Paolo Casini

Friction oscillator excited by moving base and colliding with a rigid or deformable obstacle

The dynamics of non-smooth oscillators has not yet sufficiently been investigated, when damping is simultaneously due to friction and impact. Because of the theoretical and practical interest of this type of systems, an effort is made in this paper to lighten the behaviour of a single-degree-of-freedom oscillator colliding with an obstacle and excited by a moving base, which transfers energy to the system via friction. The different nature of discontinuities arising in the combined problem of friction and impact has been recognized and discussed. Closed-form solutions are presented for both transient and steady-state response, assuming Coulombs friction law and a rigid stop-limiting motion. Furthermore, a deformable (hysteretic) obstacle has been considered, and its influence on the response has been investigated.

On the rocking-uplifting motion of a rigid block in free and forced motion : influence of sliding and bouncing

SummaryThe problem of rocking response of a rigid block in free and forced motion has been studied for a number of technical reasons. Apart from the technical interests, the problem of rigid block rocking is intrinsically of interest from a theoretical point of view. In fact, the problem is highly nonlinear in nature.Aim of this paper is to study the “contact-impact” problem of a rigid block colliding on a frictional base, by means of a numerical simulation, and to compare numerical results with analytical responses known from the literature.The influence of sliding and bouncing on the orbit type and stability is analyzed by a 3-DOF model of the system and by a new refined model of the contact forces between block and base. Furthermore, attention has been paid to two-dimensional free motion of the block with three degrees of freedom. Refined analytical stress-strain relations in either normal and tangential directions with respect to the contact surfaces are formulated which allow to account for (i) up-lifting and hysteretic damping in normal direction, (ii) coupling between shear strength and compression force, friction dissipation and cumulating damage in tangential direction.

Nonlinear features in the dynamic response of a cracked beam under harmonic forcing

Detection of damage in beam structures is usually pursued by means of methods based on the measured variations of modal quantities, like frequencies and eigenmodes. The drawback of these methods is the small sensitivity of modal quantities to concentrated damage. Since a crack introduces nonlinearities in the system, the use of nonlinear techniques of damage detection merits to be investigated. With this aim the present paper is devoted to analyze the peculiar features of the nonlinear response of a cracked beam. The problem of a cantilever beam with an asymmetric edge crack subjected to a harmonic forcing at the tip is considered as a plane problem and is solved by using two-dimensional finite element model; the behaviour of the breathing crack is simulated as a frictionless contact problem. The modification of the response with respect to the linear one is outlined: in particular, excitation of sub- and super-harmonics, period doubling, quasi-impulsive behaviour at crack interfaces are the main achievements. These response characteristics can be used in nonlinear techniques of damage identification.© 2005 ASME

Dynamics of SDOF Oscillators with Hysteretic Motion-Limiting Stop

Interest in impact vibrations is two-fold: (i) a wide range ofpractical problems involve bodies colliding with one another or/and withobstacles, and (ii) the complex dynamics of such problems is a goodtesting bench for nonlinear theories. The assumption of rigid stop isquite popular, although unfortunately it does not allow us to simulatethe actual dissipative character of the impact response, but via apriori fixed coefficient of restitution. However, the correctdescription of the energy dissipated during impact is very important.In this paper, the dynamic response of a single-degree-of-freedomsystem is studied, where hysteretic stop, which allows the simulation ofthe real behaviour of a wide range of material pairings, is assumed; adistinction between hard and soft contacts is made according to theimpulsive or nonimpulsive nature of the contact reaction. The evolutionthrough stable closed orbits and period-doubling routes to chaos arestudied in terms of the clearance between the mass in the initial placeand the obstacle. For different clearances, strange attractors arerevealed and their evolution illustrated. Furthermore, in the case ofhard contact, an equivalent coefficient of restitution is proposed whichdepends, in a simple way, on some characteristic parameters of thehysteretic contact law. Such a coefficient, not given a priori butobtained via simulation of physical behaviour, provides the definitionof an equivalent impact oscillator (i.e. with rigid stop).

Dynamics of three-block assemblies with unilateral deformable contacts. Part 1: Contact modelling

As far as the dynamics of multibody systems is concerned, a brief review has been performed in order to frame the dynamic response of a trilith (the simplest scheme of a colonnade belonging to a temple) into a wide theoretical background. Under the assumption of rigid bodies, two different approaches can be found in the literature: rigid or deformable contacts formulation. In this paper, an effort is made at outlining the principle of rigid contact formulation and of deformable contact formulation. The latter approach can be assumed within the framework of the distinct element method; for this purpose a model of deformable contact has been proposed in order to simulate the real behaviour of stone joints. The sample application referred to the trilith will be presented in Part 2. Copyright

Forced motion of friction oscillators limited by a rigid or deformable obstacle

The forced dynamics of nonsmooth oscillators have not yet been sufficiently investigated when damping is simultaneously due to friction and impact. Because of the theoretical and practical interest in this type of system, an effort is made in this article to determine the behavior of a single-degree-of-freedom oscillator colliding with an obstacle and excited by a harmonic driving force and by a moving base with constant velocity. The response of this system has been investigated under the assumptions of rigid stop and of Coulombs friction law, with a static coefficient of friction included that is different from the kinetic one. The evolution through stable closed orbits and period-doubling routes to chaos are studied in terms of the clearance between the mass in the initial place and the obstacle. Periodic solutions exhibiting more than one stop and more than one collision per cycle as well as chaotic motions are investigated. An improvement of the friction-impact model is proposed that allows simulating an exponential velocity-dependent friction law and a deformable (hysteretic) obstacle. This model was tested via a sample application. *Communicated by E. V. Zakhariev.

Dynamics of three-block assemblies with unilateral deformable contacts. Part 2: Actual application

On the basis of the formulation of multibody dynamics with deformable contacts presented in Part 1, the dynamic response of the trilith (the simplest scheme of a colonnade belonging to a temple) to half-sine-wave pulse and to horizontal harmonic ground motion is analysed and the influence of bouncing and sliding on the type of motion is studied. Attention has been given to the dependence of the system response on the excitation amplitude and frequency, on the difference of friction between lintel-column and soil-column, and on the block slenderness. As far as half-sine-wave pulse is concerned, rest, stable motion and collapse have been identified; whereas, for harmonic excitation, rest or transient up to failure have been observed: during the transient a wide variety of responses up to chaotic motion has been exhibited. Copyright

BIFURCATIONS IN HYBRID MECHANICAL SYSTEMS WITH DISCONTINUITY BOUNDARIES

The paper studies the dynamics of a stop-belt friction oscillator (SBO). The system consists of a visco-elastic oscillator which is dragged by a rough support moving with constant driving velocity and can collide with a rigid obstacle. The peculiarity of this system is that, in the phase space, it exhibits two different discontinuity boundaries. Nonsmooth responses are consequently observed with nonstandard attracting properties. The evolution of steady state limit sets as the position of the obstacle is varied is described. The nonsmoothness sets of the system and, in particular, the presence of discontinuity boundaries caused by friction and impacts, lead to nonstandard bifurcations which are studied here by means of analytical and numerical tools.

Crack detection in beam-like structures by nonlinear harmonic identification

The dynamic behavior of beam-like structures with fatigue cracks forced by harmonic excitation is characterized by the appearance of sub and super-harmonics in the response even in presence of cracks with small depth. Since the amplitude of these harmonics depends on the position and the depth of the crack, an identification technique based on such a dependency can be pursued: the main advantage of this method relies on the use of different modes of the structure, each sensitive to the damage position in its peculiar way. In this study the identification method is detailed through numerical examples tested on structures of increasing complexity to evaluate the applicability of the method to engineering applications. The amount of data to obtain a unique solution and the optimal choice of the observed quantities are discussed. Finally, a robustness analysis is carried out for each test case to assess the influence of measuring noise on the damage identification.

Nonsmooth dynamics of a double-belt friction oscillator

The model of a double-belt friction oscillator is proposed, which exhibits multiple discontinuity boundaries in the phase space. The system consists of a visco-elastic oscillator dragged by two different rough supports moving with constant driving velocities. The evolution of steady-state attractors as the discontinuity parameters are varied is described. The presence of multiple discontinuity boundaries leads to nonsmooth responses which are studied here by means of analytical and numerical tools.