Optimal design and performance evaluation of systems with Tuned Mass Damper Inerter (TMDI)

The paper concerns the optimal design and performance evaluation of a Tuned Mass Damper Inerter (TMDI) to reduce dynamic vibrations. The system exploits properties of the inerter, a two‐terminal mechanical device able to produce a force proportional to the relative acceleration between terminals, with the ability of generating an apparent mass even two orders of magnitude greater than its own physical mass. A primary single‐degree‐of‐freedom structure is equipped with a classical linear Tuned Mass Damper (TMD), the secondary structure, whose mass is connected to the ground via an inerter. The optimal design of the TMDI is conducted by assuming a white noise process as base input and utilizing three different design methodologies: displacement minimization, acceleration minimization and maximization of the ratio between the energy dissipated in the secondary system and the total input energy. Optimal results obtained with the different methodologies are carried out and compared. Two limit cases are also considered when the inerter is not contemplated: conventional and non‐conventional TMDs, characterized by a low and a large mass ratio, respectively. The TMDI performance is evaluated and compared with conventional and non‐conventional TMDs; moreover, its robustness is assessed with a sensitivity analysis varying the design parameters. Attention is focused not exclusively on the primary structure response but also on the secondary one. Finally, the effectiveness of the optimally designed TMDI is evaluated having considered earthquake base excitation. Results demonstrate the effectiveness of TMDI systems for dynamic response reduction with superior performances and robustness than classical TMDs. Copyright © 2017 John Wiley & Sons, Ltd.     

Dynamic response and optimal design of structures with large mass ratio TMD

This paper investigates the dynamic behavior and the seismic effectiveness of a non‐conventional Tuned Mass Damper (TMD) with large mass ratio. Compared with conventional TMD, the device mass is increased up to be comparable with the mass of the structure to be protected, aiming at a better control performance. In order to avoid the introduction of an excessive additional weight, masses already present on the structure are converted into tuned masses, retaining structural or architectural functions beyond the mere control function. A reduced order model is introduced for design purposes and the optimal design of a large mass ratio TMD for seismic applications is then formulated. The design method is specifically developed to implement High‐Damping Rubber Bearings (HDRB) to connect the device mass to the main structure, taking advantage of combining stiffness and noticeable damping characteristics. Ground acceleration is modeled as a Gaussian random process with white noise power spectral density. A numerical searching technique is used to obtain the optimal design parameter, the frequency ratio alpha, which minimizes the root‐mean‐square displacement response of the main structure. The study finally comprises shaking table tests on a 1:5 scale model under a wide selection of accelerograms, both artificial and natural, to assess the seismic effectiveness of the proposed large mass ratio TMD. Copyright © 2011 John Wiley & Sons, Ltd.     

Protection of seismic structures using semi‐active friction TMD

Although the design and applications of linear tuned mass damper (TMD) systems are well developed, nonlinear TMD systems are still in the developing stage. Energy dissipation via friction mechanisms is an effective means for mitigating the vibration of seismic structures. A friction‐type TMD, i.e. a nonlinear TMD, has the advantages of energy dissipation via a friction mechanism without requiring additional damping devices. However, a passive‐friction TMD (PF‐TMD) has such disadvantages as a fixed and pre‐determined slip load and may lose its tuning and energy dissipation abilities when it is in the stick state. A novel semi‐active‐friction TMD (SAF‐TMD) is used to overcome these disadvantages. The proposed SAF‐TMD has the following features. (1) The frictional force of the SAF‐TMD can be regulated in accordance with system responses. (2) The frictional force can be amplified via a braking mechanism. (3) A large TMD stroke can be utilized to enhance control performance. A non‐sticking friction control law, which can keep the SAF‐TMD activated throughout an earthquake with an arbitrary intensity, was applied. The performance of the PF‐TMD and SAF‐TMD systems in protecting seismic structures was investigated numerically. The results demonstrate that the SAF‐TMD performs better than the PF‐TMD and can prevent a residual stroke that may occur in a PF‐TMD system. Copyright © 2009 John Wiley & Sons, Ltd.     

Optimal design and seismic performance of tuned mass damper inerter (TMDI) for structures with nonlinear base isolation systems

The tuned mass damper inerter (TMDI) couples the classical tuned mass damper (TMD) with an inerter, a mechanical device whose generated force is proportional to the relative acceleration between its terminals, thus providing beneficial mass‐amplification effects. This paper deals with a dynamic layout in which the TMDI is installed below the isolation floor of base‐isolated structures in order to enhance the earthquake resilience and reduce the displacement demand. Unlike most of the literature studies that assumed a linearized behavior of the isolators, the aim of this paper is to investigate the effectiveness of the TMDI while accounting for the nonlinearity of the isolators. Two nonlinear constitutive behaviors are considered, a Coulomb friction model and a Bouc‐Wen hysteretic model, representative of friction pendulum and of lead‐rubber‐bearing isolators, respectively. Optimal design is based on the stochastic dynamic analysis of the system, by modeling the base acceleration as a Kanai‐Tajimi filtered stationary random process and resorting to the stochastic linearization technique to handle the nonlinear terms. Different tuning criteria based on displacement, acceleration, and energy‐based performance indices are defined, and their implications in a design process are discussed. It is proven that the improved robustness of the TMDI reduces its performance sensitivity to the tuning frequency and to the earthquake frequency content, which are well‐known shortcomings of TMD‐like systems. This important feature makes the TMDI particularly suitable for nonlinear base‐isolated structures that are affected by unavoidable uncertainties in the isolators' properties and that may experience changes of isolators effective stiffness depending on the excitation level.