Phenomena of Instability in Non-Conservative Dynamical Systems (original) (raw)
Related papers
Comptes Rendus Mécanique, 2003
A review on the stability analysis of solids in unilateral and frictional contact is given. The presentation is focussed on the stability of an equilibrium position of an elastic solid in frictional contact with a fixed or moving obstacle. The problem of divergence instability and the obtention of a criterion of static stability are discussed first for the case of a fixed obstacle. The possibility of flutter instability is then considered for a steady sliding equilibrium with a moving obstacle. The steady sliding solution is generically unstable by flutter and leads to a dynamic response which can be chaotic or periodic. This dynamic response leads to the generation of stick-slip-separation waves on the contact surface in a similar way as Schallamach waves in statics. Illustrating examples and principal results recently obtained in the literature are reported. Some problems of frictioninduced vibration and noise emittence, such as brake squeal for example, can be interpreted in this spirit.
Numerical Modeling of Friction-Induced Vibrations and Dynamic Instabilities
Applied Mechanics Reviews, 1994
A numerical study of dynamic instabilities and vibrations of mechanical systems with friction is presented. Of particular interest are friction-induced vibrations, self-excited oscillations and stick-slip motion. A typical pin-on-disk apparatus is modeled as the assembly of rigid bodies with elastic connections. An extended version of the Oden-Martins friction model is used to represent properties of the interface. The mechanical model of the frictional system is the basis for numerical analysis of dynamic instabilities caused by friction and of self-excited oscillations. Coupling between rotational and normal modes is the primary mechanism of resulting self-excited oscillations. These oscillations combine with high-frequency stick-slip motion to produce a significant reduction of the apparent kinetic coefficient of friction. As a particular study model, a pin-on-disk experimental setup has been selected. A good qualitative and quantitative correlation of numerical and experimental ...
Journal of the Mechanics and Physics of Solids
Unstable frictional slip motions are investigated with a rate and state friction law across the transitions from stable, quasi-static slip to dynamic, stick-slip motion, and finally to, inertia dominated quasi-harmonic vibration. We use a novel numerical method to capture the full dynamics and investigate the roles of inertial and quasistatic factors of the critical stiffness defining the transition to instability, K c. Our simulations confirm theoretical estimates of K c , which is dependent on mass and velocity. Furthermore, we show that unstable slip motion has two distinct dynamic regimes with characteristic limit cycles: (i) stick-slip motions in the quasi-static (slowly loaded) regime and (ii) quasi-harmonic oscillations in the dynamic (rapidly loaded) regime. Simulation results show that the regimes are divided by the dynamic frictional instability coefficient, η = MV 2 / σ aD c and stiffness of the system K. The quasi-static regime is governed by the ratio K/K c and both the period and magnitude of stick-slip cycles decrease with increasing loading rate. In the dynamic regime, slip occurs in harmonic limit cycles, the frequency of which increases with loading velocity to a limit set by the natural frequency of the system. Our results illuminate the origin of the broad spectrum of slip behaviors observed for systems ranging from manufacturing equipment to automobiles and tectonic faults, with particular focus on the role of elasto-frictional coupling in dictating the transition from slow slip to dynamic instability. We highlight distinct characteristics of friction-induced slip motions (stick-slip and friction-induced vibration) and show that the dynamic frictional instability coefficient (η) is a key parameter that both defines the potential for instability and determines the dynamic characteristics of instability.
Courses and lectures, 2002
The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.
Effects of damping on mode-coupling instability in friction induced oscillations
ZAMM, 2003
The mode-coupling instability has generally been acknowledged as one of the most prominent mechanisms leading to selfexcited oscillations in sliding friction systems. The influence of structural damping on this type of instability mechanism however has not yet been fully clarified. The objective of the present work therefore is to investigate qualitative and quantitative aspects of the mode-coupling instability in the presence of structural damping, which will be assumed as linear viscous. For the sake of simplicity a two-degree-of-freedom minimal model is set up and analyzed. It is shown that under specific conditions the mode-coupling instability may be regarded as a viscous instability in the sense that an increase in structural damping may render a stable system unstable. An explanation for this behavior is given by two lines of argument: First a description and explanation is given in terms of eigenvalue-analysis. Due to the mathematical formality of this approach, the insight gained remains phenomenological. Second, a feedback-loop formalism is developed that allows a more detailed understanding of the underlying mechanical processes. Based on this formalism, necessary and in sum sufficient conditions for the onset of instability can be deduced and also the role of damping can be clarified.
New trends in Dynamics and Stability Preface
Meccanica, 2017
This Special Issue, entitled New trends in Dynamics and Stability aims to provide an up-to-date overview on recent research results obtained within GADeS: the AIMETA Group of Dynamics and Stability. This group, which is part of AIMETA, the Italian Association of Theoretical and Applied Mechanics, was founded in 2012 aiming to stimulate the development of interdisciplinary research activities involving scientists with different cultural backgrounds. Applications originated from civil and mechanical engineering, that is, concerned about solid dynamics, structural dynamics, machine dynamics, dynamical system theory, stability, bifurcation and control theory: the specific themes of interest of GADeS are
Advances in stability, bifurcations and nonlinear vibrations in mechanical systems
Nonlinear Dynamics, 2021
The present Special Issue was initially conceived for presenting a survey of recent studies carried out by researchers participating in the Dynamics and Stability Group (GADeS) within the Italian Society of Theoretical and Applied Mechanics (AIMETA). GADeS was founded in 2011 thanks to the initiative of Prof. Angelo Luongo, under the umbrella of AIMETA, with the aim of sharing knowledge on the topics of dynamics and stability across different research fields, including applied mathematics, civil and mechanical engineering. Specifically, this Special Issue was supposed to present the developments of some of the research presented at the most recent GADeS symposium as part of the 2019 AIMETA Conference. The breadth of the topics covered and their importance at an international level led us, in agreement and with the support of the Editor-in-Chief, Prof. Walter Lacarbonara, to enlarge the domestic viewpoint, and to consider a fully international Special Issue by inviting worldwide renowned scientists in order to give a broader view on recent advances in stability, bifurcations and nonlinear vibrations that may involve different kinds of mechanical systems. Actually, while having old and well-consolidated roots, this is a modern, active and challenging research field, with new applications in science and engineering and lots of new exciting developments. The papers selected for the present Special Issue can be roughly collected into four broad areas, each collecting a certain number of papers, all related to the aforementioned topics. A first grouping of papers deals with problems of stability and bifurcations arising in fluid/structure problems with a special emphasis on aeroelastic systems. Problems related to flutter analysis in classical or supersonic conditions [1-3], vortex-induced vibrations [4, 5] and galloping instabilities [6, 7] are thoughtfully addressed, together with more theoretical A. Luongo (&) Dept. of Civil, Construction-Architectural and Environmental Engineering (DICEAA), M&MoCS,
Instability of systems with a frictional point contact. Part 1: basic modelling
Journal of Sound and Vibration, 2004
In a companion paper, a theory was presented which allows the study of the linear stability of a class of systems consisting of two subsystems coupled through a frictional contact point. A stability criterion in terms of transfer functions was derived and used to simulate the behaviour of generic systems. In the present paper, this approach was pursued and generalized by relaxing in turn certain of the assumptions made earlier. By doing this, it is possible to catalogue systematically all the routes to instability conceivable within the scope of linearity for the class of systems considered. The additional routes to instability identified are as follows. First, the contact point was made compliant by adding a linear contact spring at the interface between the two subsystems. This feature proved to have a significant influence on stability when the contact spring stiffness takes values of the same order of magnitude or lower than that of the average structural stiffness of the system. Second, a route to instability is possible if the system structural damping possesses a slight non-proportional component. The last and most elaborate extension consisted in allowing the coefficient of friction to vary linearly with the sliding speed. Simulation results suggest that a coefficient falling with increasing sliding speed can destabilize an otherwise stable system or can make it even more unstable. In accordance with previous results, a coefficient of friction rising with the sliding speed tends to make a system more stable, although this is not systematic. The theory presented here allows these possible routes to instability to be combined, so that data from vibration measurements or modelling and from frictional measurements can be used directly to predict the region of instability in parameter space. r
Computers & Structures, 2018
This is a study of viscoelastoplastic (VEP) vibrations and their use for the analysis of low cycle fatigue in internally damped inelastic frame structures (IDIFSs). The background of this inelastic theory is presented in the framework of a mathematical-physical analogy between the rheological model and a dynamical model with viscous damping. The rheological-dynamical analogy (RDA) is a type of inelastic analysis, which transforms one category of material non-linear problems to simpler linear dynamical problems using modal analysis. The aim of this paper is to define internal damping based on both the dynamic modulus and modal damping ratios. The idea underlying these approaches is that fatigue damage appears if internal damping is unevenly distributed over the elements of a structure. The residual force method, which requires the use of the finite element method (FEM), is used for the location of damage and derivation of the fatigue damage vector. Finally, the effective force vector is derived from damage mechanics. An analysis of damaged IDIFSs made of reinforced concrete is carried out. It is shown that the RDA, which correlates with the main mechanical properties of the material measured, can improve the prediction of fatigue damage caused by low cycle fatigue.