35 and Ohnesorge number was fixed at 0.057 ± 0.003. The wettability of solid substrate was also varied. The diameter of inkjet droplets in the present study was about 50 μm and was much smaller than the size of the previous studies on drop impact. Due to the development of a thin and long thread at the rear of the main drop the jetting window of polymer solution was much narrower than that of Newtonian fluid, and hence the experimental range of Weber number was restricted. The impact scenarios of non-Newtonian inkjet droplets were found to be qualitatively different from those of Newtonian droplets during the receding phase while they were almost the same as the Newtonian fluid case during the kinematic phase. The spreading diameter at the equilibrium was well correlated with the modified Weber number (We′ = We/(1 − cos θ_eq)) as in the case of Newtonian fluid, where θ_eq is the equilibrium contact angle. The similarity or disparity between the Newtonian and non-Newtonian cases was discussed considering the conformation of polymer chains during each stage of drop deformation.     

Green's function,continual weighted composition operators along trajectories,and hyperbolicity of linear extensions for dynamical systems

The hyperbolicity of linear skew-product flows with infinite-dimensional fibersE over a dynamical system on a compact metric spaceX is described in terms of the existence and uniqueness of Green's function and in terms of the spectra for family of the semigroups of weighted composition operators acting inL ₂(R;E) and parametrized by the points ofX.     

Optimization Problems of Controlled Multibody Systems Having Spring-Damper Actuators

The optimal control of the motion of mechanical systems is studied. A characteristic feature of these systems is the presence of passive actuators (springs, dampers, etc.). Energy-optimal control laws and structural parameters of nonlinear spring–damper actuators are determined analytically, which is necessary to impart arbitrary motion to a controllable mechanical system with n degrees of freedom. As an example, a numerical solution is presented for the problem of designing an energy-optimal spring actuator for a robot manipulator of closed kinematic structure     

Complex Parametric Vibrations of Flexible Rectangular Plates

In this paper we consider parametric oscillations of flexible plates within the model of von Kármán equations. First we propose the general iterational method to find solutions to even more general problem governed by the von Kármán–Vlasov–Mushtari equations. In the language of physics the found solutions define stress–strain state of flexible shallow shell with a bounded convex space R ² and with sufficiently smooth boundary . The new variational formulation of the problem has been proposed and his validity and application has been discussed using precise mathematical treatment. Then, using the earlier introduced theoretical results, an effective algorithm has been applied to convert problem of finding solutions to hybrid type partial differential equations of von Kármán form to that of the ordinary differential (ODEs) and algebraic (AEs) equations. Mechanisms of transition to chaos of deterministic systems with infinite number of degrees of freedom are presented. Comparison of mechanisms of transition to chaos with known ones is performed. The following cases of longitudinal loads of different sign are investigated: parametric load acting along X direction only, and parametric load acting in both directions X and Y with the same amplitude and frequency.     

Navier–Stokes Equations: Controllability by Means of Low Modes Forcing

We study controllability issues for 2D and 3D Navier–Stokes (NS) systems with periodic boundary conditions. The systems are controlled by a degenerate (applied to few low modes) forcing. Methods of differential geometric/Lie algebraic control theory are used to establish global controllability of finite-dimensional Galerkin approximations of 2D and 3D NS and Euler systems, global controllability in finite-dimensional projection of 2D NS system and L2-approximate controllability for 2D NS system. Beyond these main goals we obtain results on boundedness and continuous dependence of trajectories of 2D NS system on degenerate forcing, when the space of forcings is endowed with so called relaxation metric.     

To derive Lagrange equations of nonholonomic systems without using the Chetaev conditions

The present paper derives the equation of motion for a class of nonholonomic dynamical systems from the d’Alembert–Lagrange equation. In this paper, the relation dδ = δd is assumed only for those generalized coordinates whose variations are independent. For the remaining coordinates, the transpositional relations are derived by means of mathematics method, which are different from the Chetaev condition. Several examples are given.     

Direct Statistical Simulation of a Supersonic Flow of a Binary Mixture of Rarefied Gases around a Transversely Positioned Cylinder

A supersonic flow of a binary mixture of gases in a wide range of rarefaction (from a flow with a Knudsen number K _n = 0.1 to a free-molecular flow) around a cylinder is studied by means of direct statistical Monte Carlo simulations (DSMC method). The influence of a small fraction of heavy particles in a light gas flow on the region of significant nonequilibrium near the cylinder and on the heat flux is considered.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 5, pp. 53–59, September–October, 2005.