Showing papers in "Meccanica in 1980"
TL;DR: In this paper, a method for computing all of the Lyapunov characteristic exponents of order greater than one is presented, which is related to the increase of volumes of a dynamical system.
Abstract: Since several years Lyapunov Characteristic Exponents are of interest in the study of dynamical systems in order to characterize quantitatively their stochasticity properties, related essentially to the exponential divergence of nearby orbits. One has thus the problem of the explicit computation of such exponents, which has been solved only for the maximal of them. Here we give a method for computing all of them, based on the computation of the exponents of order greater than one, which are related to the increase of volumes. To this end a theorem is given relating the exponents of order one to those of greater order. The numerical method and some applications will be given in a forthcoming paper.
1,659 citations
TL;DR: In this article, the authors give an explicit method for computing all Lyapunov Characteristic Exponents of a dynamical system, together with some numerical examples for mappings on manifolds and for Hamiltonian systems.
Abstract: The present paper, together with the previous one (Part 1: Theory, published in this journal) is intended to give an explicit method for computing all Lyapunov Characteristic Exponents of a dynamical system. After the general theory on such exponents developed in the first part, in the present paper the computational method is described (Chapter A) and some numerical examples for mappings on manifolds and for Hamiltonian systems are given (Chapter B).
896 citations
TL;DR: In this paper, it was shown that the results established by Taylor [1] for the linearly viscous fluid are uncondi tionally true, irrespective of the time scale which characterizes the fluid or the size of the vortices in the case of incompressible second grade fluids provided they are thermodynamically compatible.
Abstract: G. I. Taylor [ 1 ] showed that the flow representing a double array of vortices which has the same periodicity in both the x and y directions is a solution to the equations of motion in two dimensions of a linearly viscous fluid. It was shown in [2] that such a result is also true for 'second order' fluids if time scale which characterizes the memory of the fluid and the size of the vortices satisfy certain apriori restrictions. In this note we show that the results established by Taylor [1] for the linearly viscous fluid are uncondi t ional ly true, irrespective of the time scale which characterizes the fluid or the size of the vortices in the case of incompressible second grade fluids provided they are thermodynamically compatible. Also, in this analysis we investigate the relationship between the rate of decay of the vortices, and the periodicity of the vortices. It is found that if the periodicity is increased in the x or y directions, the vortices decay faster. It is also found, as is to be expected, that the vortices decay faster as the coefficient of viscosity # increases, while the decay is slower if the normal stress moduli oq is larger. The Cauchy stress T in an incompressible second grade fluid is assumed to be related to the fluid motion in the following manner [3 ]
36 citations
TL;DR: In this paper, a thermal theory of monodimensional heterogeneous deflagration waves is presented from a linearized point of view, and the frequency response function is determined both for pressure and radiation driven combustion waves.
Abstract: Burning stability analyses of solid propellants are performed, within the framework of a thermal theory of monodimensional heterogeneous deflagration waves, from a linearized point of view. The frequency response function is determined both for pressure and radiation driven combustion waves. Two limiting schemes for the quasi-steady gas phase are implemented: distributed and sharp flame models. Work available from the literature in this field is reviewed, corrected, and extended. Particular attention is given to the connection between pressure and radiation driven admittance functions. Burning stability properties predicted from linear and nonlinear theories are compared. A way to rate experimentally the dynamic burning stability of condensed substances with optically opaque condensed phase and transparent flame is suggested.
13 citations
TL;DR: In this paper, the problem of two symmetric arc cracks lying between a rigid circular inclusion embedded in an infinite matrix under biaxial loading at infinity is considered, and the boundary value problem is solved and stress and displacement components are calculated along the inclusion boundary.
Abstract: The problem of two symmetric arc cracks lying between a rigid circular inclusion embedded in an infinite matrix under biaxial loading at infinity is considered. By using the complex variable tecnique, the boundary value problem is solved and stress and displacement components are calculated along the inclusion boundary. Moreover, investigating the local stress field, a stress criterion, already proposed by authors, allowing either the crack extension at the interface or its deviation into the matrix to be taken into account, is applied to study the fracture response of the elastic system. The critical applied loads as well as the angle of the incipient crack extension are expressed in terms of the central angle subtended by the crack arcs. Finally the biaxial load effects are graphically shown and discussed.
11 citations
TL;DR: In this article, the authors analyzed the existence, uniqueness and regularity of the elastic plate on unilateral elastic foundation problem and gave some results for the one-sided rigid foundation case. But they did not consider the case of a single rigid foundation.
Abstract: Solution existence, uniqueness and regularity are analyzed for the elastic plate on unilateral elastic foundation problem. Some results are also given for the one-sided rigid foundation case.
8 citations
TL;DR: In this paper, the multiple collision method is applied to solve a time-dependent problem of test particle transport as governed by the Boltzmann equation in the frame of the scattering kernel formulation for the collision term.
Abstract: The multiple collision method is applied to solve a time-dependent problem of test particle transport as governed by the Boltzmann equation in the frame of the scattering kernel formulation for the collision term. Several features of the solution found are discussed. Curves representing the approach to the steady state are presented.
7 citations
TL;DR: In this paper, the hydrodynamic lubrication of a porous metal bearing from a rigorous mathematical point of view is studied, using mainly the theory of the elliptic unilateral problems, and it is shown that the theory is applicable to the case of a single bearing.
Abstract: The hydrodynamic lubrication of a porous metal bearing is studied from a rigorous mathematical point of view. We use mainly the theory of the elliptic unilateral problems.
5 citations
TL;DR: In this article, the authors deal with the nonlinear creep analysis using equilibrium finite elements, adopting a concept of the mean value of the equivalent shear modulus, a direct iterative procedure is proposed with the minimum calculation in the modification of the global stiffness matrix.
Abstract: The paper deals with the nonlinear creep analysis using equilibrium finite elements. In adopting a concept of the mean value of the equivalent shear modulus, a direct iterative procedure is proposed with the minimum calculation in the modification of the global stiffness matrix. The difficulties due to the incompressibility of the creep flow are overcome by a numerical artifice where the hydrostatic stress component is considered as a Lagrange parameter. Some numerical results are shown and compared with the analytical method.
4 citations
TL;DR: In this paper, a flexible inextensible elastica with fixed end points and fixed equal end slopes, and varying length is considered, and the existence of at least one elastic curve has been proved when the elastica length is greater than the distance between the end points.
Abstract: A flexible inextensible elastica has been considered, with fixed end points and fixed equal end slopes, and varying length. The existence of at least one elastic curve has been proved when the elastica length is greater than the distance between the end points. A critical value of the length has been found, as a function of the given end slope only, corresponding to some elastic curves. From each of them two new elastic curves branch when the length is greater than the critical value.
4 citations
TL;DR: In this paper, the axially loaded elastic beam on a one-sided elastic foundation was analyzed and the existence of the critical load was proved and its expression was given, where the axial load was shown to be independent of the elasticity of the beam.
Abstract: We analyze the problem of the axially loaded elastic beam on a one-sided elastic foundation. The existence of the critical load is proved and its expression is given.
TL;DR: In this article, the kinematics of the transmission between skew shafts by universal coupling is analyzed, and conditions allowing constant velocity transmission are explored, and expressed in function of the geometric parameters defining the system.
Abstract: In this paper, kinematics of the transmission between skew shafts by universal coupling is analyzed. Conditions allowing constant velocity transmission are explored, and expressed in function of the geometric parameters defining the system. Subsequently, conditions allowing constant velocity transmission when specific relative displacements are introduced between input and output shafts are expressed; it can be obtained with appropriate helicoidal (with variable pitch helix) spline placed into the intermediate shalft. The same conditions are explored for displacements whatsoever; an irregularity comes into play, because functioning conditions are not yet kinematically correct; but irregularity degree can be reduced if specific conditions are respected.
TL;DR: In this article, a theory for the torque transmission with friction in a large class of multibodied systems with fixed point for the homokinetic transmission of the motion between two converging axes is proposed.
Abstract: This work proposes a theory for study of the torque transmission with friction in a large class of multibodied systems with fixed point for the homokinetic transmission of the motion between two converging axes.
TL;DR: In this article, the equilibrium stability of elastic solids under dead loads is investigated, and some relationships between the well known potential energy criterium and alternative energy techniques, among which the complementary energy technique, are presented.
Abstract: The paper is concerning the equilibrium stability of elastic solids under dead loads. Some relationships between the well known potential energy criterium and alternative energy techniques, among which the complementary energy technique, are presented. Various properties of these techniques are demonstrated; particular emphasis is given to problems characterized by multiple load parameters.
TL;DR: In this paper, the shape of the UF6 extraction scoop for the ultracentrifuges is designed to minimize the restraining moment by means of a typical variational problem.
Abstract: The aim of the present study is to design the shape of the UF6 extraction scoop for the ultracentrifuges so as to minimize the restraining moment. The local reduction of the fluid velocity is evaluated by considering the equilibrium between the accelerating and restraining forces acting on the fluid. By defining the function to be minimized and the links to be considered for the variables of the problem, the minimum is obtained by means of a typical variational problem. Some optimization examples, at various Mach numbers, and some comparisons with non optimal shape scoops are then shown.
TL;DR: In this paper, a general procedure is developed in order to calculate the vibratory motions of non-linear systems with one degree of freedom, where the vibration is considered as an infinite sequence of increasing and decreasing half-waves, for each of wich time and deplacement are considered as initial data, with initial velocity zero.
Abstract: A general procedure is developed in order to calculate the vibratory motions of non linear systems with one degree of freedom. The vibration is considered as an infinite sequence of increasing and decreasing half-waves, for each of wich time and deplacement are considered as initial data, with initial velocity zero. Recurrent formulae giving the initial data for each half-wave as a function of those relative to the preceeding half-wave are calculated. This procedure is applied to the Duffing equation and leads to study of the powers of a matrix, whose behaviour, when the exponent goes to infinity, determines the character of stability or instability or asymptotic periodicity of the solution.
TL;DR: Reynolds' equation for laminar incompressible flow is numerically integrated, with no theoretical limits due to particular bearing geometries, which allows the extension of results to most commonly encountered industrial designs.
Abstract: A Finite Element approach to the problem of stability of horizontal journal bearings is presented and compared with an alternative well-known approximate method. Reynolds' equation for laminar incompressible flow is numerically integrated, with no theoretical limits due to particular bearing geometries. This allows the extension of results to most commonly encountered industrial designs. Particular care is devoted to the computer optimization of the problem. The result is a program suitable for storage in small computers and for bearing industrial design.
TL;DR: In this paper, it was observed that pure mathematical estimates of errors involved by the introduction of approximate procedures in structural analysis may be insufficient to judge the effectiveness of the method and the adequacy of the results, and that the simultaneous presence of many other uncertainties that, making necessary the application of one or more safety coefficients, tend to adsorb, at least partially, the influence of wrong calculations on structure reliability.
Abstract: It is observed that pure mathematical estimates of errors involved by the introduction of approximate procedures in structural analysis may be insufficient to judge the effectiveness of the method and the adequacy of the results. This circumstance can be explained by the simultaneous presence of many other uncertainties that, making necessary the application of one or more safety coefficients, tend to adsorb, at least partially, the influence of wrong calculations on structure reliability.
TL;DR: In this article, the dynamic performance of a machine-tool isolated mounting base system when unstable behaviour of the moving slider is observed due to low driving speed was analyzed. But the analysis was restricted to the case of a single sliding window.
Abstract: This paper describes the theoretical analysis of the dynamic performance of a machine-tool isolated mounting-base system when unstable behaviour of the moving slider — stick slip motion — occurs owing to low driving speed. The equations of motion are derived from Lagrange's equation when the basic energy expressions of such a system are known.
TL;DR: In this article, an approach to the numerical solution of bi-harmonic problems in the non-linear field is presented, with appropriate conditions on the components of the stress tensor and of the deformation.
Abstract: The report presents an approach to the numerical solution of bi-harmonic problems in the non-linear field. Within the sphere of more recent methods based on finite elements alone, there are a large number of works that propose solutions to this problem. Here, with reference to an approach produced by Mindlin, assumptions are advanced that will make it possible to analyse thin plates in the presence of deformatory effects due to shear. The problem is also reformulated in terms of three-dimensional elasticity, with appropriate conditions on the components of the stress tensor and of the deformation. This method makes it possible to deal with the punctual quantities inside the solid in question, instead of the intermediate components on the cross-section, which are typical of classic approaches to the matter. Moreover, by means of appropriate numerical integration techniques, it reduces the resolvent system of equations to the usual dimensions for the analysis of flat plates. This procedure is particularly advantageous in the case of non-linear phenomena, which are present as laws constituting the stress-strain relationship. This report produces examples that take as assumptions of non-linearity the not completely elastic behaviour of the material, using VON MISES' limit function within the framework of the plasticity theory.
TL;DR: In this article, a suitable incremental formulation of the Ceradini's theorem on the dynamic shakedown stability property may be proven, if the comparison material is assumed to be absolutely stable.
Abstract: Starting from a Benvenuto's sufficient stability Criterion, in the elastic-plastic range, on the load paths which will systematically exclude elastic returns in the actual state, and adopting a suitable incremental formulation of the Ceradini's theorem on the dynamic shakedown, the dynamic shakedown stability property may be proven, if the comparison material is assumed absolutely stable.
TL;DR: The applicability of the Frahm dynamic vibration absorber is generally restricted to the case of constant forcing frequency; it may happen, however, that this condition is fulfilled only after a certain instant, prior to which the frequency is increasing, e.g. linearly as discussed by the authors.
Abstract: The applicability of the Frahm dynamic vibration absorber is generally restricted to the case of constant forcing frequency; it may happen, however, that this condition is fulfilled only after a certain instant, prior to which the frequency is increasing, e.g. linearly. The analysis of the transient behaviour shows that in such a situation the main mass can undergo oscillations much broader than those predictable by the constant frequency scheme.
TL;DR: In this article, a numerical investigation of a viscous incompressible rotating fluid flow in a circular cylinder with a net axial flow rate is presented, where the cylinder is opened at the bottom and closed at the top by an ideal porous rotating disk, through which the incoming fluid flows receiving an action of solid body rotation.
Abstract: A numerical investigation of a viscous incompressible rotating fluid flow in a circular cylinder with a net axial flow rate is presented. The cylinder is opened at the bottom and closed at the top by an ideal porous rotating disk, through which the incoming fluid flows receiving an action of solid body rotation. This physical model has been chosen for a realistic representation of fluid direct prerotation which takes place in the suction pipe of a centrifugal pump. The flow field was solved by the direct solution of the complete Navier-Stokes equations for values of Reynolds tangential numberRe
t up to 5 000. The numerical results give a detailed and complete sight of the principal features of such kind of flow, and, compared with experimental results in the turbolence range ofRe
t. show a significant qualitative agreement. A comparison with previous numerical investigations of other authors about rotating fluids is reported.
TL;DR: For a class of simple struts the analysis of equilibrium is accomplished on the basis of qualitative properties as mentioned in this paper, in particular, symmetries of the struts and monotonicity of their constitutive functions are used to foresee bifurcation points.
Abstract: For a class of simple struts the analysis of equilibrium is accomplished on the basis of qualitative properties. In particular, symmetries of the struts and monotonicity of their constitutive functions are used to foresee bifurcation points and to get a local description of the bifurcated branches.