Editorial

The term hysteresis is usually employed to describe a peculiar feature of the input-output relationship exhibited by various systems. More simply, a system is often said to be endowed with hysteresis if there is a lag in the arrivaI of the output with respect to the input, or if the output depends, in a rate-independent way, on the history ofthe input. Hysteresis is widely found in nature. It was first recognized in ferro- magnetic materials and subsequently in plasticity, friction and phase transitions, as well as in some what different fields such as mechanics, thermodynamics, biology, chemistry and economics among others.

    Hysteresis in a system is often the macroscopic ef fect of complex phenomena taking pIace on a smaller scale. While investigation of the causes of hysteresis calls for experiments and models on a microscopic scale, hysteresis itself can often be studied directly in scale of the system. It is thus usual for researchers in the fields in which hysteresis is observed to engage in modeling and experiments at both scales.

    Whereas the study of hysteresis in the field of magnetic materials is well established and can be considered a standard subject, this is not the case in the field of mechanics, where hysteresis is also relevant. This Special Issue of the lnternational Journal of Non-Linear Mechanics represents an attempt to focus attention on the study of hysteresis in mechanical systems using a macroscopic approach and emphasising the construction of models and the analysis of dynamic responses. The topics addressed by the 15 papers presented here do not claim to give a complete overview of the subject. Nevertheless, an effort has been made to include contributions relating to the following four aspects, which together provide a fairly comprehensive survey of hysteresis: (i) experiments, (ii) model ing, (iii) dynamic response, (iv) applications.

    The experimental and physical aspects are addressed by Abdullah, Kastner, Muller, Musolff; Xu and Zak, and by Ortin and Delaey: the papers refer to shape memory alloys (SMA), which in recent years have received much attention from researchers in the field of mechanics, and hence occupy considerable space in the Issue. For these types of alloy hysteresis is observed in stress-strain-temperature relations and is shown to arise as a consequence of various kinds of phase transformations.

    The modeling of hysteresis on a macroscopic scale is another important aspect and can be developed through different approaches. The paper by Visintin studies the mathematical aspects of hysteretic operators through the investigation of such issues as the existence of solutions to boundary value problems, continuity, and the homogenization of various models of hysteresis with an emphasis on plasticity and ferromagnetism. The paper by Bernardini and Pence presents a thermomechanically derived model for the pseudoelastic behavior of shape memory materials in which hysteresis follows from the features of the dissipation function. The paper by Mostaghel and Byrd reconsiders the Ramberg-Osgood equation, which is widely used to describe stress-strain hysteresis in many materials, and addresses the problem of the approximate inversion of the relation.

    The dynamic response of different kinds of system with hysteresis is the subject of several contributions. The response of a continuous system is considered by Krejci, who examines the existence of solutions and the dependence on initial conditions of periodic oscillations of a non-homogeneous elastic-plastic beam within a functional analytic framework.

The problem of optimal control of dynamical systems with Preisach hysteresis, both in the system and in the control, is investigated by Belbas and Mayergoyz, who derive dynamic programming equations and present a method for their numerical solution.

    Hysteretic one-degree-of-freedom shape memory alloy oscillators afe studied by Seelecke, who computes the torsional non-isothermal vibrations of a tube modeled by a statistical mechanics-based model, and by Masuda and Noori, who investigate the dynamics of SMA oscillators as models for passive vibration-reduction devices focusing on the optimal hysteresis loop characteristics that maximize the effectiveness ofthe device. The paper by Savi, Pacheco and Braga analyzes the occurrence of non-regular chaotic responses in a two-bar truss made of shape memory materials.

    The history-dependent characteristics of hysteretic systems suggest the usefulness of investigating their behavior under stochastic excitations. The paper by Bouc and Boussaa treats the problem of the drifting response of oscillators with hysteresis under stochastic excitation via a linearization method that captures the drift without simulation-calibrated parameters. The random response under non-white excitation of a particular class of hysteretic operators derived from the Duhem model is addressed in the paper by Ni, Ying, Ko and Zhu, in which an equivalent non-hysteretic model is developed in order to apply the Ito stochastic differential method.

    A discrete two-degree-of -freedom system with hysteretic restoring force, as described by Masing's model, is examined by Masiani, Capecchi and Vestroni, who present a thorough nonlinear dynamic characterization of the periodic oscilla- tions of the system by means of frequency-response curves. The problem of the adaptive identification of multi-degree-of-freedom hysteretic systems is studied by Smith, Masri, Kosmatopoulos and Chassiakos, using parametric and non-parametric models that furnish techniques able to track the response efficiently.

The Special Issue concludes with an interesting application: the dynamic characterization of a vibration-reduction device based on the hysteretic behavior of an inflected cable (the Stockbridge tuned mass damper) is investigated by Sauter and Hagedorn, using experimental and theoretical methods.

Finally, we would like to thank alI the authors who have contributed to this special volume on hystere- sis in mechanical systems. We afe also very grateful to Professor PoI Spanos and Pergamon Press, respectively editor and publisher of the Intemational Joumal of Non-Linear Mechanics.

Fabrizio Vestroni,

Dipartimento di Ingegneria Strutturale e Geotecnica,

University oJ Rome La Sapienza,

Via Eudossiana 18, 00184 Rome, Italy

E-mail address: vestroni@uniromal.it

Mohammad Noori,

Dept. oJ Mechanical and Aerospace Engineering,

North Carolina State University,

3211 Broughton Hall,

Raleigh, NC 27695-7910, USA

E-mail address: mnoori@eos.ncsu.edu