This page has only limited features, please log in for full access.

Prof. Marco Lepidi
DICCA - Department of Civil, Chemical and Environmental Engineering, University of Genoa, 16145 Genoa, Italy

Basic Info


Research Keywords & Expertise

0 Metamaterials
0 Nonlinear Dynamics
0 Smart Materials
0 Structural Health Monitoring
0 Vibration Control

Fingerprints

Metamaterials
Wave Propagation
Bridges
Cable structures
Perturbation methods
Nonlinear Dynamics
Structural Health Monitoring

Honors and Awards

The user has no records in this section


Career Timeline

The user has no records in this section.


Short Biography

The user biography is not available.
Following
Followers
Co Authors
The list of users this user is following is empty.
Following: 0 users

Feed

Journal article
Published: 28 May 2021 in International Journal of Mechanical Sciences
Reads 0
Downloads 0

Masonry-like systems composed by modular stiff units bonded by soft connections represent an efficient, versatile and ultimately successful strategy for natural and artificial macro-scale architectures. The static and dynamic behavior of masonry-like materials characterized by a running bond periodic pattern of rigid rectangular blocks and elastic interfaces is described by formulating equivalent nonlocal continuum models. The paper discusses the thermodynamic restrictions limiting the consistency of the standard continualization strategies. The inherent pathologies recognized in the macroscopic quasi-static response and/or in the dynamic dispersion properties of different continuum models motivate the original proposal of an enhanced continualization strategy. Based on the series expansion of the pseudo-differential functions accounting for shift operators and proper downscaling laws, the enhanced continualization scheme allows formulating homogeneous non-local continuum models of increasing orders, analytically featured by characteristic non-local constitutive and inertial terms. The enhanced continualization shows thermodynamic consistency in the definition of the overall elastic moduli, as well as qualitative agreement and convergent matching of the frequency dispersion functions. The theoretical findings are successfully verified though the solution of representative static and dynamic benchmark problems.

ACS Style

Andrea Bacigalupo; Luigi Gambarotta; Marco Lepidi. Thermodynamically consistent non-local continualization for masonry-like systems. International Journal of Mechanical Sciences 2021, 205, 106538 .

AMA Style

Andrea Bacigalupo, Luigi Gambarotta, Marco Lepidi. Thermodynamically consistent non-local continualization for masonry-like systems. International Journal of Mechanical Sciences. 2021; 205 ():106538.

Chicago/Turabian Style

Andrea Bacigalupo; Luigi Gambarotta; Marco Lepidi. 2021. "Thermodynamically consistent non-local continualization for masonry-like systems." International Journal of Mechanical Sciences 205, no. : 106538.

Journal article
Published: 24 April 2021 in International Journal of Mechanical Sciences
Reads 0
Downloads 0

Architected metamaterials offering superior dynamic performances can be conceived by inducing local mechanisms of inertia amplification in the periodic microstructure. A one-dimensional cellular lattice characterized by a pantograph mechanism in the tetra-atomic cell is proposed as minimal physical realization of inertially amplified metamaterial. A discrete model is formulated to describe the undamped free dynamics of the cell microstructure. The ordinary differential equations of motion feature quadratic and cubic inertial nonlinearities, induced by the indeformability of the pantograph arms connecting the principal atoms with the secondary atoms, serving as inertial amplifiers. An asymptotic approach is employed to analytically determine the dispersion properties governing the free propagation of harmonic waves in the pantographic metamaterial. First, the linear wavefrequencies and waveforms are obtained by solving the eigenproblem governing the lowest asymptotic order. An invariant parametric form is achieved for the pass and stop band structure, corresponding to propagation and attenuation branches of the dispersion spectrum in the plane of complex wavenumbers. The major effects due to the mass ratio of the inertial amplifiers are discussed. Particularly, the existence conditions, amplitude and centerfrequency of the band gap separating the acoustic and optical pass bands are determined analytically. Second, the nonlinear wavefrequencies and waveforms are obtained by solving the hierarchical linear problems governing the higher asymptotic orders. Analytical, although asymptotically approximate, functions are achieved for the nonlinear wavefrequencies and waveforms, which show quadratic dependence on the oscillation amplitudes. The mechanical conditions for the softening/hardening behaviour of the nonlinear wavefrequencies and the different topological properties of the invariant manifolds associated to the nonlinear waveforms are discussed. Finally, numerical simulations are provided to validate the analytical results.

ACS Style

Valeria Settimi; Marco Lepidi; Andrea Bacigalupo. Nonlinear dispersion properties of one-dimensional mechanical metamaterials with inertia amplification. International Journal of Mechanical Sciences 2021, 201, 106461 .

AMA Style

Valeria Settimi, Marco Lepidi, Andrea Bacigalupo. Nonlinear dispersion properties of one-dimensional mechanical metamaterials with inertia amplification. International Journal of Mechanical Sciences. 2021; 201 ():106461.

Chicago/Turabian Style

Valeria Settimi; Marco Lepidi; Andrea Bacigalupo. 2021. "Nonlinear dispersion properties of one-dimensional mechanical metamaterials with inertia amplification." International Journal of Mechanical Sciences 201, no. : 106461.

Journal article
Published: 31 December 2020 in Computer Methods in Applied Mechanics and Engineering
Reads 0
Downloads 0

Architected materials and metamaterials are a challenging frontier for the development of optimal design strategies targeted at the active and passive control of elastic wave propagation. Within this research field, the microstructural optimization of mechanical metamaterials for achieving desired spectral functionalities may require considerable computational resources. Based on this motivating framework, the present paper illustrates a machine learning methodology to attack the inverse design problem concerning the optimization of the dispersion properties characterizing a novel layered mechanical metamaterial, conceived starting from the bi-tetrachiral periodic topology. Specifically, an adaptive technique is adopted to surrogate and maximize the objective function purposely defined to determine the optimal beam lattice microstructure characterized by the largest stop bandwidth at the lowest centerfrequency (low-cutting mechanical metafilter). The technique is computationally efficient in identifying the existing optimal solution in the physically admissible parameter space. The designed bi-tetrachiral metamaterial provides satisfying broadband low-frequency filtering performances, not achievable by the component tetrachiral layers.

ACS Style

Andrea Bacigalupo; Giorgio Gnecco; Marco Lepidi; Luigi Gambarotta. Computational design of innovative mechanical metafilters via adaptive surrogate-based optimization. Computer Methods in Applied Mechanics and Engineering 2020, 375, 113623 .

AMA Style

Andrea Bacigalupo, Giorgio Gnecco, Marco Lepidi, Luigi Gambarotta. Computational design of innovative mechanical metafilters via adaptive surrogate-based optimization. Computer Methods in Applied Mechanics and Engineering. 2020; 375 ():113623.

Chicago/Turabian Style

Andrea Bacigalupo; Giorgio Gnecco; Marco Lepidi; Luigi Gambarotta. 2020. "Computational design of innovative mechanical metafilters via adaptive surrogate-based optimization." Computer Methods in Applied Mechanics and Engineering 375, no. : 113623.

Journal article
Published: 07 October 2020 in International Journal of Mechanical Sciences
Reads 0
Downloads 0

Beam lattice materials are characterized by a periodic microstructure realizing a geometrically regular pattern of elementary cells. The dispersion properties governing the free dynamic propagation of elastic waves can be studied by formulating parametric discrete models of the cellular microstructure and applying the Floquet-Bloch theory. Within this framework, governing the wave propagation by means of spectral design techniques and/or energy dissipation mechanisms is a major issue of theoretical and applied interest. Specifically, the wave propagation can be inhibited by purposely designing the microstructural parameters to open stop bands in the material spectrum at target center frequencies. Based on these motivations, a general dynamic formulation is presented for determining the dispersion properties of mechanical metamaterials, modeled as locally resonant beam lattices with generic coordination number. The mechanism of local resonance is realized by tuning periodic auxiliary oscillators, viscoelastically coupled with the beam lattice microstructure. As peculiar aspect, the viscoelastic coupling is derived by a mechanical formulation based on the Boltzmann superposition integral, whose kernel is approximated by a Prony series. Consequently, the free propagation of damped waves is governed by a linear homogeneous system of integro-differential equations of motion. Therefore, differential equations of motion with frequency-dependent viscoelastic coefficients are obtained by applying the in-space Z-transform and in-time bilateral Laplace transform. The complex-valued branches characterizing the dispersion spectrum are determined and parametrically analyzed for the beam lattice characterized by quadrilateral periodic cell. The spectral branches may exceed the model dimension, due to the occurrence of pure-damping spectral components. Particularly, the spectra corresponding to Laurent series approximations of the viscoelastic coefficients are investigated and the solution admissibility and convergence for increasing order series is analyzed. The standard dynamic equations with linear viscous damping are recovered at the first-order approximation. Low-order approximations are found to underestimate the real and imaginary parts of the spectrum, as well as the low-frequency stop bandwidth. Finally, the forced response to a harmonic mono-frequent external point excitation is investigated. The metamaterial responses to non-resonant, resonant and quasi-resonant external forces are compared and discussed from a qualitative and quantitative viewpoint.

ACS Style

Francesca Vadalá; Andrea Bacigalupo; Marco Lepidi; Luigi Gambarotta. Free and forced wave propagation in beam lattice metamaterials with viscoelastic resonators. International Journal of Mechanical Sciences 2020, 193, 106129 .

AMA Style

Francesca Vadalá, Andrea Bacigalupo, Marco Lepidi, Luigi Gambarotta. Free and forced wave propagation in beam lattice metamaterials with viscoelastic resonators. International Journal of Mechanical Sciences. 2020; 193 ():106129.

Chicago/Turabian Style

Francesca Vadalá; Andrea Bacigalupo; Marco Lepidi; Luigi Gambarotta. 2020. "Free and forced wave propagation in beam lattice metamaterials with viscoelastic resonators." International Journal of Mechanical Sciences 193, no. : 106129.

Chapter
Published: 07 July 2020 in Advanced Structured Materials
Reads 0
Downloads 0

Acoustic metamaterials are synthetic architected media featured by a periodic microstructured cell hosting one or more resonant oscillators. The cellular microstructure can be parametrically design to functionalize the dispersion properties of elastic waves. A one–dimensional crystal lattice, characterized by a diatomic periodic cell, is considered to prototypically simulate the essential undamped dynamics of weakly nonlinear acoustic waveguides. A cubic nonlinearity affects the intracellular elastic coupling between the primary atom and the secondary atom (resonator). In the small-amplitude oscillation range, the dispersion relations for the linear wavefrequencies ω(β) and linear waveforms ϕ(β) are determined as analytical functions of the wavenumber β. A general asymptotic approach, based on the multiple scale method, is employed to determine the amplitude-dependent dispersion relations for the nonlinear wavefrequencies ϖ(β) and nonlinear waveforms ψ(β). The actual existence of stable periodic oscillations orbits, confined on the invariant manifolds in the space of the two principal coordinates corresponding to the nonlinear waveforms, is successfully verified by numerical simulations.

ACS Style

Marco Lepidi; Andrea Bacigalupo. Nonlinear Dispersion Properties of Acoustic Waveguides with Cubic Local Resonators. Advanced Structured Materials 2020, 377 -392.

AMA Style

Marco Lepidi, Andrea Bacigalupo. Nonlinear Dispersion Properties of Acoustic Waveguides with Cubic Local Resonators. Advanced Structured Materials. 2020; ():377-392.

Chicago/Turabian Style

Marco Lepidi; Andrea Bacigalupo. 2020. "Nonlinear Dispersion Properties of Acoustic Waveguides with Cubic Local Resonators." Advanced Structured Materials , no. : 377-392.

Research article
Published: 13 December 2019 in Earthquake Engineering & Structural Dynamics
Reads 0
Downloads 0

Vibration tests are encountering a growing success in earthquake engineering as a valuable tool for the seismic assessment of buildings. Ambient vibration measurements, in particular, offer reliable support for the updating of mechanical models, as well as the enhancement of seismic mitigation strategies for existing buildings. In this respect, the common description of the floor diaphragms as planar rigid bodies tends to oversimplify the actual mechanical behaviour of some traditional structural solutions, especially in masonry buildings. This assumption can be violated even in modern concrete and steel buildings due to inadequate design, poor manufacturing, or damage. The paper addresses the mathematical validation of the rigid diaphragm simplification using vibration measurements. To this purpose, a model‐based inverse kinematic problem is stated and solved to discriminate the in‐plane rigid motion and the angular deformation time histories from vibration data. Simple formulas, leveraging the approximate solution in the case of problem under‐determinacy, exploit the spectral content of vibration data to discuss the diaphragm deformability. Natural modes exhibiting different (rigid, quasi‐rigid, or nonrigid) diaphragm behaviour are distinguishable by comparing the power spectral densities of the rigid motion and angular deformation. Modes of pure floor deformability can also be identified. The influence of adverse testing conditions is discussed through pseudo‐experimental data simulating the dynamic response of a simple frame structure. As a complementary contribution, the procedure effectiveness is experimentally verified by analysing vibration data related to, first, laboratory tests on a scaled concrete‐steel frame and, finally, full‐scale tests on a masonry building.

ACS Style

Daniele Sivori; Marco Lepidi; Serena Cattari. Ambient vibration tools to validate the rigid diaphragm assumption in the seismic assessment of buildings. Earthquake Engineering & Structural Dynamics 2019, 49, 194 -211.

AMA Style

Daniele Sivori, Marco Lepidi, Serena Cattari. Ambient vibration tools to validate the rigid diaphragm assumption in the seismic assessment of buildings. Earthquake Engineering & Structural Dynamics. 2019; 49 (2):194-211.

Chicago/Turabian Style

Daniele Sivori; Marco Lepidi; Serena Cattari. 2019. "Ambient vibration tools to validate the rigid diaphragm assumption in the seismic assessment of buildings." Earthquake Engineering & Structural Dynamics 49, no. 2: 194-211.

Article
Published: 11 December 2019 in Journal of Optimization Theory and Applications
Reads 0
Downloads 0

Recently, an increasing research effort has been dedicated to analyze the transmission and dispersion properties of periodic acoustic metamaterials, characterized by the presence of local resonators. Within this context, particular attention has been paid to the optimization of the amplitudes and center frequencies of selected stop and pass bands inside the Floquet–Bloch spectra of the acoustic metamaterials featured by a chiral or antichiral microstructure. Novel functional applications of such research are expected in the optimal parametric design of smart tunable mechanical filters and directional waveguides. The present paper deals with the maximization of the amplitude of low-frequency band gaps, by proposing suitable numerical techniques to solve the associated optimization problems. Specifically, the feasibility and effectiveness of Radial Basis Function networks and Quasi-Monte Carlo methods for the interpolation of the objective functions of such optimization problems are discussed, and their numerical application to a specific acoustic metamaterial with tetrachiral microstructure is presented. The discussion is motivated theoretically by the high computational effort often needed for an exact evaluation of the objective functions arising in band gap optimization problems, when iterative algorithms are used for their approximate solution. By replacing such functions with suitable surrogate objective functions constructed applying machine-learning techniques, well-performing suboptimal solutions can be obtained with a smaller computational effort. Numerical results demonstrate the effective potential of the proposed approach. Current directions of research involving the use of additional machine-learning techniques are also presented.

ACS Style

Andrea Bacigalupo; Giorgio Gnecco; Marco Lepidi; Luigi Gambarotta. Machine-Learning Techniques for the Optimal Design of Acoustic Metamaterials. Journal of Optimization Theory and Applications 2019, 187, 630 -653.

AMA Style

Andrea Bacigalupo, Giorgio Gnecco, Marco Lepidi, Luigi Gambarotta. Machine-Learning Techniques for the Optimal Design of Acoustic Metamaterials. Journal of Optimization Theory and Applications. 2019; 187 (3):630-653.

Chicago/Turabian Style

Andrea Bacigalupo; Giorgio Gnecco; Marco Lepidi; Luigi Gambarotta. 2019. "Machine-Learning Techniques for the Optimal Design of Acoustic Metamaterials." Journal of Optimization Theory and Applications 187, no. 3: 630-653.

Preprint
Published: 01 November 2019
Reads 0
Downloads 0

Beam lattice materials are characterized by a periodic microstructure realizing a geometrically regular pattern of elementary cells. In these microstructured materials, the dispersion properties governing the free dynamic propagation of elastic waves can be studied by formulating parametric lagrangian models and applying the Floquet-Bloch theory. Within this framework, governing the wave propagation by means of spectral design techniques and/or energy dissipation mechanisms is a major issue of theoretical and applied interest. Specifically, the wave propagation can be inhibited by purposely designing the microstructural parameters to open band gaps in the material spectrum at target center frequencies. Based on these motivations, a general dynamic formulation for determining the dispersion properties of beam lattice metamaterials, equipped with local resonators is presented. The mechanism of local resonance is realized by tuning periodic auxiliary masses, viscoelastically coupled with the beam lattice microstructure. As peculiar aspect, the viscoelastic coupling is derived by a mechanical formulation based on the Boltzmann superposition integral, whose kernel is approximated by a Prony series. Consequently, the free propagation of damped waves is governed by a linear homogeneous system of integral-differential equations of motion. Therefore, differential equations of motion with frequency-dependent coefficients are obtained by applying the bilateral Laplace transform. The corresponding complex-valued branches characterizing the dispersion spectrum are determined and parametrically analyzed. Particularly, the spectra corresponding to Taylor series approximations of the equation coefficients are investigated.

ACS Style

F Vadalà; A Bacigalupo; M Lepidi; L Gambarotta. Free and forced wave propagation in beam lattice metamaterials with viscoelastic resonators. 2019, 1 .

AMA Style

F Vadalà, A Bacigalupo, M Lepidi, L Gambarotta. Free and forced wave propagation in beam lattice metamaterials with viscoelastic resonators. . 2019; ():1.

Chicago/Turabian Style

F Vadalà; A Bacigalupo; M Lepidi; L Gambarotta. 2019. "Free and forced wave propagation in beam lattice metamaterials with viscoelastic resonators." , no. : 1.

Original paper
Published: 17 June 2019 in Nonlinear Dynamics
Reads 0
Downloads 0

Acoustic metamaterials are artificial microstructured media, typically characterized by a periodic locally resonant cell. The cellular microstructure can be functionally customized to govern the propagation of elastic waves. A one-dimensional diatomic lattice with cubic inter-atomic coupling—described by a Lagrangian model—is assumed as minimal mechanical system simulating the essential undamped dynamics of nonlinear acoustic metamaterials. The linear dispersion properties are analytically determined by solving the linearized eigenproblem governing the free wave propagation in the small-amplitude oscillation range. The dispersion spectrum is composed by a low-frequency acoustic branch and a high-frequency optical branch. The two frequency branches are systematically separated by a stop band, whose amplitude is analytically derived. Superharmonic 3:1 internal resonances can occur within a wavenumber-dependent locus defined in the mechanical parameter space. A general asymptotic approach, based on the multiple scale method, is employed to determine the nonlinear dispersion properties. Accordingly, the nonlinear frequencies and waveforms are obtained for the two fundamental cases of non-resonant and superharmonically 3:1 resonant or nearly resonant lattices. Moreover, the invariant manifolds associated with the nonlinear waveforms are parametrically determined in the space of the two principal coordinates. Finally, some examples of non-resonant and resonant lattices are selected to discuss their nonlinear dispersion properties from a qualitative and quantitative viewpoint.

ACS Style

Marco Lepidi; Andrea Bacigalupo. Wave propagation properties of one-dimensional acoustic metamaterials with nonlinear diatomic microstructure. Nonlinear Dynamics 2019, 98, 2711 -2735.

AMA Style

Marco Lepidi, Andrea Bacigalupo. Wave propagation properties of one-dimensional acoustic metamaterials with nonlinear diatomic microstructure. Nonlinear Dynamics. 2019; 98 (4):2711-2735.

Chicago/Turabian Style

Marco Lepidi; Andrea Bacigalupo. 2019. "Wave propagation properties of one-dimensional acoustic metamaterials with nonlinear diatomic microstructure." Nonlinear Dynamics 98, no. 4: 2711-2735.

Journal article
Published: 29 May 2019 in Materials & Design
Reads 0
Downloads 0

Microstructured honeycomb materials may exhibit exotic, extreme and tailorable mechanical properties, suited for innovative technological applications in a variety of modern engineering fields. The paper is focused on analysing the directional auxeticity of tetrachiral materials, through analytical, numerical and experimental methods. Theoretical predictions about the global elastic properties have been successfully validated by performing tensile laboratory tests on tetrachiral samples, realized with high precision 3D printing technologies. Inspired by the kinematic behaviour of the tetrachiral material, a newly-design bi-layered topology, referred to as bi-tetrachiral material, has been theoretically conceived and mechanically modelled. The novel topology virtuously exploits the mutual collaboration between two tetrachiral layers with opposite chiralities. The bi-tetrachiral material has been verified to outperform the tetrachiral material in terms of global Young modulus and, as major achievement, to exhibit a remarkable auxetic behaviour. Specifically, experimental results, confirmed by parametric analytical and computational analyses, have highlighted the effective possibility to attain strongly negative Poisson ratios, identified as a peculiar global elastic property of the novel bi-layered topology.

ACS Style

Ferdinando Auricchio; Andrea Bacigalupo; Luigi Gambarotta; Marco Lepidi; Simone Morganti; Francesca Vadalà. A novel layered topology of auxetic materials based on the tetrachiral honeycomb microstructure. Materials & Design 2019, 179, 107883 .

AMA Style

Ferdinando Auricchio, Andrea Bacigalupo, Luigi Gambarotta, Marco Lepidi, Simone Morganti, Francesca Vadalà. A novel layered topology of auxetic materials based on the tetrachiral honeycomb microstructure. Materials & Design. 2019; 179 ():107883.

Chicago/Turabian Style

Ferdinando Auricchio; Andrea Bacigalupo; Luigi Gambarotta; Marco Lepidi; Simone Morganti; Francesca Vadalà. 2019. "A novel layered topology of auxetic materials based on the tetrachiral honeycomb microstructure." Materials & Design 179, no. : 107883.

Original paper
Published: 23 April 2019 in Nonlinear Dynamics
Reads 0
Downloads 0

Quadratic and cubic modal interactions characterize the geometrically nonlinear dynamics of a parametric analytical model composed by two cantilever beams connected by a suspended shallow cable. The natural frequencies and modes of the linearized model are determined exactly, by solving the integral–differential eigenproblem governing the undamped free oscillations. Interesting phenomena of linear cable–beam interaction (frequency veering and modal hybridization) are recognized in the spectrum. Global and local modes are distinguished by virtue of the two localization factors measuring the modal kinetic energy stored in the beams and cable, respectively. The localization level is also put in relation to the magnitude of the quadratic and cubic nonlinearities. Therefore, the exact linear eigensolution is employed to formulate a nonlinearly coupled two-degrees-of-freedom model, defined in the reduced space of the modal amplitudes corresponding to a global and a local mode. The modal interactions between the two modes are analyzed, with focus on the autoparametric excitation mechanisms that can be favored by the occurrence of integer frequency ratios (1:2 and 2:1). Such internal resonance conditions enable significant transfers of mechanical energy—essentially governed by the quadratic coupling terms—from the small amplitudes of the externally excited global mode to the high amplitudes of the autoparametrically excited local mode. Different regimes of periodic and quasi-periodic oscillations are identified.

ACS Style

Vincenzo Gattulli; Marco Lepidi; Francesco Potenza; Umberto Di Sabatino. Modal interactions in the nonlinear dynamics of a beam–cable–beam. Nonlinear Dynamics 2019, 96, 2547 -2566.

AMA Style

Vincenzo Gattulli, Marco Lepidi, Francesco Potenza, Umberto Di Sabatino. Modal interactions in the nonlinear dynamics of a beam–cable–beam. Nonlinear Dynamics. 2019; 96 (4):2547-2566.

Chicago/Turabian Style

Vincenzo Gattulli; Marco Lepidi; Francesco Potenza; Umberto Di Sabatino. 2019. "Modal interactions in the nonlinear dynamics of a beam–cable–beam." Nonlinear Dynamics 96, no. 4: 2547-2566.

Mechanics of extreme materials
Published: 28 February 2019 in Meccanica
Reads 0
Downloads 0

The acoustic dispersion properties of monodimensional waveguide filters can be assessed by means of the simple prototypical mechanical system made of an infinite stack of periodic massive blocks, connected to each other by elastic joints. The linear undamped dynamics of the periodic cell is governed by a two degree-of-freedom Lagrangian model. The eigenproblem governing the free propagation of shear and moment waves is solved analytically and the two dispersion relations are obtained in a suited closed form fashion. Therefore, the pass and stop bandwidths are conveniently determined in the minimal space of the independent mechanical parameters. Stop bands in the ultra-low frequency range are achieved by coupling the stacked material with an elastic half-space modelled as a Winkler support. A convenient fine approximation of the dispersion relations is pursued by formulating homogenised micropolar continuum models. An enhanced continualization approach, employing a proper Maclaurin approximation of pseudo-differential operators, is adopted to successfully approximate the acoustic and optical branches of the dispersion spectrum of the Lagrangian models, both in the absence and in the presence of the elastic support.

ACS Style

Andrea Bacigalupo; Luigi Gambarotta; Marco Lepidi; Francesca Vadalà. Acoustic waveguide filters made up of rigid stacked materials with elastic joints. Meccanica 2019, 54, 2039 -2052.

AMA Style

Andrea Bacigalupo, Luigi Gambarotta, Marco Lepidi, Francesca Vadalà. Acoustic waveguide filters made up of rigid stacked materials with elastic joints. Meccanica. 2019; 54 (13):2039-2052.

Chicago/Turabian Style

Andrea Bacigalupo; Luigi Gambarotta; Marco Lepidi; Francesca Vadalà. 2019. "Acoustic waveguide filters made up of rigid stacked materials with elastic joints." Meccanica 54, no. 13: 2039-2052.

Original research article
Published: 31 January 2019 in Frontiers in Materials
Reads 0
Downloads 0

Sonic or acoustic metamaterials may offer a mechanically robust and highly customizable solution to open large band gaps in the low-frequency dispersion spectrum of beam lattice materials. Achieving the largest possible stop bandwidth at the lowest possible center frequency may be a challenging multi-objective optimization issue. The paper presents a first effort of analysis, systematization and synthesis of some recent multi-disciplinary studies focused on the optimal spectral design of beam lattice materials and metamaterials. The design parameter vector is a finite set including all the microstructural properties characterizing the periodic material and the local resonators. Numerical algorithms are employed as leading methodology for solving various instances of the optimization problem. Methodological alternatives, based on perturbation methods and computational modeling, are also illustrated. Some optimal results concerning the dispersion spectrum of hexachiral, tetrachiral and anti-tetrachiral materials and metamaterials are summarized. The concluding remarks are accompanied by preliminary ideas to overcome some operational issues in solving the optimization problem.

ACS Style

Andrea Bacigalupo; Marco Lepidi; Giorgio Gnecco; Francesca Vadalà; Luigi Gambarotta. Optimal Design of the Band Structure for Beam Lattice Metamaterials. Frontiers in Materials 2019, 6, 1 .

AMA Style

Andrea Bacigalupo, Marco Lepidi, Giorgio Gnecco, Francesca Vadalà, Luigi Gambarotta. Optimal Design of the Band Structure for Beam Lattice Metamaterials. Frontiers in Materials. 2019; 6 ():1.

Chicago/Turabian Style

Andrea Bacigalupo; Marco Lepidi; Giorgio Gnecco; Francesca Vadalà; Luigi Gambarotta. 2019. "Optimal Design of the Band Structure for Beam Lattice Metamaterials." Frontiers in Materials 6, no. : 1.

Journal article
Published: 01 October 2018 in Composite Structures
Reads 0
Downloads 0

The periodic cellular topology characterizing the microscale structure of a heterogeneous material may allow the finest functional customization of its acoustic dispersion properties. The paper addresses the free propagation of elastic waves in micro-structured cellular materials. Focus is on the alternative formulations suited to describe the wave propagation in the material, according to the classic canons of solid or structural mechanics. Adopting the centrosymmetric tetrachiral microstructure as prototypical periodic cell, the frequency dispersion spectrum resulting from a synthetic lagrangian beam-lattice formulation is compared with its counterpart derived from different continuous models (high-fidelity first-order heterogeneous and equivalent homogenized micropolar continuum). Asymptotic perturbation-based approximations and numerical spectral solutions are cross-validated. Adopting the low-frequency band gaps of the material band structures as functional targets, parametric analyses are carried out to highlight the descriptive limits of the synthetic models and to explore the enlarged parameter space described by high-fidelity models. The final tuning of the mechanical properties of the cellular microstructure is employed to successfully verify the wave filtering functionality of the tetrachiral material.

ACS Style

F. Vadalà; A. Bacigalupo; M. Lepidi; L. Gambarotta. Bloch wave filtering in tetrachiral materials via mechanical tuning. Composite Structures 2018, 201, 340 -351.

AMA Style

F. Vadalà, A. Bacigalupo, M. Lepidi, L. Gambarotta. Bloch wave filtering in tetrachiral materials via mechanical tuning. Composite Structures. 2018; 201 ():340-351.

Chicago/Turabian Style

F. Vadalà; A. Bacigalupo; M. Lepidi; L. Gambarotta. 2018. "Bloch wave filtering in tetrachiral materials via mechanical tuning." Composite Structures 201, no. : 340-351.

Journal article
Published: 01 August 2018 in International Journal of Solids and Structures
Reads 0
Downloads 0

The free propagation of acoustic plane waves through cellular periodic materials is generally accompanied by a flow of mechanical energy across the adjacent cells. The paper focuses on the energy transport related to dispersive waves propagating through non-dissipative microstructured materials. The generic microstructure of the periodic cell is described by a beam lattice model, suitably reduced to the minimal space of dynamic degrees-of-freedom. The linear eigenproblem governing the wave propagation is stated and the complete eigensolution is considered to study both the real-valued dispersion functions and the complex-valued waveforms of the propagating elastic waves. First, a complete family of nondimensional quantities (polarization factors) is proposed to quantify the linear polarization or quasi-polarization, according to a proper energetic criterion. Second, a vector variable related to the periodic cell is introduced to assess the directional flux of mechanical energy, in analogy to the Umov-Poynting vector related to the material point in solid mechanics. The physical-mathematical relation between the energy flux and the velocity of the energy transport is recognized. The formal equivalence between the energy and the group velocity is pointed out, according to the mechanical assumptions. Finally, all the theoretical developments are successfully applied to the prototypical beam lattice material characterized by a periodic tetrachiral microstructure. As case study, the tetrachiral material offers interesting examples of perfect and nearly-perfect linear polarization. Furthermore, the nonlinear dependence of the energy fluxes on the elastic waveforms is discussed with respect to the acoustic and optical surfaces featuring the energy spectrum of the material. As final remark, the occurrence of negative refraction phenomena is found to characterize the high-frequency optical surface of the frequency spectrum.

ACS Style

Andrea Bacigalupo; Marco Lepidi. Acoustic wave polarization and energy flow in periodic beam lattice materials. International Journal of Solids and Structures 2018, 147, 183 -203.

AMA Style

Andrea Bacigalupo, Marco Lepidi. Acoustic wave polarization and energy flow in periodic beam lattice materials. International Journal of Solids and Structures. 2018; 147 ():183-203.

Chicago/Turabian Style

Andrea Bacigalupo; Marco Lepidi. 2018. "Acoustic wave polarization and energy flow in periodic beam lattice materials." International Journal of Solids and Structures 147, no. : 183-203.

Journal article
Published: 01 April 2018 in International Journal of Solids and Structures
Reads 0
Downloads 0
ACS Style

Marco Lepidi; Andrea Bacigalupo. Multi-parametric sensitivity analysis of the band structure for tetrachiral acoustic metamaterials. International Journal of Solids and Structures 2018, 136-137, 186 -202.

AMA Style

Marco Lepidi, Andrea Bacigalupo. Multi-parametric sensitivity analysis of the band structure for tetrachiral acoustic metamaterials. International Journal of Solids and Structures. 2018; 136-137 ():186-202.

Chicago/Turabian Style

Marco Lepidi; Andrea Bacigalupo. 2018. "Multi-parametric sensitivity analysis of the band structure for tetrachiral acoustic metamaterials." International Journal of Solids and Structures 136-137, no. : 186-202.

Journal article
Published: 13 November 2017 in Buildings
Reads 0
Downloads 0

The experience of the recent earthquakes in Italy caused a shocking impact in terms of loss of human life and damage in buildings. In particular, when it comes to ancient constructions, their cultural and historical value overlaps with the economic and social one. Among the historical structures, churches have been the object of several studies which identified the main characteristics of the seismic response and the most probable collapse mechanisms. More rarely, academic studies have been devoted to ancient palaces, since they often exhibit irregular and complicated arrangement of the resisting elements, which makes their response very difficult to predict. In this paper, a palace located in L’Aquila, severely damaged by the seismic event of 2009 is the object of an accurate study. A historical reconstruction of the past strengthening interventions as well as a detailed geometric relief is performed to implement detailed numerical models of the structure. Both global and local models are considered and static nonlinear analyses are performed considering the influence of the input direction on the seismic vulnerability of the building. The damage pattern predicted by the numerical models is compared with that observed after the earthquake. The seismic vulnerability assessments are performed in terms of ultimate peak ground acceleration (PGA) using capacity curves and the Italian code spectrum. The results are compared in terms of ultimate ductility demand evaluated performing nonlinear dynamic analyses considering the actual registered seismic input of L’Aquila earthquake.

ACS Style

Francesco Cannizzaro; Bartolomeo Pantò; Marco Lepidi; Salvatore Caddemi; Ivo Caliò. Multi-Directional Seismic Assessment of Historical Masonry Buildings by Means of Macro-Element Modelling: Application to a Building Damaged during the L’Aquila Earthquake (Italy). Buildings 2017, 7, 106 .

AMA Style

Francesco Cannizzaro, Bartolomeo Pantò, Marco Lepidi, Salvatore Caddemi, Ivo Caliò. Multi-Directional Seismic Assessment of Historical Masonry Buildings by Means of Macro-Element Modelling: Application to a Building Damaged during the L’Aquila Earthquake (Italy). Buildings. 2017; 7 (4):106.

Chicago/Turabian Style

Francesco Cannizzaro; Bartolomeo Pantò; Marco Lepidi; Salvatore Caddemi; Ivo Caliò. 2017. "Multi-Directional Seismic Assessment of Historical Masonry Buildings by Means of Macro-Element Modelling: Application to a Building Damaged during the L’Aquila Earthquake (Italy)." Buildings 7, no. 4: 106.

Preprint
Published: 27 June 2017
Reads 0
Downloads 0

Tetrachiral materials are characterized by a cellular microstructure made by a periodic pattern of stiff rings and flexible ligaments. Their mechanical behaviour can be described by a planar lattice of rigid massive bodies and elastic massless beams. The periodic cell dynamics is governed by a monoatomic structural model, conveniently reduced to the only active degrees-of-freedom. The paper presents an explicit parametric description of the band structure governing the free propagation of elastic waves. By virtue of multiparametric perturbation techniques, sensitivity analyses are performed to achieve analytical asymptotic approximation of the dispersion functions. The parametric conditions for the existence of full band gaps in the low-frequency range are established. Furthermore, the band gap amplitude is analytically assessed in the admissible parameter range. In inertial tetrachiral metamaterials, stop bands can be opened by the introduction of intra-ring resonators. Perturbation methods can efficiently deal with the consequent enlargement of the mechanical parameter space. Indeed high-accuracy parametric approximations are achieved for the band structure, enriched by the new optical branches related to the resonator frequencies. In particular, target stop bands in the metamaterial spectrum are analytically designed through the asymptotic solution of inverse spectral problems.

ACS Style

Marco Lepidi; Andrea Bacigalupo. Multi-parametric sensitivity analysis of the band structure for tetrachiral inertial metamaterials. 2017, 1 .

AMA Style

Marco Lepidi, Andrea Bacigalupo. Multi-parametric sensitivity analysis of the band structure for tetrachiral inertial metamaterials. . 2017; ():1.

Chicago/Turabian Style

Marco Lepidi; Andrea Bacigalupo. 2017. "Multi-parametric sensitivity analysis of the band structure for tetrachiral inertial metamaterials." , no. : 1.

Journal article
Published: 01 April 2017 in Composites Part B: Engineering
Reads 0
Downloads 0

The elastic wave propagation is investigated in a beam lattice material characterized by a square periodic cell with anti-tetrachiral microstructure. With reference to the Floquet-Bloch spectrum, focus is made on the band structure enrichments and modifications which can be achieved by equipping the cellular microstructure with tunable local resonators. By virtue of its composite mechanical nature, the so-built inertial meta-material gains enhanced capacities of passive frequency-band filtering. Indeed the number, placement and properties of the inertial resonators can be designed to open, shift and enlarge the band gaps between one or more pairs of consecutive branches in the frequency spectrum. In order to improve the meta-material performance, several nonlinear optimization problems are formulated. The largest among the band gap amplitudes in the low-frequency range is selected as suited objective function. Proper inequality constraints are introduced to restrict the admissible solutions within a compact set of mechanical and geometric parameters, including only physically realistic properties of both the lattice and the resonators. The optimization problems related to full and partial band gaps are solved by using a globally convergent version of the numerical method of moving asymptotes, combined with a quasi-Monte Carlo multi-start technique. The optimal solutions are numerically computed, discussed and compared from the qualitative and quantitative viewpoints, bringing to light the limits and potential of the meta-material performance. The clearest trends emerging from the numerical analyses are pointed out and interpreted from the physical viewpoint. Finally, some specific recommendations about the microstructural design of the meta-material are synthesized

ACS Style

Andrea Bacigalupo; Giorgio Gnecco; Marco Lepidi; Luigi Gambarotta. Optimal design of low-frequency band gaps in anti-tetrachiral lattice meta-materials. Composites Part B: Engineering 2017, 115, 341 -359.

AMA Style

Andrea Bacigalupo, Giorgio Gnecco, Marco Lepidi, Luigi Gambarotta. Optimal design of low-frequency band gaps in anti-tetrachiral lattice meta-materials. Composites Part B: Engineering. 2017; 115 ():341-359.

Chicago/Turabian Style

Andrea Bacigalupo; Giorgio Gnecco; Marco Lepidi; Luigi Gambarotta. 2017. "Optimal design of low-frequency band gaps in anti-tetrachiral lattice meta-materials." Composites Part B: Engineering 115, no. : 341-359.

Recent advances on the mechanics of materials
Published: 27 February 2017 in Meccanica
Reads 0
Downloads 0

Lattice materials are often investigated to determine how small parameter variations in the periodic microstructrure can influence the elastic wave propagation. A general hierarchical scheme, based on asymptotic perturbation techniques, is outlined to analytically assess the parametric sensitivity of the material band structure to a generic multi-parametric perturbation (direct problem). Modeling refinements, parameters updates, microstructural damages and manufacturing irregularities can be treated indifferently and simultaneously. According to a converse strategy, based on the inversion of the sensitivity problem, a hierarchical scheme is sketched to identify the parameter combinations which realize a design band structure (inverse problem). The direct and inverse problem are applied to the sensitivity analysis and band structure design of the anti-tetrachiral lattice material. Despite the high spectral density and the high-dimensional parameter space, the multi-parameter perturbation technique demonstrates its suitability in, first, analytically—although asymptotically—describe the material spectrum and, second, designing the material microstructure to obtain the desired spectral components. The inverse problem solution is discussed in terms of existence, uniqueness, asymptotic consistency and physical admissibility.

ACS Style

Marco Lepidi; Andrea Bacigalupo. Parametric design of the band structure for lattice materials. Meccanica 2017, 53, 613 -628.

AMA Style

Marco Lepidi, Andrea Bacigalupo. Parametric design of the band structure for lattice materials. Meccanica. 2017; 53 (3):613-628.

Chicago/Turabian Style

Marco Lepidi; Andrea Bacigalupo. 2017. "Parametric design of the band structure for lattice materials." Meccanica 53, no. 3: 613-628.