S. Lenci

• full professor
• Marche Polytechnic University

This special issue compiles 20 contributions, covering a wide range of latest achievements on dynamical modeling, data-driven algorithms, response predictions, multiple practical applications, and inverse problems. Data science plays a crucial role, helping us constructing more accurate dynamical models that capture and reflect the true dynamical c...

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...

The Lotka-Volterra model is instrumental for understanding the dynamic interactions between predator and prey populations, especially as human activities like habitat destruction, pollution, and climate change rapidly alter living environments, making it more important than ever to understand the underlying mechanisms that drive population changes...

Floating Modular Energy Islands (FMEIs) are modularized, interconnected floating structures that function together to produce, store, possibly convert and transport renewable energy. Recent technological advancements in the offshore energy sector indicate that the concept of floating offshore energy islands has the potential to become more cost-eff...

In this paper, we propose a spring-rods-mass system being of smooth and discontinuous property which can be designed as a vibration isolator due to its SQZS (stable-quasi-zero-stiffness). Both smooth and discontinuous bifurcation sets are obtained including pitchfork-like bifurcation and heteroclinic-like bifurcation, based upon which the complicat...

There is a clear and compelling need to correctly write the equations of motion of structures in order to adequately describe their dynamics. Two routes, indeed very different from a philosophical standpoint, can be used in classical mechanics to derive such equations, namely the Newton vectorial approach (i.e., roughly, sum of forces equal to mass...

Nonlinear energy sinks (NESs) have been extensively studied to develop passive suppression strategies, with the primary objective of minimizing hazardous oscillatory responses in structures. In this work, we investigate the dynamical regimes of a parametrically excited one-degree-of-freedom system with a rotary NES (RNES) acting as a passive suppre...

We analyze the nonlinear Helmholtz oscillator in the presence of fractional damping, a characteristic feature in several physical situations. In our specific scenario, as well as in the non-fractional case, for large enough excitation amplitudes, all initial conditions are escaping from the potential well. To address this, we incorporate the phase...

The reliability of a pitch-plunge hypersonic airfoil in random fluctuating flow with both cubic and freeplay nonlinearity is examined. The Hopf bifurcation and dynamic responses of the hypersonic airfoil are performed. To analyze the reliability, the effects of stochasticity on the dynamic behaviors of the hypersonic airfoil model are discussed in...

In this work, nonlinear free vibrations of fully geometrically exact Timoshenko–Ehrenfest beams are investigated. First, the exact strong form of the Timonshenko–Ehrenfest beam, considering the geometrical nonlinearity, is derived, and the required formulations are obtained. Since the strong forms of governing equations are highly nonlinear, a nonl...

In this study, the vibration control of suspended cables is achieved through the implementation of a longitudinal time delay feedback control strategy. Based on the Hamiltonian variational principle and using boundary conditions, the motion differential equations for the suspension cable under longitudinal time-delayed feedback control are derived....

The stability of the parametric resonance of a controlled stay cable with time delay is investigated. The in-plane nonlinear equations of motion are initially determined via the Hamilton principle. Then, utilizing the method of multiple scales, the modulation equations that govern the nonlinear dynamics are obtained. These equations are then utiliz...

This chapter summarizes the main elements of dynamical integrity, the branch of the dynamical systems theory that is aimed at checking the robustness, or practical stability, of solutions of evolutionary systems governed by differential equations (continuous time) or maps (discrete time). Although developed in the field of engineering, the ideas an...

Two weakly nonlinear integral equations of motion commonly used in the literature to study the nonlinear dynamics of straight and initially not rectilinear Euler‐Bernoulli beams, respectively, are further investigated. Attention is focused on the process known as “static condensation”, which consists of neglecting the axial inertia in the exact, fu...

Seminar exploring the achievements of my post-doctoral research at UNIVPM under the supervision of professors Paulo Gonçalves, Stefano Lenci, and Giuseppe Rega.

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...

In this work we examine the nonlinear dynamics of an inverted pendulum between lateral rebounding barriers. We continue the numerical investigation started in [1] by adding the contribution of the second harmonic in the external forcing term. We investigate the behaviour of the periodic attractors by bifurcation diagrams with respect to each amplit...

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...

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...

This study examines the nonlinear dynamics in tapping-mode atomic force microscopy (AFM) with tip-surface interactions that include Van der Waals and Derjaguin-Müller-Toporov contact forces. We investigate the periodic solutions of the hybrid system by performing numerical pseudo-arclength continuation. Through the use of bifurcation locus maps in...

The recycling and reuse of wastes, especially Construction Waste (CW), is a fundamental way for sustainability. The act of reusing is not a modern practice; as early as in Ancient Rome and even more during the Middle Ages, materials were already being taken from existing buildings in order to reuse them in different ways. Starting from these genera...

In this paper the construction of a neural-network based closed-loop control of a discontinuous capsule drive is analyzed. The foundation of the designed controller is an optimized open-loop control function. A neural network is used to determine the dependence between the output of the open-loop controller and the state of the system. Robustness o...

Artificial neural networks (ANNs) are an effective data-driven approach to model chaotic dynamics. Although ANNs are universal approximators that easily incorporate mathematical structure, physical information, and constraints, they are scarcely interpretable. Here, we develop a neural network framework in which the chaotic dynamics is reframed int...

The free wave propagation of periodic flexural waves on an infinite elastic Euler-Bernoulli nonlocal beam embedded in bilinear Winkler-type foundation is investigated. A general formulation of the elastic potential energy leads to a nonlinear nonlocal model with spatial derivatives up to the sixth order. The effect of the nonlocal parameters and of...

We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped and overdamped regimes. In both we have studied the relation between the fractional parameter, the amplitude of...

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...

In this work, we consider the problem of having a transit in a nonlinear SDOF system from a given rest position to another one, both associated to given and constant values of the external force, without spurious undershoots or overshoots of the solution after the final state is reached. It extends to the nonlinear regime the same problem considere...

This paper investigates the nonlinear dynamics in tapping-mode atomic force microscopy (AFM) with tip-surface interactions that include Van der Waals and Derjaguin-Müller-Toporov contact forces. We study the periodic solutions of the hybrid system by performing numerical pseudo-arclength continuation. The overall dynamical response scenario is eval...

A recurrent task in mechanical and structural engineering is to estimate safe working regimes. For dynamical systems, it means to guarantee that the designed motion will be maintained despite perturbing events. Therefore, in order to assess the practical stability, a global analysis must be performed by employing basins of attraction. The phase-spa...

Modal interactions are pervasive effects that commonly emerge in nanomechanical systems. The coupling of vibrating modes can be leveraged in many ways, including to enhance sensing or to disclose complex phenomenologies. In this work we show how machine learning and data-driven approaches could be used to capture intermodal coupling. We employ a qu...

The wave propagation problem in a second-order nonlinear PDE, with specific reference to a mechanical system consisting of a taut cable, or string, resting on a piecewise linear foundation is investigated, without and with a distribute transversal load. The piecewise nature of the problem offers a sufficiently simple kind of nonlinearity as to perm...

We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped and overdamped regimes. In both we have studied the relation between the fractional parameter, the amplitude of...

In this paper, the dynamic characterisation of the civic bell-tower of Rotella (a small village in the Marche region, Central Italy) is presented. The tower after being monitored, using four tri-axial piezo-electric accelerometers, and obtaining its dynamic characteristics, was modelled through a finite element software. The difference between meas...

On the Italian territory, there are many monumental structures that need to be preserved. Given their great historical and architectural value, it is essential to use minimally invasive, but effective, techniques able to evaluate their current structural capabilities and monitor their structural health. The technique that currently appears most app...

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...

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...

This paper investigates the advantages or issues of different reduced-order models (ROMs) for the analysis of elastic cables hanging between two supports at different height. The cable is considered immersed in still fluid and under the action of an imposed boundary motion at the upper support. Nine ROMs are explored, obtained from the combination...

The present work shows the seismic vulnerability analysis of a building located in Matelica, a village that has reported extensive damages, especially to the monumental historical structures, after the Central Italy Earthquakes. The building is studied with local and global analysis, these last are performed using accurate 30 Finite Element Models...

The wave propagation problem on a taut cable resting on a bilinear substrate is investigated, without and with a distribute transversal load. The piecewise nature of the problem offers a sufficiently simple kind of nonlinearity as to permit a closed form solution both for the wave phase velocity and the wave form. We show that the solution depends...

The exact analytical solution of a system made of two coupled Duffing oscillators is obtained. The mathematical solution is illustrated by means of some examples aimed at showing the dynamical phenomena occurring in the considered system. Frequency response curves are reported for different value of the parameters, highlighting the effects of the l...

This work investigates the dynamics of a hinged-simply supported beam with an axial spring in the neighborhood of a 3:1 internal resonance between two successive transversal vibration modes. Multiple time scale method is applied to the analytical model of the planar extensible-shearable beam with associated boundary conditions, and a second order a...

We present an efficient data-driven sparse identification of dynamical systems. The work aims at reconstructing the different sets of governing equations and identifying discontinuity surfaces in hybrid systems when the number of discontinuities is known a priori. In a two-stages approach, we first locate the switches between separate vector fields...

We show that shear waves traveling towards the surface of a half-space medium can be attenuated via buried one-dimensional arrays of resonators -- here called metapiles -- arranged according to sparse patterns around a site to be isolated. Our focus is on shear waves approaching the surface along a direction perpendicular to the surface itself. Fir...

We show that shear waves traveling towards the surface of a half-space medium can be attenuated via buried one-dimensional arrays of resonators -- here called metapiles -- arranged according to sparse patterns around a site to be isolated. Our focus is on shear waves approaching the surface along a direction perpendicular to the surface itself. Fir...

This work is concerned with a mechanical model of a sympodial tree with first-level branches, which has been shown to exhibit certain properties potentially suitable for biomimetic applications. To investigate these potential benefits further from the viewpoint of the system nonlinear behaviour under external periodic excitation, modern numerical t...

The paper provides an evaluation of the nonlinear dynamic response of a cantilever beam made of composite material subjected to low-velocity impacts. The structure is assumed to respond in a quasi-static manner and modelled by a continuous beam in large displacement with a lumped mass attached. First, an analytical model was developed to study the...

We present an efficient data-driven sparse identification of dynamical systems. The work aims at reconstructing the different sets of governing equations and identify discontinuity surfaces in hybrid systems when the number of discontinuities is known a priori. In our approach, we first focus to identify the switches between the separate vector fie...

In this study, we investigate the nonlinear resonant response of a magnetorheological (MR) damper–stay cable system with time delay, and the one-to-one internal resonance is considered. Based on Hamilton’s principle, the motion equations of the MR damper–cable system are derived, and the Galerkin method is applied to obtain the discrete model. Then...

The propagation of periodic flexural waves in an Euler-Bernoulli beam resting on a bilinear elastic foundation is investigated. Although the problem is nonlinear, the closed form solution is obtained thanks to its piecewise linear nature. The dependence of the phase velocity on the two stiffnesses of the substrated is investigated in depth, and it...

A new surgical procedure for the treatment of primary bladder neck obstruction with maintenance of anterograde ejaculation is proposed. In place of monolateral or bilateral bladder neck incision, associated with a loss of ejaculation rate of up to 30%, the new surgical procedure consists of laser drilling the bladder neck with a number of holes and...

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...

The aim of this research was to investigate the mechanical performance of an earthen massive cladding, recently used for external/internal layers in Platform Frame technology, through an extensive experimental campaign. The masonry is built with extruded unbaked earth blocks and characterized by dovetail horizontally staggered bed joints. The wall...

The paper deals with the experimental and numerical characterization of the in-plane axial and shear mechanical behavior of sprayed in-situ reinforced concrete (RC) sandwich panels, used as structural walls. Axial compression tests were carried out on specimens with different slenderness ratios to study their behavior under axial vertical loads. Wh...

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...

Increasing the signal-to-noise ratio in dynamic atomic force microscopy plays a key role in nanomechanical mapping of materials with atomic resolution. In this work, we develop an experimental procedure for increasing the sensitivity of higher harmonics of an atomic-force-microscope cantilever without modifying the cantilever geometry but instead b...

This paper investigates the nonlinear dynamic behavior of a cantilever beam made of composite material without and with lumped mass fixed along its length. The analysis compares the results coming from analytical and numerical modeling with experimental observations. The first part focuses on the analytical model. The model takes into account the n...

The aim of this paper is to present the development of discontinuous approaches to simulate the nonlinear dynamic behaviour of the civic clock tower of Rotella, in the province of Ascoli Piceno (Italy). The study involves the use of the Non-Smooth Contact Dynamics method implemented in the LMGC90© code, where sliding motions are governed by Signori...

Complementing the time-history solution by the frequency-domain analysis can provide a better understanding of micro-structures dynamics. Nevertheless, there exist no research studies in the literature dealing with the dynamics of plate-type MEMS undergoing mechanical shock via the frequency-domain analysis. Therefore, the main object of the presen...

The paper presents the results of an experimental campaign aimed at investigating the in-plane and out of-plane behavior of tuff and fired clay brick masonry panels reinforced by a commercial, not yet tested, Textile Reinforced Mortar (TRM) system. The TRM, consisting of hydraulic lime mortar coupled with a bidirectional glass fabric (total thickne...

The dynamic behaviour and the seismic vulnerability of different masonry "Apennine Churches", dramatically damaged by the last shocks sequence of 2016 that occurred in Central Italy, have been studied in this paper by means of advanced 3D numerical analyses with the Discrete Element Method (DEM). Thus, a discontinuous approach has been used to asse...

The preliminary results of an ambient-vibration based investigation conducted on a large sample of historic masonry towers in the Marche region (Central Italy) are presented, with a focus on the belfry of Collegiata of Santa Maria in Visso (Italy). The assessment procedure includes full-scale ambient vibration testing, ambient modal identification,...

Italy is a high seismic risk country. Since 1900 more than 30 earthquakes with magnitude greater than Mw=5.8 occurred, and the last one is the Central Italy seismic sequence. The first shock aroused in the 24th August (Mw=6.2) followed by another stronger quake in the 30th October (Mw=6.5). It heavily hit the regions of Marche, Umbria, and Abruzzo...

An analytical solution for the problem of an immersed flexible and vertical heavy rod subjected to a vertical top motion is developed using the multiple scales method directly applied to the partial differential equations of motion. The obtained results show good agreement with a numerical solution obtained using the finite element method for a stu...

Dynamics of a rotor composed of a flexible beam attached to a slewing rigid hub is presented in the paper. Dynamics of the structure is studied for a slender beam model, based on extended Bernoulli-Euler theory, which takes into account a nonlinear curvature, coupled transversal and longitudinal oscillations and non-constant angular velocity of the...

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...

2020 European Association for Structural Dynamics. All rights reserved. In the present paper has been reported the Non-Smooth Contact Dynamics method (NSCD) used for the damage evaluation of the multiple leaf masonry walls of the medieval fortress of Arquata del Tronto, strongly affected by the last Centre Italy earthquakes of August and October 20...

An exact analytical solution for transversal free vibrations of a beam subjected to an arbitrary distributed axial load and a tip tension is obtained by means of a power series representation, whose coefficients are determined recursively in an easy way. The dependence on the natural frequencies on the load is then investigated, and the buckling lo...

In this work, we show that perfectly localised modal vibrations can be obtained in continuous linear elastic structures, provided that, in addition to the regular boundary and continuity/jump conditions, extra (admissibility) conditions are met. They are derived with the aid of: (i) new parameters and/or DOFs of auxiliary systems, and/or (ii) admis...

The dynamic identification of the modal parameters of a structure, in order to gain control of its functionality under operating conditions, is currently under discussion from a scientific and technical point of views. The experimental observations obtained through structural health monitoring (SHM) are a useful calibration reference of numerical m...

In modern engineering applications it is needed to determine the robustness of stable steady states, which depends on the shape and size of the associated basins of attraction. Once the basins are known, the quantitative measures can be computed by means of dynamical integrity tools and arguments. Those numerical techniques applied to strongly nonl...

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...

The aim of this research is to investigate, through the Digital Image Correlation (DIC) technique, the mechanical performance of a new type of earth masonry, built with extruded blocks and characterized by dovetail horizontally staggered bed joints. The experimental program consists of two levels of investigations: (i) preliminary phase on componen...