Vibration analysis of the civic tower in Rieti

In the last decades the definition of a suitable monitoring system for identifying the dynamic behavior of structures has had a central position in the civil engineering research area. The vibration analysis leads to the recognition of the reference state of structures which is essential to determine the integrity level when extreme events occur, such as earthquakes. The latest seismic events occurred in the world have shown the essential role of the new passive seismic techniques which aim to protect structures and the importance of supervising the building construction operations and the adopted improvement measures. In this work the structural monitoring of the civic tower located in Rieti is presented. In the tower a non-conventional TMD has been installed via an inter-story isolation system at the top floor by means of High Damping Rubber Bearings (HDRB). The general goal is to define a monitoring system suitable with this experimental case through the vibration analysis. Several aspects will be taken into account: the choice of sensors setup, the measured quantities and the extraction of structural information. Firstly this will allow to define the structure’s reference state featured by frequencies, damping ratios and mode shapes. Moreover the effective design of the monitoring system would lead to the characterization of the dynamic behavior of the structure equipped with a passive vibration control system. Different tests have been carried forward: ambient vibration test (AVT), forced vibration test (FVT) with vibrodyne and seismic test (ST). The AVT and the FVT enable to define the monitoring system and check the reliability of the adopted identification tools, among which an Output Only algorithm stands out: the Observer Kalman Filter System Id. On the other hand the ST will point out some preliminary information about the dynamic behaviour of the structure equipped with a non conventional Tuned Mass Damper referring it to higher levels of vibrations

Optimal tuning and assessment of inertial dampers with grounded inerter for vibration control of seismically excited base-isolated systems

In this paper, the concept of an ideal grounded linear inerter, endowing supplemental inertia to passive linear tuned mass-dampers (TMDs) through its inertance property without increasing the TMD mass, is considered to reduce lateral displacement demands in base isolated structural systems (BISs). Optimal tuned mass-damper-inerter (TMDI) design parameters are numerically determined to maximize energy dissipation by the TMDI under stationary white noise support excitation. Performance of these optimally designed TMDI-equipped BISs is assessed for stationary white and colored noise excitations as well as for four recorded earthquake acceleration ground motions (GMs) with different non-stationary frequency content. It is found that for fixed mass ratio the inclusion of the grounded inerter reduces significantly secondary mass displacement and stroke for all considered excitations while it improves appreciably BIS displacement demands except for the particular case of a near-fault accelerogram characterized by early arrival of a high-energy low-frequency pulse as captured in its wavelet spectrogram. More importantly, it leads further to reductions to BIS acceleration demands with the exception of colored noise excitation for which an insignificant increase is noted. The positive effects of the inerter saturate with increasing inertance and BIS damping ratio demonstrating that small inertance values are more effective in vibration suppression of BISs with low inherent damping. Overall, it is recommended to combine low damping isolation layers with large inertance and low secondary mass TMDIs

Experimental seismic performance assessment and numerical modelling of nonlinear inerter vibration absorber (IVA)-equipped base isolated structures tested on shaking table

In recent years, inerter vibration absorbers (IVAs), such as the tuned mass damper inerter (TMDI), attracted much attention in the literature for reducing seismic displacement demands of base isolated structures (BISs). Several theoretical studies reported reduced BIS seismic demands with increasing inertance endowed by a grounded inerter element but adopted mostly idealized linear dynamical models. Herein, the potential of TMDI-configured IVAs for seismic response reduction of BISs modelled as single-mass structures is assessed under the combined effects of nonlinear inerter and structural behaviour. To this aim, experimental data from a shaking table testing campaign are considered utilizing a custom-built flywheel rack-and-pinion grounded inerter prototype with variable inertance along with high damping rubber bearings in the isolation layer and in the BIS-to-absorber link. White noise excitation and an ensemble of six ground motions (GMs) with different frequency content are used in the tests for which bearings exhibit softening nonlinear behaviour. Experimental results demonstrate improvement of BIS nonlinear seismic response in terms of displacement and base shear with increasing inertance for nonlinear and non-optimally designed TMDIs. It is found though that non-optimally tuned IVAs may be detrimental to BIS acceleration response depending on the GMs time-varying frequency content signatures as captured by the continuous wavelet transform spectrogram. Lastly, it is concluded that representing the inerter device by a simplified linear dissipative model as opposed to a nonlinear model with friction and gear backlash suffices to trace the BIS response with acceptable accuracy and, thus, can be used for optimal seismic TMDI design

Shake table testing of a tuned mass damper inerter (Tmdi)-equipped structure and nonlinear dynamic modeling under harmonic excitations

This paper presents preliminary experimental results from a novel shaking table testing campaign investigating the dynamic response of a two-degree-of-freedom (2DOF) physical specimen with a grounded inerter under harmonic base excitation and contributes a nonlinear dynamic model capturing the behavior of the test specimen. The latter consists of a primary mass connected to the ground through a high damping rubber isolator (HDRI) and a secondary mass connected to the primary mass through a second HDRI. Further, a flywheel-based rack-and-pinion inerter prototype device is used to connect the secondary mass to the ground. The resulting specimen resembles the tuned mass damper inerter (TMDI) configuration with grounded inerter analytically defined and numerically assessed by the authors in a number of previous publications. Physical specimens with three different inerter coefficients are tested on the shake table under sine-sweep excitation with three different amplitudes. Experimental frequency response functions (FRFs) are derived manifesting a softening nonlinear behavior of the specimens and enhanced vibration suppression with increased inerter coefficient. Further, a 2DOF parametric nonlinear model of the specimen is established accounting for non-ideal inerter device behavior and its potential to characterize experimental response time-histories, FRFs, and force-displacement relationships of the HDRIs and of the inerter is verified

Experimental study and numerical modeling of nonlinear dynamic response of SDOF system equipped with tuned mass damper inerter (TMDI) tested on shaking table under harmonic excitation

This paper considers a novel shaking table testing campaign to assess the tuned mass-damper-inerter (TMDI) vibrations suppression attributes in harmonically excited structures under the combined effect of nonlinear structural response and nonlinear inerter device behavior deviating from the ideal linear inerter element developing acceleration-dependent force proportional to the inertance constant. Physical specimens of TMDI-equipped single-degree-of-freedom (SDOF) structure are considered featuring a custom-built rack-and-pinion flywheel inerter device with nonlinear behavior due to friction and backlash effects to connect the TMDI secondary mass to the ground. Damping and elastic properties are endowed to the SDOF structure and to the TMDI via high damping rubber bearings (HDRBs) exhibiting softening nonlinear elastic behaviour. Comprehensive experimental data in time and frequency domains are presented for 9 specimens with different sets of secondary mass and inertance subject to sine-sweep excitations for three different amplitudes. The data demonstrate that the main practical advantage of the TMDI established in the literature for linear structures and ideal inerter elements (i.e., improved vibration suppression through increasing inertance without increasing secondary mass leading to lightweight vibration absorbers) is maintained for nonlinear structures and inerter devices. Moreover, a comparison of experimental data with data derived from two different nonlinear parametric numerical models capturing faithfully the HDRBs response, one using a nonlinear mechanical model to represent the inerter device and the other using an ideal linear inerter element instead, demonstrate that displacement, acceleration and base shear response of the SDOF structure is insignificantly influenced by the nonlinear attributes of the inerter device. This outcome paves the way for developing simplified, thus practically meritorious, optimal TMDI tuning approaches adopting the ideal inerter element assumption to model physical inerter devices

Defective two adjacent single degree of freedom systems linked by spring-dashpot-inerter for vibration control

The paper deals with the analytical formulation of two adjacent single degree of freedom systems coupled by spring-dashpot-inerter elements adequately tuned in order to build a defective system. From modal analysis analytical expressions of eigenvalues, damping factor and connection parameters in order to build defective systems are given. It is demonstrated that is always possible to realize a defective system when a connection with spring-dashpot-inerter elements is utilized, irrespectively of the assumed structural parameters. Given a couple of oscillators, it is possible to build infinite defective systems by conveniently varying one parameter of the connection, chosen as independent variable. Among the feasible choices of parameters, a design criterion for the connection is proposed maximizing the modal damping factor and closed-form expressions of the design parameters are carried out. Maps of the natural frequency, damping factor and the damped frequency of the defective system with maximum modal damping factor are furnished. A procedure to obtain the eigenvectors forming a complete base to compute the system response analytically is given. For these systems, the response to free vibration with initial conditions and to base harmonic motion is investigated. The main characteristics of the response are discussed and considerations about the dynamics and effectiveness of the connection for control purposes are outlined

Optimal design of the ideal grounded tuned mass damper inerter for comfort performances improvement in footbridges with practical implementation considerations

The paper focuses on the optimal design of the grounded tuned mass damper inerter (TMDI) in footbridges and on some practical implementation issues. An optimal design procedure is implemented for the perfectly grounded ideal TMDI (infinite stiffness of the connection at the ground plus linear and nondissipative inerter). The procedure is based on reduced-order models of the footbridge by assuming the frequency ratio and damping factor as design parameters, for a given number of values of the TMDI the inertance and mass ratios aiming at minimizing the maximum acceleration response of the system for users' comfort improvement under performance criteria defined in Human-induced Vibration of Steel Structures (HiVoSS) guidelines. The procedure is applied to an existing footbridge suffering excessive human-induced vibrations. After the optimal design of the TMDI has been found, its performances are assessed by the avail of a fully 3D finite element model of the case-study footbridge, which has been calibrated toward an in situ experimental identification campaign. Alternative proposals for practical implementation of the control system are analyzed. Finally, a performance sensitivity analysis is carried out regarding the deviations from the initial assumption of perfectly grounded TMDI system, by varying the stiffness of the connection at the ground of the ideal inerter. Results show that the proposed procedure makes the TMDI a very efficient control system for footbridges and that changes of the stiffness of the grounded connection drop the beneficial effect of the TMDI, also if consequences of such errors are less than the ones occurring in classical TMDs for detuning or malfunctioning

On the optimal design and placement of Tuned-Mass-Damper-Inerter for Multi-Degree-Of-Freedom structures

Even if Tuned-Mass-Damper-Inerter (TMDI) design for Multi-Degree-Of-Freedom (MDOF) structures is a topic largely addressed in the current literature, some aspects still deserving insight emerge from a literature review. The state of the art presented in the paper highlights that Inerter-Vibration-Absorber (IVA) design is typically conducted based on simplified models (e.g. generalized 2-Degree-Of-Freedom (2-DOF) models) or sophisticated ones but a comparison between the two approaches is rarely made. Moreover, the device placement along the structure is not often addressed in the design formulation; nevertheless, a proper location greatly influences the absorber performance and its physical dimensions. The paper aims to be a comprehensive study that investigates in a unique formulation the optimal design together with the optimal placement of a TMDI in a MDOF structure and aims to make a comparison between the use of a 2-DOF model and a complete MDOF model for its optimal design and placement. The overall design methodology and performance evaluation is formulated considering a stationary white noise input. An exemplificative literature case study of a 10-DOF structure is utilized to apply the design procedure, evaluate the performance and make the comparisons. It is demonstrated that a reduced order model is useful for a first estimate of the TMDI design parameters but some, especially the damping coefficient, need improvement adopting more refined models. Structural performance is well cached with reduced order models, especially for those quantities that mainly depend on the first natural mode. An optimal placement, tradeoff between structural performances and absorber physical dimensions, is proposed. TMDI effectiveness is assessed also considering non-stationary input with natural earthquakes and comparisons with conventional and non-conventional Tuned-Mass-Damper (TMD) are conducted

Experimental study and numerical modeling of nonlinear dynamic response of SDOF system equipped with tuned mass damper inerter (TMDI) tested on shaking table under harmonic excitation

This paper considers a novel shaking table testing campaign to assess the tuned mass-damper-inerter (TMDI) vibrations suppression attributes in harmonically excited structures under the combined effect of nonlinear structural response and nonlinear inerter device behavior deviating from the ideal linear inerter element developing acceleration-dependent force proportional to the inertance constant. Physical specimens of TMDI-equipped single-degree-of-freedom (SDOF) structure are considered featuring a custom-built rack-and-pinion flywheel inerter device with nonlinear behavior due to friction and backlash effects to connect the TMDI secondary mass to the ground. Damping and elastic properties are endowed to the SDOF structure and to the TMDI via high damping rubber bearings (HDRBs) exhibiting softening nonlinear elastic behaviour. Comprehensive experimental data in time and frequency domains are presented for 9 specimens with different sets of secondary mass and inertance subject to sine-sweep excitations for three different amplitudes. The data demonstrate that the main practical advantage of the TMDI established in the literature for linear structures and ideal inerter elements (i.e., improved vibration suppression through increasing inertance without increasing secondary mass leading to lightweight vibration absorbers) is maintained for nonlinear structures and inerter devices. Moreover, a comparison of experimental data with data derived from two different nonlinear parametric numerical models capturing faithfully the HDRBs response, one using a nonlinear mechanical model to represent the inerter device and the other using an ideal linear inerter element instead, demonstrate that displacement, acceleration and base shear response of the SDOF structure is insignificantly influenced by the nonlinear attributes of the inerter device. This outcome paves the way for developing simplified, thus practically meritorious, optimal TMDI tuning approaches adopting the ideal inerter element assumption to model physical inerter devices

A generalized 2-DOF model for optimal design of MDOF structures controlled by Tuned Mass Damper Inerter (TMDI)

The paper illustrates a methodology to perform the optimal design of a Tuned Mass Damper Inerter (TMDI) equipped on a multi degree of freedom (MDOF) structure through a generalized model. The TMDI is considered in both configurations grounded and ungrounded. A generalized 2-DOF model is obtained: the primary oscillator, representing the original MDOF structure and the secondary oscillator, representing the control system. A Gaussian zero mean white noise random process is adopted for the excitation. The TMDI design is carried out adopting an energy objective function, maximized over the space of the design parameters which are: the mass and inertance ratios, the frequency ratio, the damping factor and a parameter that accounts for the TMDI location on the MDOF structure. Synthetic performance-based design maps of the TMDI parameters are carried out. It is shown that is possible to have different design configurations to achieve a target performance level. The maps furnish, as limit cases, the design of a Tuned Inerter Damper (TID) and a Tuned Mass Damper (TMD), when the mass or the inertance ratios are respectively assumed null. It is shown straightforwardly the regions of the design parameters where the inerter enhances the performances achievable by classical TMD. Furthermore, an analytical expression which links the optimal design variables necessary to obtain a desired target performance is proposed. Frequency response functions and modal parameters of certain 2-DOF models with optimally designed control system are reported and considerations on how the design parameters influence the system dynamics and the damping capabilities are highlighted. Comparisons of the TMDI optimally designed with cases of no control and same mass TMD are evidenced throughout the paper. Finally, the main responses of the primary structure and the TMDI are estimated in the space of variation of the design parameters in order to assess the effectiveness of the control system