Marco Lepidi

Nonlinear interactions in the planar dynamics of cable-stayed beam

Abstract An analytical model is proposed to study the nonlinear interactions between beam and cable dynamics in stayed-systems. The integro-differential problem, describing the in-plane motion of a simple cable-stayed beam, presents quadratic and cubic nonlinearities both in the cable equation and at the boundary conditions. Mainly studied are the effects of quadratic interactions, appearing at relatively low oscillation amplitude. To this end an analysis of the sensitivity of modal properties to parameter variations, in intervals of technical interest, has evidenced the occurrence of one-to-two and two-to-one internal resonances between global and local modes. The interactions between the resonant modes evidences two different sources of oscillation in cables, illustrated by simple 2dof discrete models. In the one-to-two global–local resonance, a novel mechanism is analyzed, by which cable undergoes large periodic and chaotic oscillations due to an energy transfer from the low-global to high-local frequencies. In two-to-one global–local resonance, the well-known parametric-induced cable oscillation in stayed-systems is correctly reinterpreted through the autoparametric resonance between a global and a local mode. Increasing the load the saturation of the global oscillations evidences the energy transfer from high-global to low-local frequencies, producing large cable oscillations. In both cases, the effects of detuning from internal and external resonance are presented.

Optimal design of auxetic hexachiral metamaterials with local resonators

A parametric beam lattice model is formulated to analyse the propagation properties of elastic in-plane waves in an auxetic material based on a hexachiral topology of the periodic cell, equipped with inertial local resonators. The Floquet-Bloch boundary conditions are imposed on a reduced order linear model in the only dynamically active degrees-offreedom. Since the resonators can be designed to open and shift band gaps, an optimal design, focused on the largest possible gap in the low-frequency range, is achieved by solving a maximization problem in the bounded space of the significant geometrical and mechanical parameters. A local optimized solution, for a the lowest pair of consecutive dispersion curves, is found by employing the globally convergent version of the Method of Moving asymptotes, combined with Monte Carlo and quasi-Monte Carlo multi-start techniques.

Damage Identification in Elastic Suspended Cables through Frequency Measurement

Structural cables in cable-stayed systems are subject to potential damage, mainly due to fatigue phenomena and galvanic corrosion. The paper analyzes how the dynamical behavior of cables is affected by diffuse damage, and investigates whether the damage can be identified through information selected from the dynamical response. A continuous monodimensional model of a damaged cable is used for this purpose. Damage is described as a reduction of the cable cross section, and defined in terms of its intensity, extent and position. The major effects of these different damage parameters on the cable static response and spectral properties are evidenced and discussed to verify the observability of the damage. The frequencies of the dominant transversal motion of the cable are chosen as damage indicators, since they are sufficiently sensitive to the damage intensity and extent, while the damage position requires additional information. The damage identification problem is formulated by defining an objective error function between the measured and the model frequencies, to be minimized in the space of the damage parameters. Pseudo-experimental data are initially used to test the effectiveness and resolution of the procedure. The results confirm the uniqueness of the problem solution and its correctness. The robustness of the solution is discussed while considering the presence of random errors of increasing amplitude. The procedure is also positively verified with experimental measures from a prototype model of an artificially damaged spiral strand.

An Integrated Approach to the Design of Wireless Sensor Networks for Structural Health Monitoring

Wireless Sensor Networks are a promising technology for the implementation of Structural Health Monitoring systems, since they allow to increase the diffusion of measurements in the structure and to reduce the sensor deployment effort and the overall costs. In this paper, possible benefits and critical issues related with the use of Wireless Sensor Networks for structural monitoring are analysed, specifically addressing network design strategies oriented to the damage detection problem. A global cost function is defined and used for the definition of possible design methodologies. Among the various approach, the use of an integrated strategy, able to take advantage of a preliminary structural analysis is considered. Moreover, the implementation of a distributed processing is an explored strategy for an overall improvement of system performances. Benefits of this methodology are finally demonstrated through the analysis of a representative case study, the IASC-ASCE benchmark problem.

Multi-parametric sensitivity analysis of the band structure for tetrachiral acoustic metamaterials

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.

Design of acoustic metamaterials through nonlinear programming

The dispersive wave propagation in a periodic metamaterial with tetrachiral topology and inertial local resonators is investigated. The Floquet-Bloch spectrum of the metamaterial is compared with that of the tetrachiral beam lattice material without resonators. The resonators can be designed to open and shift frequency band gaps, that is, spectrum intervals in which harmonic waves do not propagate. Therefore, an optimal passive control of the frequency band structure can be pursued in the metamaterial. To this aim, suitable constrained nonlinear optimization problems on compact sets of admissible geometrical and mechanical parameters are stated. According to functional requirements, sets of parameters which determine the largest low-frequency band gap between selected pairs of consecutive branches of the Floquet-Bloch spectrum are soughted for numerically. The various optimization problems are successfully solved by means of a version of the method of moving asymptotes, combined with a quasi-Monte Carlo multi-start technique.

Passive control of wave propagation in periodic anti-tetrachiral meta-materials

Periodic anti-tetrachiral materials are strongly characterized by a marked auxeticity, the unusual and fascinating mechanical property mathematically expressed by negative values of the Poisson’s ratio. The auxetic behavior is primarily provided by pervasive rolling-up mechanisms developed by the doubly-symmetric micro-structure of the periodic cell, composed by a regular pattern of rigid rings connected by tangent flexible ligaments. Adopting a beam-lattice model to describe the linear free dynamics of the elementary cell, the planar wave propagation along the bi-dimensional material domain can be studied according to the Floquet-Bloch theory. Parametric analyses of the dispersion curves, carried out with numerical or asymptotic tools, typically reveal a highly-dense spectrum, with persistent absence of total band-gaps in the low-frequency range. The paper analyses the wave propagation in the meta-material developed by introducing rigid massive inserts, locally housed by all the rings and working as undamped linear oscillators with assigned inertia and/or stiffness properties. The elastic coupling between the cell microstructure and the oscillators, if properly tuned (inertial resonators), is found to significantly modify the Floquet-Bloch spectrum of the material. The effects of the resonator parameters (tuning frequency and mass ratio) on the low-frequency band structure of the metamaterial are discussed, with focus on the valuable possibility to (i) open total band gaps, by either the widening of an existing partial band gap or the avoidance of a crossing point between adjacent dispersion curves, (ii) finely control the total band-gap amplification, in order to assess the maximum achievable performance of the meta-material against the vibration propagation

Semiactive Control Using MR Dampers of a Frame Structure under Seismic Excitation

The paper approaches the multifaceted task of semiactively controlling the seismic response of a prototypal building model, through interstorey bracings embedding magnetorheological dampers. The control strategy is based on a synthetic discrete model, purposely formulated in a reduced space of significant dynamic variables, and consistently updated to match the modal properties identified from the experimental response of the modeled physical structure. The occurrence of a known eccentricity in the mass distribution, breaking the structural symmetry, is also considered. The dissipative action of two magnetorheological dampers is governed by a clipped‐optimal control strategy. The dampers are positioned in order to deliver two eccentric and independent forces, acting on the first‐storey displacements. This set‐up allows the mitigation of the three‐dimensional motion arising when monodirectional ground motion is imposed on the non‐symmetric structure. Numerical investigations on the model response to natura...

Design of Damper Viscous Properties for Semi-active Control of Asymmetric Structures

A method to design semi-active control strategies of asymmetric structures is presented. The method is based on the optimal sizing of an equivalent Kelvin-Voight model describing the constitutive behavior of semi-active magneto-rheological devices, through the evaluation of the maximum achievable modal damping when they work in passive modality. The complex eigenvalue loci of the passively-controlled system versus the device mechanical characteristics are spanned for symmetric and asymmetric frame structures. A coherent representation of the reference effect ensured by an optimized linear active feedback on the eigenvalues loci is selected to drive the design of the adjustable properties of the semi-active device. A clipped-optimal control algorithm is used in a prototype experimental application whose performance are highlighted by the presented design method.