Alessio Ageno

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Publications Symmetry Properties in the Symmetry-Breaking of Non-smooth Dynamical Systems Ancient Astrological and Musical Analogies in the Renaissance: Palladio’s Villa Rotunda and a Geometric Construction by Leonardo Lyapunov’s Exponents for Non-smooth Dynamics with Impacts: Stability Analysis of the Rocking Block’ Non-smooth formulation for the ancient and strongly non-linear problem of block dynamics Theory and History of The Thrust Line For Masonry Arches. A Brief Account From empirics to calculation in Gauthey’s Mémoire sur l'application des principes de la méchanique à la construction des voûtes et des dômes

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Alessandro Camiz, Ph.D.

Università degli Studi "G. d'Annunzio" Chieti Pescara

Giorgio Ortolani

Roma Tre University, Rome, Italy

Elisa Chiara Portale

Università degli Studi di Palermo

Jacopo De Grossi Mazzorin

University of Salento

Flavia Frisone

University of Salento

Francesca Spatafora

Regione Siciliana

Dimitris P. Drakoulis

Aristotle University of Thessaloniki

Ivana Vranic

Columbia College Vancouver

Maurizio Carta

Università degli Studi di Palermo

Giorgio Verdiani

Università degli Studi di Firenze (University of Florence)

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Papers by Alessio Ageno

Stability Analysis of the Rocking Block: Numerical Investigations on Analytical Stability Boundaries

Stability Analysis of a Free-Standing Block With Friction on a Moving Foundation

The problem analyzed here concerns the dynamic response of a bidimensional polygonal rigid body s... more The problem analyzed here concerns the dynamic response of a bidimensional polygonal rigid body simply supported on a harmonically moving rigid ground. The immediate scientific purpose of the paper is to obtain and analyze the dynamic response by using a variational formulation, recently proposed by one of the authors [1], where the dynamics is described as a differential inclusion. This formulation allows us to determine the instantaneous accelerations of the system by means of a mechanical model with friction and unilateral constraints, which does not reduce the degrees of freedom or impose an “a priori” choice of the mechanism activated during the motion. By treating the friction coefficient as a stability parameter, it has been possible to obtain different kind of responses, ranging from rocking to sliding-rocking, and compare them with those obtained in the literature. Sliding-rocking motions obtained so far have exhibited not only harmonic but also interesting and more complex behaviors with chaotic features. The search for theoretical and numerical instruments able to identify and classify these more complex motions was first performed in the case of rocking, characterized by a smaller number of degrees of freedom. A technique was then implemented for calculating Lyapunov’s exponents also during the time intervals of the impacts. The introduction and evaluation of these exponents can also permit us to perform the stability analysis with respect to overturning, by limiting the analysis and evaluation to the first impact that the system undergoes by starting at rest: in fact, large values of Lyapunov’s exponents before the first impact are connected with overturning during the motion which follows. This circumstance can make it easier to carry out the stability analysis with respect to overturning, as a function of the amplitude and frequency of the excitation.

Lyapunov's Exponents for Nonsmooth Dynamics with Impacts: Stability Analysis of the Rocking Block

International Journal of Bifurcation and Chaos, Jun 1, 2005

Lyapunov’s Exponents for Non-Smooth Dynamical Systems: Behavior Identification Across Stability Boundaries With Bifurcations

Architecture as talisman: the hidden links between Vitruvius' theatre and Palladio's villa Rotonda

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Stability Analysis of a Free-Standing Block With Friction on a Moving Foundation

Volume 6B: 18th Biennial Conference on Mechanical Vibration and Noise

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Architecture as talisman: the hidden links between Vitruvius' theatre and Palladio's villa Rotonda

Proceedings of the First International Congress on Construction History Madrid 20th 24th January 2003 Vol 1 2003 Isbn 84 9728 071 7 Pags 151 160, 2003

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DETC2003/VIB-48478 Stability Analysis of the Rocking Block: Numerical Investigations on Analytical Stability Boundaries

ABSTRACT

Lyapunov’s Exponents for Non-Smooth Dynamical Systems: Behavior Identification Across Stability Boundaries With Bifurcations

Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, 2005

In this paper some recently developed techniques to evaluate both analytically and numerically st... more In this paper some recently developed techniques to evaluate both analytically and numerically stability features of a non-smooth dynamical system, are used to investigate in detail the stability boundaries of regions corresponding to given stable periodic responses. The problem analyzed is that of a rocking block simply supported on a harmonically moving rigid ground; in this case, if the block is assumed to be a rigid body, the strong discontinuities characterizing the dynamic evolution are due to the impacts occurring each time the block crosses the initial equilibrium configuration. Therefore some special tools, specific for non-smooth functions, must be introduced to perform the stability analysis. In the present study, the theory due to Müller [19] is used to handle the evaluation of Lyapunov's exponents upon discontinuities, by introducing the treatment, both analytical and numerical, of "saltation matrices". Such a general theoretical method on one hand has been adapted to the numerical algorithms needed for the solution of the complete, non-linearized, problem and on the other hand, it allowed the development of the closed-form analytical reference solutions, obtained by linearizing assumptions less restrictive than those used by Hogan . The approximated stability boundaries obtained by the linearized closed-form solutions have been the starting point to guide the choice of the system parameters values to locate the responses in regions where bifurcations can arise. Inside these ranges several examples can be presented to illustrate the trends exhibited by the numerically evaluated Lyapunov's exponents when the values of the forcing amplitude increase over the stability boundary of the symmetric responses while the value of the forcing frequency is fixed. Among these, investigations on sequences of responses composing period doubling cascades toward chaos, can provide a good and interesting test to appreciate the indications offered by the numerically derived Lyapunov's exponents.

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Stability Analysis of the Rocking Block: Numerical Investigations on Analytical Stability Boundaries

Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2003

The present paper illustrates some recently developed techniques to evaluate stability features, ... more The present paper illustrates some recently developed techniques to evaluate stability features, such as characteristic multipliers and Lyapunov’s exponents, for a problem with strong discontinuities. The problem analyzed concerns the plane dynamics of a rigid block simply supported on a harmonically moving rigid ground. In previous papers [1–3] many aspects have been investigated and the following results have been carried out: 1. the general procedure to approach numerically the problem has been outlined; 2. a rigorous method has been established to calculate characteristic multipliers and Lyapunov’s exponents at the instants of discontinuities; 3. the stability boundaries of symmetric sub-harmonic responses have been drafted by means of closed-form analytical methods based on various hypotheses of linearization. In this paper the new capacities allowed by the techniques and methods pointed out at the previous points 1., 2. and 3. are exploited with the aims: • to investigate nume...

Ancient Astrological and Musical Analogies in The Renaissance: Palladio’s Villa Rotunda and a Geometric Construction by Leonardo

Two Cultures, 2006

The conclusions about the pure and exclusively musical nature of the proportions used by Palladio... more

Symmetry Properties in the Symmetry-Breaking of Nonsmooth Dynamical Systems

Journal of Computational and Nonlinear Dynamics, 2010

In this paper, the block simply supported on a harmonically moving ground is assumed as a system ... more In this paper, the block simply supported on a harmonically moving ground is assumed as a system well representing a typical nonsmooth dynamical behavior. The aim of the work is to carry out the existence conditions of asymmetric responses; an analysis that comes first in any stability investigation. By using simple definitions belonging to the symmetry group theory, it is possible to completely clarify the relationships between the various initial conditions that allow simple asymmetric responses, and to develop tools, which will be very useful in the stability analysis of more complex asymmetric responses.

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Lyapunov's Exponents for Nonsmooth Dynamics with Impacts: Stability Analysis of the Rocking Block

International Journal of Bifurcation and Chaos, 2005

The plane dynamics of a rigid block simply supported on a harmonically moving rigid ground is a p... more The plane dynamics of a rigid block simply supported on a harmonically moving rigid ground is a problem which still needs investigating, although the matter has been the subject of much research since the last century. Unilateral contacts, Coulomb friction and impacts make the system hybrid as it reveals a mixed continuous and discontinuous nature. Thus, stability analysis requires the extension and adaptation of concepts with regard to variational-perturbative procedures. In particular, discontinuous systems exhibit discontinuities or "saltations" in the fundamental solution matrix which must be analyzed carefully. In this paper, the adaptation of numerical methods that permit us to obtain characteristic multipliers and…

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Stability Analysis of the Rocking Block: Numerical Investigations on Analytical Stability Boundaries

Stability Analysis of a Free-Standing Block With Friction on a Moving Foundation

Lyapunov's Exponents for Nonsmooth Dynamics with Impacts: Stability Analysis of the Rocking Block

International Journal of Bifurcation and Chaos, Jun 1, 2005

Lyapunov’s Exponents for Non-Smooth Dynamical Systems: Behavior Identification Across Stability Boundaries With Bifurcations

Architecture as talisman: the hidden links between Vitruvius' theatre and Palladio's villa Rotonda

Download

Stability Analysis of a Free-Standing Block With Friction on a Moving Foundation

Volume 6B: 18th Biennial Conference on Mechanical Vibration and Noise

Download

Architecture as talisman: the hidden links between Vitruvius' theatre and Palladio's villa Rotonda

Proceedings of the First International Congress on Construction History Madrid 20th 24th January 2003 Vol 1 2003 Isbn 84 9728 071 7 Pags 151 160, 2003

Download

DETC2003/VIB-48478 Stability Analysis of the Rocking Block: Numerical Investigations on Analytical Stability Boundaries

ABSTRACT

Lyapunov’s Exponents for Non-Smooth Dynamical Systems: Behavior Identification Across Stability Boundaries With Bifurcations

Volume 6: 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C, 2005

Download

Stability Analysis of the Rocking Block: Numerical Investigations on Analytical Stability Boundaries

Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C, 2003