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one of the more applied (Hagedorn 1982, Markiewicz 1995. In many cases the connection that realizes the transfer of energy from the main system to the TMD is idealized as a linear spring and dashpot; however this simplification is in contrast with the fact that large relative displacement are expected, thus recent investigation are devoted to nonlinear TMD (Sauter and Hagedorn 2002, Lacarbonara andVestroni 2002).Investigations on the effects of an added mass have permitted to evaluate the optimal mechanical characteristics of the linear device which maximize the critical value at which the dynamic instability phenomenon occurs (Rowbottom 1981, Fujino andAbé 1993). However, in order to investigate system performance when the flow velocity exceeds the critical value, an analysis of the post-critical behavior is needed. Investigations on the system postcritical behavior has been performed by means of both numerical, analytical and experimental methods (Fujino, et al. 1985, Abdel-Rohman 1994. A first study of the system postcritical behavior as a 2DOF system has been presented by the authors in Gattulli, et al. (2001), with the aim to describe the postcritical scenario in the complete parameter-space. In this study, the primary system (PS) and the added mass (TMD) are assumed to posses a SDOF and to be linear, with the only source of nonlinearities arising from the flow-structure interaction. Using a perturbation method, simple and double Hopf bifurcations, occurring at different values of the parameters, have been analyzed. The effectiveness of TMDs has been shown to persist even in the postcritical range, since TMDs generally reduce the amplitude of oscillations in the supercritical case. However, the analysis developed, was only partial, since it was assumed that (a) a pair of conjugate eigenvalues of the Jacobian matrix is stable (simple Hopf) or (b) the two pairs are both critical but distinct (nonresonant double Hopf). In a second paper (Gattulli, et al. 2003) the same model has been considered and the postcritical behavior of the system analyzed for a Hopf bifurcation in the region of 1:1 resonance. The novel analysis leads to a second-order complex bifurcation equation in the amplitude of the unique critical mode. This has permitted to analyze the entire postcritical scenario in the bifurcation parameter space, evidencing the limits of validity of the concept of equivalent single DOF introduced in Fujino, et al. (1985), Abdel-Rohman (1994). An important conclusion of the past analysis is the following: if the control parameters are selected to maximize the critical wind velocity (optimal TMD), then the limit cycle amplitude for large velocities also reaches a minimum. Therefore the optimal TMD keeps its peculiarities even in the nonlinear range. However, since the control parameters are all determined by the required optimal conditions, no other parameters are available to try to further improve the system postcritical behaviour. With the aim to enhance the performance of the TMD, a suitable nonlinearity sh...

The paper presents the experimental investigation carried out on wall specimens reproducing the ancient masonry of several monumental building located in the old city centre of L' Aquila (Italy) and damaged by the April 2009 earthquake. The wall specimens were prepared in accordance with the traditional technique, using original stone elements and typical poor mortar. Subsequently, the specimens were consolidated with mortar injections. Other specimens were also reinforced with Ultra High Tensile Strength Steel wires applied as coating technique (not wrapped). Shear-compression tests were carried out on the wall specimens to evaluate the effects of the reinforcements both in terms of final stiffness and strength of the specimens. A non-linear Finite Element Model (FEM) was developed to reproduce the experimental tests and to better understand the damage phenomena. The load-displacement curves predicted by the FEM compared quite well with the experimental ones. The failure mode of the specimens was properly captured by the FEM. The effectiveness of the external reinforcement was proved to strictly depend on the coating adhesiveness to the walls surface. The premature debonding of the external reinforcement was demonstrated to cause the fragile post-peak behaviour during both the actual experimental test and the numerical simulations.

The authors investigated the dynamic behaviour of the San Silvestro belfry in L’Aquila (Italy). The 2009 earthquake in L’Aquila caused severe damages to the entire masonry complex. Extensive rehabilitation works, ended in 2019, repaired the structure and enhanced its seismic safety. In this paper, the authors discuss three aspects typical of masonry towers by interpreting the outcomes of Operational Modal Analysis carried out on December 2019: the interactions between the tower and the masonry complex, the dynamic effects of the bell, and the seismic reliability assessment of the tower. Specifically, the experimental mode shapes drive the estimation of an equivalent cross-section, whose principal axes of inertia match with the directions of oscillation of the mode shapes, and the parameters of an equivalent cantilevered beam roughly representative of the tower dynamics. In a second step, a two-degrees-of-freedom analytical model simulates the dynamic coupling between the tower and the more massive bell. The response of the system to a set of seven strong-motion earthquakes yields the assessment of the bell effects over the seismic performance of the masonry tower.