Pendulum vibration absorbers with spatially-varying tangential friction: modelling and design

Passive vibration absorbers are widely used in structural control. They usually consist in a single-degree-of-freedom appendage of the main structure, tuned to a selected structural target mode by means of frequency and damping optimization. A classical configuration is the pendulum type, whose mass is bilaterally constrained along a curved trajectory and is typically connected to the structure through viscous dashpots. Although the principle is well known, the search for improved arrangements is still under way. In recent years this investigation has inspired a new type of bidirectional pendulum absorber (BPA), consisting of a mass moving along an optimal three-dimensional (3D) concave-up surface. For the BPA, the surface principal curvatures are conceived to ensure a bidirectional tuning to both principal modes of the structure, while damping is provided either by horizontal viscous dashpots or by vertical friction dampers between the BPA and the structure. In this paper, a BPA variant is proposed, in which damping is produced by the variable tangential friction force developing between the pendulum mass and the 3D surface, because of a spatially-varying friction coefficient. In fact, a friction coefficient pattern is proposed that varies along the pendulum surface proportionally to the modulus of the surface gradient. With this assumption, the absorber dissipative model proves nonlinear homogeneous at low response amplitudes. The resulting homogeneous BPA (HBPA) has a fundamental advantage over conventional friction-type absorbers, in that its equivalent damping ratio is independent of the amplitude of oscillations, i.e. its optimal performance is independent of the excitation level. At the same time, the HBPA is more compact and simpler than viscously damped BPAs, not requiring the installation of dampers. This paper presents the analytical modelling framework of the HBPA and a method for its optimal design. Numerical simulations under wind and earthquake loads are reported to compare the HBPA with classical viscously damped BPAs. Finally, the HBPA proves a promising alternative to existing pendulum absorbers, and the homogeneous tangential friction proves an effective way to realize amplitude-independent damping in structural systems

Lifecycle cost optimization of tuned mass dampers for the seismic improvement of inelastic structures

The seismic performance of tuned mass dampers (TMDs) on structures undergoing inelastic deformations may largely depend on the ground motion intensity. By estimating the impact of each seismic intensity on the overall cost of future seismic damages, lifecycle cost (LCC) proves a rational metric for evaluating the benefits of TMDs on inelastic structures. However, no incorporation of this metric into an optimization framework is reported yet. This paper presents a methodology for the LCC‐optimal design of TMDs on inelastic structures, which minimizes the total seismic LCC of the combined building‐TMD system. Its distinctive features are the assumption of a mass‐proportional TMD cost model, the adoption of an iterative suboptimization procedure, and the initialization of the TMD frequency and damping ratios according to a conventional linear TMD design technique. The methodology is applied to the seismic improvement of the SAC‐LA benchmark buildings, taken as representative of standard steel moment‐resisting frame office buildings in LA, California. Results show that, despite their limited performance at the highest intensity levels, LCC‐optimal TMDs considerably reduce the total LCC, to an extent that depends on both the building vulnerability and the TMD unit cost. They systematically present large mass ratios (around 10%) and frequency and damping ratios close to their respective linearly designed optima. Simulations reveal the effectiveness of the proposed design methodology and the importance of adopting a nonlinear model to correctly evaluate the cost‐effectiveness of TMDs on ordinary structures in highly seismic areas

A novel bidirectional pendulum tuned mass damper using variable homogeneous friction to achieve amplitude‐independent control

Passive tuned mass dampers (TMDs) are widely used in controlling structural vibrations. Although their principle is well established, the search for improved arrangements is still under way. This effort has recently produced an innovative paradigm of bidirectional pendulum TMD (BTMD) that, moving along a specially designed three‐dimensional (3D) surface, can simultaneously control two in‐plane orthogonal structural modes. In existing versions of BTMDs, energy dissipation is provided either by ordinary horizontal viscous dampers or by an original arrangement of vertical friction dampers. In this paper, a new paradigm is proposed, in which energy dissipation comes from the tangential friction arising along the pendulum surface out of an optimal spatially variable friction coefficient pattern. Within this paradigm, if the friction coefficient is taken proportional to the modulus of the pendulum surface gradient, the dissipation model results nonlinear homogeneous in the smalldisplacement domain, and the performance of the absorber, herein called the homogeneous tangential friction BTMD (HT‐BTMD), results independent from the excitation level. The present work introduces this concept, derives the analytical model of the HT‐BTMD, establishes a method for its optimal design, and numerically verifies its seismic effectiveness in comparison with viscously damped devices. The validity and feasibility of the concept are demonstrated through experimental tests on a small‐scale lab prototype, which also show the efficacy of a stepwise approximation of the homogeneous friction pattern. The new device proves a competing alternative to existing BTMDs, and homogeneous tangential friction proves a promising new paradigm to provide pendular systems with amplitude‐independent structural damping

Modeling and design of bidirectional pendulum tuned mass dampers using axial or tangential homogeneous friction damping

As a development of the classical pendulum vibration absorber, bidirectional pendulum TMDs (BTMDs) have been recently proposed, capable to resonate with the main structure along both its horizontal directions by virtue of their optimally designed three-dimensional (3D) pendulum surface. To provide BTMDs with the required energy dissipation capability, two damping mechanisms based on respectively axial and tangential friction were invented as an alternative to ordinary viscous dashpots. The first one consists of a vertical axial-friction damper connecting the BTMD to the main structure. The second one consists of a tangential friction spatially variable along the pendulumsurface in proportion to the modulus of the surface gradient vector. Both mechanisms are fundamentally characterized by a nonlinear but homogeneous first-order model which makes their effectiveness independent from the excitation level. This paper compares the two friction paradigms with the classical viscous one. To this purpose, first a unifying fully nonlinear 3D model is established through Lagrangian mechanics, then an optimal design method is proposed, based on either H1 or H2 norm minimization criteria. Extensive numerical simulations are performed to show the pros and cons of the three damping options and of the two optimization approaches. Results demonstrate that the three types exhibit a similar performance against unidirectional excitation but that the axial-friction type loses most of its effectiveness under bidirectional excitation whenever the pendulum surface is axial- or nearly axial-symmetrical, because of the insurgence of a peculiar rotational motion which virtually deactivates the friction damper. Results also show that theH1 design criterion is more robust than theH2 design criterion, and that both criteria outperform previous simplified approaches proposed in the literature. It is concluded that, once properly designed and until stroke demand does not exceed their intrinsic stroke limitations, BTMDsare an effective vibration control strategy, which can be implemented through a variety of damping options, and that the two homogeneous friction mechanisms, and particularly the tangential one, are promising paradigms to provide amplitude-independent damping to engineering pendular systems

Modeling and design of tuned mass dampers using sliding variable friction pendulum bearings

AbstractAn effective vibration control device, the pendulum tuned mass damper (P-TMD), can be easily realized as a mass supported on rolling or sliding pendulum bearings. While the bearings' concavity provides the desired gravitational restoring force, the necessary dissipative force can be obtained either from additional dampers installed in parallel with the bearings or from the same friction resistance developing within each bearing between the roller/slider and the rolling/sliding surface. The latter solution may prove cheaper and more compact but implies that the P-TMD effectiveness will be amplitude dependent if the friction coefficient is kept uniform along the rolling/sliding surface, as in conventional friction bearings. In this case, the friction P-TMD will be as efficient as a viscous P-TMD only at a given vibration level, with large performance reductions at other levels. To avoid this inconvenience, this paper proposes a new type of sliding variable friction pendulum (VFP) TMD, called the VFP-TMD, in which the sliding surface is divided into two concentric regions: a circular inner region, having the lowest possible friction coefficient and the same dimensions of the slider, and an annular outer region, having a friction coefficient set to an optimal value. A similar arrangement has been recently proposed to realize adaptive seismic isolation devices, but no specific application to TMDs is reported. To assess the VFP-TMD performance, first its analytical model is derived, rigorously accounting for geometric nonlinearities as well as for the variable (in time and space) pressure distribution along the contact area, and then, an optimal design methodology is presented. Finally, numerical simulations show the influence of the main design parameters on the device behavior and demonstrate that the VFP-TMD can achieve nearly the same effectiveness of viscous P-TMDs, while considerably outperforming conventional uniform-friction P-TMDs. The proposed analytical model can be used to enhance or validate existing models of VFP isolators that assume a constant and uniform contact pressure distribution

Innovative technique for the base isolation of existing buildings

An innovative base isolation system has been recently proposed for the retrofitting of existing buildings, in which the isolation layer is inserted under the building foundations so that the building, along with its foundations, is isolated from the surrounding soil. The isolation layer resides in closely-spaced micro-tunnels, constructed under the entire width of the building. These micro-tunnels, along with the trenches around the building, isolate the structure from the surrounding soil. The execution of these micro-tunnels is the most critical construction stage, because it may result in settlements which can damage the structure. In this paper, the behaviour of an existing structure, consisting of a masonry wall subjected to tunnelling-induced ground subsidence, is analysed. A parametric study is conducted using 2-D nonlinear finite element analyses to understand the role of key factors such as strength and stiffness of soil and masonry, roughness of soil-structure interface, excavation sequence of tunnels, wall dimensions and openings configuration. The study identifies the design variables which influence the most the risk of structural damage and suggests the most effective damage symptoms to be monitored during constructio

Identificazione dinamica sperimentale di edifici strategici sotto sisma

Edifici pubblici quali ospedali, scuole, chiese e municipi costituiscono un patrimonio di importanza strategica per la vita di una comunità. La loro gestione richiede un periodico monitoraggio delle condizioni di sicurezza sia a breve che a lungo termine che può oggi essere condotto in modo efficace ed oggettivo mediante sistemi automatici e permanenti di misura delle vibrazioni strutturali. All'occorrenza di un evento sismico, tali sistemi hanno il merito di cogliere l'effettivo comportamento dinamico della struttura, permettendo la calibrazione sperimentale di modelli numerici, utili per una accurata valutazione del livello di sicurezza sismico e per la progettazione di interventi migliorativi. In quest'ottica assume particolare rilievo la rete di monitoraggio dinamico permanente di edifici strategici realizzata dal Dipartimento di Protezione Civile. Quattro di questi edifici sono stati scelti come casi studio allo scopo di analizzarne la risposta acquisita durante il recente evento sismico del Gennaio 2012 in Lunigiana/Garfagnana. Il presente articolo riporta i risultati della caratterizzazione dinamica condotta su uno di essi: il municipio di San Romano in Garfagnana (LU

Innovative technique for the base isolation of existing buildings

An innovative base isolation system has been recently proposed for the retrofitting of existing buildings, in which the isolation layer is inserted under the building foundations so that the building, along with its foundations, is isolated from the surrounding soil. The isolation layer resides in closely-spaced micro-tunnels, constructed under the entire width of the building. These micro-tunnels, along with the trenches around the building, isolate the structure from the surrounding soil. The execution of these micro-tunnels is the most critical construction stage, because it may result in settlements which can damage the structure. In this paper, the behaviour of an existing structure, consisting of a masonry wall subjected to tunnelling-induced ground subsidence, is analysed. A parametric study is conducted using 2-D nonlinear finite element analyses to understand the role of key factors such as strength and stiffness of soil and masonry, roughness of soil-structure interface, excavation sequence of tunnels, wall dimensions and openings configuration. The study identifies the design variables which influence the most the risk of structural damage and suggests the most effective damage symptoms to be monitored during constructio

An optimal sensor placement strategy for reliable expansion of mode shapes under measurement noise and modelling error

Modal expansion techniques are typically used to expand the experimental modal displacements at sensor positions to all unmeasured degrees of freedom. Since in most cases, sensors can be attached only at limited locations in a structure, an expansion is essential to determine mode shapes, strains, stresses, etc. throughout the structure which can be used for structural health monitoring. Conventional sensor placement algorithms are mostly aimed to make the modal displacements at sensor positions of different modes as linearly independent as possible. However, under the presence of modelling errors and measurement noise, an optimal location based on this criterion is not guaranteed to provide an expanded mode shape which is close to the real mode shape. In this work, the expected value of normal distance between the real mode shape and the expanded mode shape is used as a measure of closeness between the two entities. Optimal sensor locations can be determined by minimizing this distance. This new criterion is applied on a simple cantilever beam and an industrial milling tower. In both cases, by using an exhaustive search of all possible sensor configurations it was possible to find sensor locations which resulted in a significant reduction in the distance when compared to a conventional optimal sensor placement strategy. Sufficiently accurate sub-optimal sequential sensor placement algorithm is also suggested as an alternative to the exhaustive search which is then compared with a genetic algorithm-based search. The efficiency of this new sensor placement criterion is further verified using Monte Carlo simulations for some realistic modelling error conditions

Identificazione dinamica sperimentale di edifici strategici sotto sisma

Edifici pubblici quali ospedali, scuole, chiese e municipi costituiscono un patrimonio di importanza strategica per la vita di una comunità. La loro gestione richiede un periodico monitoraggio delle condizioni di sicurezza sia a breve che a lungo termine che può oggi essere condotto in modo efficace ed oggettivo mediante sistemi automatici e permanenti di misura delle vibrazioni strutturali. All'occorrenza di un evento sismico, tali sistemi hanno il merito di cogliere l'effettivo comportamento dinamico della struttura, permettendo la calibrazione sperimentale di modelli numerici, utili per una accurata valutazione del livello di sicurezza sismico e per la progettazione di interventi migliorativi. In quest’ottica assume particolare rilievo la rete di monitoraggio dinamico permanente di edifici strategici realizzata dal Dipartimento di Protezione Civile. Quattro di questi edifici sono stati scelti come casi studio allo scopo di analizzarne la risposta acquisita durante il recente evento sismico del Gennaio 2012 in Lunigiana/Garfagnana. Il presente articolo riporta i risultati della caratterizzazione dinamica condotta su uno di essi: il municipio di San Romano in Garfagnana (LU)