Giuseppe Rega

Giuseppe Rega
Sapienza University of Rome | la sapienza · Department of Structural and Geotechnical Engineering

PhD

About

312
Publications
48,937
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6,834
Citations
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August 2013 - December 2013
Sapienza University of Rome
Position
  • Professor

Publications

Publications (312)
Article
Full-text available
The sea excitation is added into a reduced nonlinear model of floating offshore wind turbine, in order to assess its effect on the system dynamics. To this aim, the sea wave motion is modelled as heave displacement of the turbine tower, which results in a parametric excitation to the along-wind displacement. The occurrence of the 1:1 internal reson...
Chapter
The chapter provides a state-of-the-art, qualitative and application-oriented overview of topics in the global nonlinear dynamics of mechanical systems and structures. Models, methods, phenomena, practical examples are addressed with the aim of highlighting the enormous potential of global analysis as regards in-depth description and understanding...
Article
Full-text available
Reduced-order models derived by routine finite mode Galerkin truncation of nonlinear continuous structures may lead to errors in the results, especially for quadratic nonlinearity dominated structures (say, sagged cables, shallow arches, imperfect beams). Many different approaches like invariant manifold method (including center manifold, nonlinear...
Article
Full-text available
A general methodology for reduced-order modeling of geometrically nonlinear structures is proposed. This approach is built upon equivalent elimination of low-order nonlinear terms by employing a key concept termed ‘passive patterns’, defined to be essential dynamic features of nonlinear structures, produced by, namely slaved to, the active mode via...
Presentation
Seminar exploring the achievements of my post-doctoral research at UNIVPM under the supervision of professors Paulo Gonçalves, Stefano Lenci, and Giuseppe Rega.
Conference Paper
The problem of controlling the chaotic response of a simple mechanical system — an inverted pendulum subjected to an external periodic base excitation — has been analyzed. The controlling procedure consists in inhibiting the transverse homoclinic intersection by acting on the shape of the excitation. The optimal solution of the global control probl...
Article
Full-text available
An adaptative phase-space discretization strategy for the global analysis of stochastic nonlinear dynamical systems with competing attractors considering parameter uncertainty and noise is proposed. The strategy is based on the classical Ulam method. The appropriate transfer operators for a given dynamical system are derived and applied to obtain a...
Article
Full-text available
This work aims to study the effect of uncertainties and noise on the nonlinear global dynamics of a micro-electro-mechanical arch obtained from an imperfect microbeam under an axial load and electric excitation. An adaptative phase-space discretization strategy based on an operator approach is proposed. The Ulam method, a classical discretization o...
Article
Full-text available
The nonlinear dynamics of composite plates with thermomechanical coupling is analytically addressed in order to describe the main bifurcation phenomena triggering the involved pre- and post-buckling response scenario. The static buckling occurrence and two resonance conditions around the unbuckled and buckled equilibria are investigated by means of...
Article
In a global dynamic analysis, the coexisting attractors and their basins are the main tools to understand the system behavior and safety. However, both basins and attractors can be drastically influenced by uncertainties. The aim of this work is to illustrate a methodology for the global dynamic analysis of nondeterministic dynamical systems with c...
Preprint
Full-text available
An adaptative phase-space discretization strategy for the global analysis of stochastic nonlinear dynamical systems with competing attractors considering parameter uncertainty or noise is proposed. The strategy is based on the classical Ulam method. The appropriate transfer operators for a given dynamical system are derived and applied to obtain an...
Preprint
Full-text available
This paper explores the influence of uncertainties and noise on the global dynamics of nonlinear systems, with emphasis on the basins and attractors’ topology and on the dynamic integrity of coexisting solutions. For this, the adaptive phase-space discretization strategy proposed in Part I [1] is employed. Two well-known archetypal oscillators foun...
Chapter
A summary of the contributions by senior yet still active authors appearing in this volume is presented, with the aim to provide an overview of the Italian research in Mechanics in the last few decades, with regard to both ‘classical’ and ‘novel’ topics, and a glimpse of ongoing developments and open perspectives. The contributions are discussed ac...
Article
Starting from a recent classification of the development stages of nonlinear dynamics in mechanics, this review builds on the idea that the level of scientific maturity of the area is now such as to involve a gradual shift of its core interests from the inherent theoretical and practical findings to the application benefits that they can bring to s...
Article
Boundary-interior coupled structures are an important class of complex combined structural systems, with one component kinematically excited at its boundary and the other excited by coupling force in its interior domain. Nonlinear mode localization of boundary-interior coupled structures is fully investigated in this paper, with a general asymptoti...
Chapter
The history of AIMETA has been made up by the scholars of mechanics who have engaged in it, putting their scientific personality and achievements into play, and contributing in a non-trivial way to its recognition as the reference Italian association in the field of mechanical sciences. This contribution is a tribute paid to earlier recognized Ital...
Chapter
This chapter collects short memories written by some retired Italian scholars of structural mechanics, already engaged with AIMETA in various official positions, as a dutiful representative tribute to all scholars and scientists who have contributed to building AIMETA’s role as a showcase of Italian Theoretical and Applied Mechanics.KeywordsAIMETAS...
Chapter
This contribution aims at providing a survey on the evolution of theoretical and applied mechanics in Italy in about the last fifty years, as observed through the perspective of the Italian Association of Theoretical and Applied Mechanics (AIMETA). Stages of its development are overviewed, by referring to the carefully collected and organized data/...
Article
Discretized perturbation analysis based upon a structure's single (finite) mode Galerkin-truncated model may lead to erroneous results in comparison with full-basis discretization (or, equivalently, direct perturbation method). This error is due to the two involved analytical steps, i.e., multi-scale expansion and mode truncation, being non-commuta...
Chapter
Several simplified models have been developed for planar nonlinear dynamics of beams based on specific geometrical assumptions and negligibility of some terms. A Timoshenko beam is considered, whose equations of motion up to the third order contain several nonlinear terms. This chapter provides a detailed comparison of the role of nonlinear terms i...
Article
Full-text available
The internal resonances between the longitudinal and transversal oscillations of a forced Timoshenko beam with an axial end spring are studied in depth. In the linear regime, the loci of occurrence of 1 : ir, ir ∈ N ir ∈ N, internal resonances in the parameters space are identified. Then, by means of the multiple time scales method, the 1 : 2 case...
Article
In Part 1 of this series papers (Part 1 & Part 2 (Guo and Rega, 2020) [1]), a general operator-based boundary analysis approach is proposed for free vibrations of coupled structural systems, with the new coupled modal frequencies and modal shapes being directly extracted in a systematic manner from the uncoupled components Green’s functions. Theref...
Article
This Part 2 (continued from Part 1 [1]) focuses on mode localization phenomenon in boundary-interior coupled structures, aiming to establish an asymptotic interpretation based upon the general operator formulation given in Part 1, i.e., without referring to particular structure types. It is found that a large mass ratio of combined components is th...
Article
Full-text available
In about the last two decades, global nonlinear dynamics has been evolving in a revolutionary way, with the development of sophisticated techniques employing concepts/tools of dynamical systems, bifurcation, and chaos theory, and applications to a wide variety of mechanical/structural systems. The relevant achievements entail a substantial change o...
Article
An overview of extended research recently pursued on unified continuous/reduced-order modeling and nonlinear dynamics of thermomechanical composite plates of interest in aerospace, mechanical and civil engineering is presented. Reduced models exhibit the fundamental features of geometrical nonlinearity and thermomechanical coupling of the underlyin...
Article
Full-text available
Notwithstanding the presence of some books summarizing specific research bodies on structural systems, reviews on nonlinear dynamics and chaos in mechanical systems and structures are quite few. This paper aims at giving a first contribution in this direction, focusing on chaos in one-dimensional structural mechanics, and reviewing fundamental stud...
Article
The internal resonance of a two degree-of-freedom mechanical system with all typical (quadratic and cubic) geometric nonlinearities is studied, limiting to the case of free dynamics. The Multiple Time Scale method is used to provide an analytical, closed form, approximation of the backbone curves. The cornucopia of different possible behaviours tha...
Article
It is well-known that qualitative and/or quantitative differences will be possibly induced, when applying direct (i.e., attacking directly the partial differential equations) or discretized (i.e., using a low-order Galerkin truncated model) perturbation methods to nonlinear structures using multi-scale expansions, especially for spatially continuou...
Article
Thermoelastic analysis of a shear deformable reduced model of laminated plates with von Kármán nonlinearities and cubic temperature along the thickness is presented. Parametric investigation of the response is accomplished by means of bifurcation diagrams, phase portraits and planar cross sections of the four-dimensional basins of attraction, in or...
Article
Minimal thermal modeling of two-way thermomechanically coupled plates is addressed in the framework of a unified formulation of the underlying continuum problem. Variably refined reduced-order models are considered, and some main features of the relevant transient and steady responses to a variety of active thermal sources are investigated, by prop...
Article
Full-text available
Nonlinear dynamics of engineering systems has reached the stage of full maturity in which it makes sense to critically revisit its past and present in order to establish an historical perspective of reference and to identify novel objectives to be pursued. This paper makes a first step in this direction, focusing on the mechanics of machines, solid...
Chapter
A reduced model of third-order shear deformable plate with cubic temperature is used to investigate the system nonlinear dynamic response in a full thermomechanical coupling framework. Numerical investigations of local and global dynamics allow to highlight distinct response features as occurring under different (constant or dome-shaped) prescribed...
Chapter
Ali H. Nayfeh has been the most influential scholar and scientist of the contemporary era of nonlinear dynamics in mechanics and engineering. Upon summarizing his publications and achievements, due to space restriction attention is only paid to his successful activity as a books’ author, discussing specific/novel aspects and highlighting some commo...
Chapter
A new multimodal theory is developed analytically using the method of multiple scales to investigate the dynamic behavior of arbitrarily sagged and inclined cables oscillating around a catenary static profile. Fully non-condensed kinematics are adopted to solve the eigenvalue problem and the enhanced modal properties obtained at this stage are used...
Article
Full-text available
The dynamical behavior of a mono-dimensional bar with distributed microcracks is addressed in terms of free and forced wave propagation. The multiscale model, derived from a generalized continuum formulation, accounts for the microstructure by means of a microdisplacement variable, added to the standard macrodisplacement, and of internal parameters...
Article
A nonlinear cable excited by an inclined boundary motion, termed as cable's moving boundary problem, is attacked by two different perturbation approaches, i.e., the boundary modulation formulation and the quasi-static drift formulation. The former transforms the boundary motion into a weak modulation on cable's high-order dynamics, while the latter...
Article
A general operator-based solvability condition is established for multi-scale analysis of continuous structures with non-homogeneous boundaries, extending the commonly used solvability conditions to account for the time varying/nonlinear boundary effects. The orthogonality relations between adjoint mode and resonant source terms of structure, formu...
Chapter
Different reduced order models of thermomechanically coupled von Kármán shear indeformable plate with prescribed linear temperature along the thickness are comparatively investigated in terms of local and global dynamics exhibited in active thermal regime, under harmonic transverse and constant axial mechanical excitations. Two-d.o.f. one-way coupl...
Chapter
The chapter offers an overview of the effects of the research advancements in nonlinear dynamics on the evaluation of system safety. The achievements developed over the last 30 years entailed a substantial change of perspective. After recalling the outstanding contributions due to Euler and Koiter, we focus on Thompson’s intuition of global safety....
Chapter
The role of local and global dynamics to assess a system robustness and actual safety in operating conditions is investigated, by also studying the effect of different local and global control techniques on the nonlinear behavior of a noncontact AFM. First, the nonlinear dynamical behavior of a single-mode model of noncontact AFM is analyzed in ter...
Chapter
The nonlinear dynamics of two archetypal structural systems exhibiting interactive modal post-buckling behavior is addressed, the discrete Augusti’s model and a reduced-order model of the axially loaded cylindrical shell. The uncoupled models exhibit a stable post-buckling response. However, the modal interaction leads to unstable post-buckling pat...
Article
Concepts and tools of global dynamics play a meaningful role in enhancing the engineering design and safety of multistable structural systems in a dynamic environment. Basins of attraction topology can vary meaningfully as a function of system parameters, and the basin boundaries can be smooth or fractal. Fractal boundaries have important practical...
Article
Full-text available
Unified 2D continuum formulation of the nonlinear dynamic problem for a von Kármán shear indeformable symmetric cross-ply composite plate in a thermomechanical environment is presented, along with the ensuing reduction procedure ending up to a three-mode discretized model with unknown transverse displacement and membrane/bending temperatures. Syste...
Article
Full-text available
The nonlinear response of a reduced model of an orthotropic single-layered plate with thermomechanical coupling is investigated in the presence of thermal excitations, in addition to mechanical ones. Different issues are addressed via accurate and extended local and global analyses. (i) Assessing the possible occurrence, disappearance or modificati...
Article
Anisometric integrity measures defined as improvement and generalization of two existing measures (LIM, local integrity measure, and IF, integrity factor) of the extent and compactness of basins of attraction are introduced. Non-equidistant measures make it possible to account for inhomogeneous sensitivities of the state space variables to perturba...
Article
This paper investigates the free undamped vibrations of cables of arbitrary sag and inclination according to the catenary theory. The proposed approach accounts for the catenary effect on the static profile around which the cable motion is defined. Considering first order geometric nonlinearities, exact expression of the curvature is obtained along...
Article
Full-text available
The nonlinear free oscillations of a planar, initially straight Timoshenko beam are investigated by means of the asymptotic development method. Attention is focus on the difference in considering the “mechanical” vs the “geometric” curvature of the axis of the beam, which are different for extensible beams. A comparison of the results obtained by t...
Article
Full-text available
The role of a global dynamics analysis to assess a system robustness and actual safety in operating conditions is investigated by studying the effect of different local and global control techniques on the nonlinear behavior of a noncontact AFM via dynamical integrity concepts and tools.
Article
Full-text available
Dynamic vibration absorbers (DVAs) have received special attention in recent years due to their capability to reduce structural vibrations of a primary structure. In this work, a DVA of the Tuned Mass Damper type based on a Shape Memory Alloy (SMA) element with pseudoelastic behavior is considered. Owing to their rich thermomechanical response, SMA...
Article
Full-text available
Thermomechanically coupled, geometrically nonlinear, laminated plates are addressed through a unified 2D formulation, by considering classical and third-order shear-deformable von Karman models, along with correspondingly consistent linear and cubic variations of the temperature along the thickness. Minimal dimension reduction of the mechanical pro...
Article
Full-text available
The elastic von Mises truss model is a prototype for bi-stable structures. It allows a deep understanding of the static and dynamic buckling of several planar and spatial truss systems and shallow lattice shell structures, including the geodesic dome, and has a theoretical and practical interest. This structure has a highly nonlinear response in th...
Conference Paper
Full-text available
Computational issues in the global dynamics of two systems in micro-and macro-mechanics, with different dimensionality, are addressed. Attention is focused on calculation of integrity measures, determination of saddle manifolds undergoing global bifurcations, implementation of a control procedure for delaying basins erosion, selection of 2D cross-s...
Article
Full-text available
Digitization and time delay are known to modify the stability properties of feedback controlled systems. Although their effects have been widely investigated and they occur in most of the systems equipped with digital processors, they are usually neglected in industrial approaches, by virtue of the high sampling frequencies of modern processors. Ho...
Article
The nonlinear dynamics of Shape Memory Alloys (SMA) oscillators with pseudoelastic behaviour has been studied extensively in the last years by using different constitutive models for the restoring force. The response of SMA devices is rather complex and is characterized by several aspects that, usually, are not taken into account within a single mo...
Article
Full-text available
Two approximate solutions for the nonlinear free oscillations of a planar Timoshenko beam are compared to each other. The beam has an axial spring that permits to consider different boundary conditions, from axially free (which has a softening nonlinear behaviour) to perfectly axially restrained (which has a hardening nonlinear behaviour). The firs...
Article
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 probl...
Conference Paper
Full-text available
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 mean...
Article
In the framework of a unified 2D continuum formulation of the fully coupled thermomechanical laminated plate with von Karman nonlinearities, a consistent model with third order shear deformability and cubic temperature distribution along the thickness is proposed. Focusing on symmetric cross-ply laminates, an effective minimal dimension reduction i...
Article
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 equatio...
Article
Full-text available
The exact equations of motion of a planar, initially straight, beam are determined within the large displacement framework, by considering geometrical nonlinearities and linear elastic behaviour of the material. With the aim of investigating the behaviour also for low slenderness, shear deformations and rotational inertia are taken into account, to...
Article
Full-text available
A control procedure of global dynamics is applied to a reduced order model of noncontact AFM with the aim to shift the homoclinic bifurcation involving the system hilltop saddle. The method consists of adding to the system harmonic excitation controlling superharmonics to be properly identified by solving an optimization problem. The analytical bif...
Article
Full-text available
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...
Article
Full-text available
Dynamical integrity of a noncontact AFM model with external feedback control is investigated to evaluate the effects of such local control procedure on the erosion of the basins of attraction of the system bounded solutions. Two-dimensional cross sections of the five-dimensional basins of attraction have been systematically constructed, and the rel...
Article
The dynamic response of structures subjected to high-amplitude vibration is often dangerous and undesirable. Dynamic vibration absorbers (DVA) have received special attention in recent years due to vibration attenuation offered by them. Thus, the present study analyzes the nonlinear dynamics of a system with a dynamic vibration absorber (DVA) using...
Article
This paper investigates the nonlinear dynamics and stability of the shallow von Mises truss, which is a prototype for buckling analysis of several planar and spatial truss systems and shallow lattice shell structures, including the geodesic dome, and which has a theoretical and practical interest in many engineering fields. These structural systems...
Article
Full-text available
The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. T...
Article
Full-text available
A control technique exploiting the global dynamical features is applied to a reduced order model of noncontact AFM, aiming to obtain an enlargement of the system’s safe region in parameters space. The method consists of optimally modifying the shape of the system excitation by adding controlling superharmonics, to delay the occurrence of the global...
Article
Full-text available
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 r...
Article
The free nonlinear oscillations of a planar elastic beam are investigated based on a comprehensive asymptotic treatment of the exact equations of motion. With the aim of investigating the behaviour also for low slenderness, shear deformations and rotational inertia are taken into account. Attention is payed to the influence of the geometrical and m...
Article
The achievements occurred in nonlinear dynamics over the last 30 years entail a substantial change of perspective when dealing with vibration problems, since they are now deemed ready to meaningfully affect the analysis, control, and design of mechanical and structural systems. This paper aims at overviewing the matter, by highlighting and discussi...
Article
This paper discusses the nonlinear dynamical response of a shape-memory non-ideal oscillator. The non-ideal excitation originates from a DC electric motor with limited power supply driving an unbalanced rotating mass. The restoring force provided by the shape-memory device is described by a thermomechanical model capable to account for the hysteret...
Article
The dynamical analysis of a single-mode model of non-contact AFM with external feedback control is carried out in the strongly non-linear regime. The aim of the study is to investigate and verify the effects of the control introduction on the system overall behavior, which could be unexpectedly influenced by the local nature of the control techniqu...
Article
The nonlinear dynamics of a shape memory oscillator (SMO) subjected to an ideal or nonideal excitation is studied. The restoring force of the oscillator is provided by a shape memory device (SMD), described by a thermomechanical model capable of reproducing the hysteretic behavior via the evolution of a suitable internal variable. Due to nonlineari...
Article
Spatially periodic and stationary localized solutions arising from the dynamics of chains of linearly coupled mechanical oscillators characterized by on site cubic nonlinearity are addressed aiming to explore their relationship with the underlying nonlinear wave propagation regions. Softening and hardening nonlinearities are considered, and regions...
Article
Full-text available
An external feedback control is inserted in a nonlinear continuum formulation of a noncontact AFM model. The aim of the feedback is to keep the system response to an operationally suitable one, thus allowing reliable measurement of the sample surface by avoiding possible unstable microcantilever sensor motions. The study of the weakly nonlinear sys...
Conference Paper
In this paper a method for controlling the global nonlinear dynamics of mechanical systems is applied to the elastic von Mises truss model, which is a prototype for buckling analysis of several planar and spatial truss systems and shallow lattice shell structures, including the geodesic dome, and which has a theoretical and practical interest. The...