Toward Optimizing Dynamic Characteristics of Non-conventional TMDs in Multi-degree-of-Freedom Systems
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RESEARCH PAPER
Toward Optimizing Dynamic Characteristics of Non‑conventional TMDs in Multi‑degree‑of‑Freedom Systems Mahmood Yahyai1 · Leila Zebarjad1 · Monique Head2 · Mehdi Shokouhian3 Received: 12 June 2019 / Accepted: 27 December 2019 © Shiraz University 2020
Abstract This study proposes a new method toward optimizing the design of non-conventional tuned mass dampers in multi-degreeof-freedom systems. An important application of the proposed method is in mega-sub-controlled structures in which the seismic vibration of the system is controlled by using isolated sub-structures. The method estimates the optimum parameters of the sub-structures including frequency ratio and damping ratio based on formulations derived for optimal design of SDOF systems with tuned mass dampers. The method is verified by comparing the results with a numerical method. It is shown that the proposed method returns the optimum parameters with acceptable accuracy (less than 5% difference from numerical results), and in some cases the results are identical to the numerical method. In the final part, the method is applied to three mega-structures with different control systems in order to examine its accuracy in predicting the optimum parameters of the non-conventional tuned mass dampers. It is concluded that the method is efficient and can be used for optimal design of such systems. Keywords Non-conventional TMDs · Mega-sub-control structure · Optimum properties · Frequency · Damping
1 Introduction The paper proposes a new method to optimal design of nonconventional tuned mass dampers (TMDs) in multi-degreeof-freedom (MDOF) systems. The manner in which tuned mass dampers (TMD) function is based on an old concept, dating back to 1909, when it was first studied by Frahm (1911). The parameters of TMD, i.e., the frequency ratio and the damping ratio must be tuned optimally to obtain the best * Leila Zebarjad [email protected] Mahmood Yahyai [email protected] Monique Head [email protected] Mehdi Shokouhian [email protected] 1
Civil Engineering Department, Khaje Nasir Toosi University of Technology, P.O. Box 15875‑4416, Tehran 19697, Iran
2
Department of Civil Engineering, University of Delaware, Newark, USA
3
Civil and Environmental Department, Morgan State University, Baltimore, USA
performance. Hartog (1956) developed closed form relationships to predict the optimum parameters for undamped single-degree-of-freedom (SDOF) systems under harmonic loading excitations. Similarly, Warburton (1982) developed expressions to estimate the parameters under harmonic and white noise excitations. Vakakis and Paipetis (1986) used SDOF TMDs to suppress the vibration of the first mode of a MDOF structure. With a certain amount of damping in the main system, it is not possible to derive optimum design formulas. Therefore, the optimum parameters of a TMD are found by using numerical trials (Rana and Soong 1998) or using metaheuristic algorithms such as genetic algorithm, particle swarm optimization, and harmony search method (Bekdaş an
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