Giuseppe Rega

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Papers by Giuseppe Rega

Special Issue on ‘Recent Developments in Engineering Vibration’

International Journal of Mechanical Sciences, Jul 1, 2023

Modeling, Dimension Reduction, and Nonlinear Vibrations of Thermomechanically Coupled Laminated Plates

Procedia Engineering, 2016

Abstract A unified formulation of thermomechanical, geometrically nonlinear, laminated plates tha... more Abstract A unified formulation of thermomechanical, geometrically nonlinear, laminated plates that integrates mechanical and thermal aspects is presented. It allows for constructing and comparing a variety of continuous models of different mechanical richness and with full thermoelastic coupling embedded, as well as for deriving minimal reduced order models suitable to provide useful information on fundamental thermomechanical phenomena occurring in the system nonlinear and complex dynamics. Comparative numerical investigations of free and forced vibrations can be carried out through both models of three, fully coupled, ordinary differential equations and simplified, partially coupled, models of two, or even one, ODEs, with the aim to unveil the actual importance of accounting for the various terms to reliably describe the most important thermomechanical effects on the system response.

Non-linearity, bifurcation and chaos in the finite dynamics of different cable models

Chaos Solitons & Fractals, Oct 1, 1996

The finite dynamics of a suspended cable are discussed as a possible archetypal picture of the ri... more The finite dynamics of a suspended cable are discussed as a possible archetypal picture of the rich non-linear and chaotic behaviour occurring in the important class of elastic structural systems with initial curvature. The problem is attacked from different viewpoints concerned with both the modelization and the solution approach. A single degree-of-freedom model retaining some of the main features of

Patrizia Trovalusci: An Open-Minded Scholar of Mechanics, an Architect, a Determined Woman

International Journal for Multiscale Computational Engineering, 2022

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Nonlinear dynamics in mechanics and engineering: 40 years of developments and Ali H. Nayfeh's legacy

Zenodo (CERN European Organization for Nuclear Research), Apr 29, 2020

Licensees may copy, distribute, display and perform the work and make derivative works and remixe... more Licensees may copy, distribute, display and perform the work and make derivative works and remixes based on it only if they give the author or licensor the credits (attribution) in the manner specified by these. Licensees may copy, distribute, display, and perform the work and make derivative works and remixes based on it only for non-commercial purposes. Licensees may copy, distribute, display and perform only verbatim copies of the work, not derivative works and remixes based on it.

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Italian Mechanics: Overviews, Viewpoints, Perspectives

Springer eBooks, 2022

Memoirs of a Few Senior AIMETA Officers

Springer eBooks, 2022

Nonlinear mode localization in boundary–interior coupled structures by an asymptotic approach

International Journal of Non-linear Mechanics, May 1, 2022

Geometric Nonlinearities Effect on Cable Linear Vibrations

The present work investigates the free undamped vibrations of arbitrarily sagged cables according... more The present work investigates the free undamped vibrations of arbitrarily sagged cables according to the catenary theory. Defining the dynamic equilibrium configuration around the catenary static profile, an exact solution of the free linear transverse vibrations is developed analytically. The effectiveness of the established model is shown by means of comparisons between with results determined by classic formulations in case of horizontal and inclined shallow/non-shallow cables. MEDYNA 2017 25-27 Apr 2017, Sevilla (Spain)

Experimental validation of the act-and-wait control concept through the Aeropendulum

Digitization and time delay are known to modify the stability properties of feed-

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Catenary-based nonlinear multimodal theory of cable free vibrations

HAL (Le Centre pour la Communication Scientifique Directe), Feb 17, 2019

Keeping the linear elastic material assumption and accounting for the sole axial extensibility, a... more Keeping the linear elastic material assumption and accounting for the sole axial extensibility, a new multi-modal theory of cable nonlinear free vibrations is developed analytically, by means of a Galerkin discretization of partial differential equations of motion and the Method of Multiple Scales used to investigate the dynamic behaviour of arbitrarily sagged and inclined cables oscillating around a catenary static profile.

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Non-linear oscillations of a four-degree-of-freedom model of a suspended cable under multiple internal resonance conditions

Journal of Sound and Vibration, May 1, 1995

A four-degree-of-freedom model able to capture the main phenomena which are likely to occur in th... more A four-degree-of-freedom model able to capture the main phenomena which are likely to occur in the non-planar finite dynamics of an elastic suspended cable subjected to external forcings and support motions is developed from the continuum equations. It contains two in-plane and two out-of-plane components, one symmetric and one antisymmetric. An order two multiple time scales solution is obtained for the case of primary external resonance and three simultaneous internal resonances (cable at crossover frequency). Possible classes of steady state (planar/non-planar, unimodal/multimodal) regular motions of the system are identified, and their linearized stability analysis is performed. Some results are presented to highlight the role played by key perturbations on the onset of various classes, the rich behaviour of the system and the influence of some control parameters on the response.

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1/2 Subharmonic Resonance and Chaotic Motions in a Model of Elastic Cable

The finite motions of a suspended elastic cable subjected to a planar harmonic excitation is stud... more The finite motions of a suspended elastic cable subjected to a planar harmonic excitation is studied through one ordinary equation with quadratic and cubic nonlinearities. The onset of chaotic motions in the neighbourhood of the 1/2 subharmonic resonance condition is analysed via numerical simulations.

Revisited modelling and multimodal nonlinear oscillations of a sagged cable under support motion

Meccanica, Jun 8, 2016

Sagged cable vibrations caused by support motion and possible external loading are investigated v... more Sagged cable vibrations caused by support motion and possible external loading are investigated via the four-degree-of-freedom model proposed in Benedettini et al. (J Sound Vib 182(5):775-798, 1995). The model has a considerable potential in terms of forcing cases to be possibly addressed, with the physical motion of the supports naturally giving rise to a variety of external and parametric excitation terms. Dynamics of the system is studied close to the multiple internal resonance at cable crossover, which involves two in-plane and two out-of plane vibration modes. Solutions are found by the multiple time scale method. In the numerical investigation, attention is focused on the effects of planar support motion (symmetric and/or antisymmetric) at primary resonance, with the addition of planar symmetric external excitation entailing a nice cancellation phenomenon in the system response. Results are discussed also in the background of theoretical and experimental outcomes available in the literature. Comparison with a computer simulation of original equations of motion shows that analytical results are correct for moderately large oscillations, whereas a different scenario of multimodal responses may occur at higher excitation amplitudes. The nonlinear modal coupling is investigated through bifurcation scenarios and other dynamics tools, showing also transitions to complex response regimes. Keywords Suspended cable Á Support motion Á External/parametric excitations Á Nonlinear oscillations Á Multimodal response Dedicated to the memory of Francesco Benedettini, who was the first assistant and a lifelong friend of GR, as well as the unforgettable first mentor of DZ.

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Non-linear dynamics of an elastic cable under planar excitation

International Journal of Non-linear Mechanics, 1987

The phenomena of the finite forced dynamics of a suspended cable associated with the quadratic an... more

Nonlinear Vibrations of Beams Including Shear Deformations and Rotatory Inertia

Lecture notes in engineering, 1987

The free large-amplitude oscillation of a beam with whatever boundary conditions are investigated... more The free large-amplitude oscillation of a beam with whatever boundary conditions are investigated on the basis of a polar continuum model in which a priori ordering assumptions are avoided. The dynamic configuration is described through three displacement variables which allow to account for the shear deformation and rotatory inertia. By using an assumed mode technique and Hamilton’s principle, two ordinary differential equations with nonlinearities up to order three are obtained. They are solved by Lindstedt-Poincare perturbation method to study the frequency-amplitude relationship of a transverse mode of shear-deformable beam, taking into account the coupling with the longitudinal displacement. Numerical investigation has been performed for simply-supported beams with movable and immovable ends and the influence of shear deformations and rotatory inertia has been evidenced.

Bending–twisting vibrations of a rotating hub–thin-walled composite beam system

Mathematics and Mechanics of Solids, Mar 3, 2016

The dynamics of a system consisting of a rotating rigid hub and a flexible composite thin-walled ... more The dynamics of a system consisting of a rotating rigid hub and a flexible composite thin-walled beam is discussed. The nonclassical effects like material anisotropy, rotary inertia and transverse shear are considered in the mathematical model of the structure. Moreover, the hub mass moment of inertia is taken into account. The differential equations of motion featuring beam bending–twist elastic coupling are derived using the Hamilton principle, and the Galerkin method is applied in order to reduce the partial differential governing equations to the ordinary differential equations. Parametric studies are conducted to evaluate beam stiffness coefficients depending on the fiber lamination angle. Next, numerical results are obtained to investigate the impact of hub to beam relative inertia on the natural frequencies of the structure. Cases of forced vibrations of the system are examined where the driving torque is considered as the sum of a constant (mean value) and a periodic component. Simulations show the importance of the hub inertia on the complete system dynamics. A shift of the resonance zones and a vibration absorption are observed.

Multiple internal resonances and nonplanar dynamics of a cruciform beam with low torsional stiffness

International Journal of Solids and Structures, Aug 1, 2017

The three-dimensional motion of a slender clamped-free beam with a cruciform cross-section of low... more The three-dimensional motion of a slender clamped-free beam with a cruciform cross-section of low torsional stiffness, subject to lateral harmonic excitation, is investigated. Special attention is given to the nonlinear oscillations at multiple internal resonances, and to its influence on the bifurcations and instabilities of the structure, a problem not tackled in the previous literature on the subject. The nonlinear integro-differential equations describing the flexural-flexural-torsional coupling of the beam are used, together with the Galerkin method, to obtain a minimal (three-degree-of-freedom) reduced order model, whose response is investigated through continuation of the relevant ordinary differential equations. Both inertial and geometric nonlinearities are considered. By varying the stiffness parameters of the beam and using tools of nonlinear dynamics, a complex dynamic behavior is observed around 1:1:1 resonance, where a variety of local bifurcations lead to multiple coexisting solutions which include planar and nonplanar motions. Notwithstanding the topologically involved portraits of the attractor-basin response, the analysis of system global dynamics may provide hints for safe structural design.

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Modal coupling in the free nonplanar finite motion of an elastic cable

Meccanica, Mar 1, 1986

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Periodic Solutions Leading to Chaos in an Oscillator with Quadratic and Cubic Nonlinearities

Birkhäuser Basel eBooks, 1991

Regions of periodic and chaotic response, types of bifurcation and strange attractors of an unsym... more

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