SHORT COMMUNICATION A method for tuning tuned mass dampers for seismic applications Julio C. Miranda* ,† CH2M HILL, 1737 N. First Street, Suite 300, San Jose CA 95112, USA ABSTRACT This paper studies tuned mass dampers (TMDs) resulting in high modal damping for mechanical systems incorporating such devices for the purpose of seismic response reduction. Focusing on the determination of damping and tuning, the proposed methodology identifies a point of multiplicity of complex eigenvalues and eigenvectors, resulting in different parameters for TMDs according to their location with respect to such multiplicity condition. It is shown that significant equal modal damping and average modal damping can be induced by properly tuning highly damped TMDs, obtaining parameters intrinsic to the mechanical systems, and excitation independent. Further, it is shown that the methodology yields, as particular cases, two proposals by others using TMDs for the same purpose of seismic response abatement. Copyright © 2012 John Wiley & Sons, Ltd. Received 14 May 2012; Revised 20 September 2012; Accepted 18 October 2012 KEY WORDS: passive control; energy dissipation; seismic design; tuned mass dampers; building technology 1. INTRODUCTION It is currently accepted that properly implemented tuned mass dampers (TMDs) are effective in controlling seismic response. Such action employs induced damping, as for conventional structures, damping increases within certain bounds, resulting in decreased seismic response. Hence, focusing on the generation of high damping through proper tuning, this paper examines highly damped TMDs, deriving their efficiency from the equality of damping coefficients for two real or complex modes. The initial research along this direction was performed by Villaverde [1], who proposed to use small roof- mounted, highly damped resonant masses to induce two complex modes with damping ratios approximately equal to the average of the damping of the TMD and the building’s resonant mode. Subsequently, Sadek et al. [2] suggested inducing two complex modes with equal frequencies and damping ratios. Miranda [3] presented a numerical study of TMDs considering the equality of damping ratios for two real modes, identifying parameters that coincided with the results by Sadek et al. [2]. Hoang et al. [4] numerically optimized a TMD for the protection of a large bridge in Japan, minimizing its mean square displacement response to an earthquake characterized by a Kanai–Tajima type of power spectra density. Recently, Moutinho [5] proposed TMDs with equal modal damping ratios, with an optimum damping that would minimize the system’s amplification factor. The procedure proposed in this paper yields parameters at any desired TMD damping coefficient, and not only at a specific damping and tuning (usually denominated as the ‘optimum’ values). The methodology used makes a comparative analysis of the characteristic equations of the system expressed in both structural and modal forms. It is shown that there are specific frequency and *Correspondence to: Julio C. Miranda, CH2M HILL, 1737 N. First Street, Suite 300, San Jose CA 95112, USA. † E-mail: julio.miranda@ch2m.com Copyright © 2012 John Wiley & Sons, Ltd. EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. (2012) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/eqe.2271