Article Advances in Structural Engineering 2016, Vol. 19(10) 1620–1636 Ó The Author(s) 2016 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1369433216646018 ase.sagepub.com Designing optimal tuned mass dampers using improved harmony search algorithm HA Yazdi 1 , H Saberi 2 , H Saberi 3 and F Hatami 4 Abstract In this article, the optimum parameters of tuned mass dampers for suppressing the dynamic responses of multi degree-of-freedom structures induced by base excitations are proposed. The improved harmony search algorithm, which has been successfully applied in many fields, is used for tuning the tuned mass dampers under seismic loading. The parameters of tuned mass dampers including mass, damping coefficient, spring stiffness, and location are assumed as design variables and two objective functions have been considered. The results of the numerical simulations modeling of two 10-story shear structures show that tuned mass dampers are very effective in the reduction in energy responses of structures under recorded earthquakes. Also, the objective function offered in this article with better uniform distribution in transfer functions is more reliable than those which will be discussed in the following sections. Furthermore, in all earthquakes, the maximum displacement of tuned mass dampers and force exerted by tuned mass dampers on the structure for the offered objective function are considerably less. A discussion on the validity of the model used by Bekdas x and Nigdeli is also presented in detail. The results indicate that for developing reliable preliminary-design criteria, the proposed analysis- based approach presented herein has the potential to provide better calculation of the responses of such structures. Keywords base excitation, improved harmony search, multi degree-of-freedom structure, optimization, structural control, tuned mass damper Introduction In order to reduce the structural responses under dynamic loading, numerous methods have been pro- posed. Tuned mass dampers (TMDs) are considered as the most useful tools in the field of vibration control of flexible structures. TMD is a device consisting of mechanical components such as mass, spring, and a dashpot implemented on the primary structure to reduce the dynamic responses of the structure. The basic form of TMD was proposed by Frahm (1911) for damping the mechanical vibration induced by monotonic harmonic forces. Nguyen et al. (2012) have investigated the application of TMD in an analytical and experimental study conducted on a real floor. This study shows that using distributed multiple viscoelastic TMD system successfully reduced the floor vibrations by at least 40% to a level that was well within the acceptable limit for human comfort in an office envi- ronment. Yang et al. (2015a) proposed an innovative practical approach to optimally design the distributed TMD system. The results clearly showed that the optimal-distributed TMD system can suppress the structural response effectively, provide better vibration suppression performance, and are more robust than that for a single TMD under the close total mass ratio. Based on the aim of using TMD, different methods have been developed for determining the optimum val- ues of TMD parameters. Two optimization criteria that are widely used to select optimum design para- meters of TMD are H2 and HN. The objective of H2 optimization is minimizing the area under the fre- quency response function when the structure is excited by random loading, whereas the objective of HN opti- mization is minimizing the maximum value of the fre- quency response function when the structure is excited 1 Swinburne University of Technology, Melbourne, VIC, Australia 2 Department of Civil & Environmental Engineering, Amirkabir University of Technology, Tehran, Iran 3 Yazd University, Yazd, Iran 4 Structure & Earthquake Research Center (SERC), Amirkabir University of Technology, Tehran, Iran Corresponding author: HAYazdi, Department of Civil and Construction Engineering, Swinburne University of Technology, John St, Hawthorn, Melbourne, VIC 3122, Australia. Email: hyazdi@swin.edu.au