PSI - Issue 64

Amir Shamsaddinlou et al. / Procedia Structural Integrity 64 (2024) 360–367 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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mass, spring, and damper elements, which Lee et al. (2006) investigated comprehensively. Initially conceptualized by Den Hartog (1985), TMDs are designed to attenuate structural responses to external forces, preventing damage and enhancing overall performance. Different studies have investigated considerable strategies, including the use of evolutionary methods and different configurations, to optimize TMD parameters and enhance the performance of controlled structures by De Domenico et al. (2020), Bekdaş and Nigdeli (2011) , De Domenico et al. (2018), Shamsaddinlou et al. (2023), Fahimi Farzam and Kaveh (2020), Raeesi et al. (2020), Marrazzo et al. (2024). The development of optimization approaches, with improved computer science, particularly metaheuristic algorithms, has significantly impacted the design of engineering problems. Metaheuristic algorithms are optimization strategies that draw inspiration from natural phenomena and principles. Robust Algorithms inspired by their behaviors in nature are the genetic algorithm (GA) by Holland (1992) and particle swarm optimization (PSO) by Kennedy and Eberhart (1995). Also, in the animal realm, there are different metaheuristic algorithms such as Ant Colony Optimization (ACO) by Dorigo et al. (2006), Grey Wolf Optimization (GWO) by Mirjalili et al. (2014), and Grasshopper Optimization algorithm (GOA) by Saremi et al. (2017). Moreover, in the mathematical concepts, the Sine Cosine Algorithm (SCA) by Mirjalili (2016) and Chaos Game Optimization (CGO) by Talatahari and Azizi (2021) are popular. Furthermore, inspired by the laws of physics, Harmony Search (HS) by Geem et al. (2001) and charged system search (CSS) by Kaveh and Talatahari (2010) are well-known ones for identifying optimal solutions aiming to discover the global optimum in problem-solving scenarios. The optimum design of TMD has been considered from different aspects. In some studies, the TMD optimization problem has been solved based on objective functions of seismic responses. Some researchers have designed these dampers based on the response transfer function. This problem has also been considered in the frequency domain. However, in previous studies, the problem of TMD design has not been considered in the pole placement scheme. Therefore, the essence of this study is based on optimizing TMD parameters using metaheuristic algorithms, mainly concentrating on the pole placement scheme to improve system stability and performance. By comparing three different cost functions — relative controlled drift response, the transfer function (TF) of acceleration response, and the pole placement scheme — the present work aims to show the most effective strategy for parameter optimization, thereby advancing the practical application and theoretical knowledge of TMDs in attenuating induced forces. 2. Dynamic Analysis of Structures Equipped with TMD The equation of motion for an N-degree of freedom structural model with a shear frame system equipped with a tuned mass damper installed at the top floor Cheng et al. (2008) can be written as: ̈ + ̇ + = ( ) (1) where M , C , and K are mass, stiffness, and damping matrices with the formulations as follows: = [ 1 2 ⋱ ] (2) = [ 1 + 2 − 2 − 2 2 + 3 − 3 − 3 . . . . + ] (3) = [ 1 + 2 − 2 − 2 2 + 3 − 3 − 3 . . . . + ] (4) ( ) = [ 1 2 … ] (5) where , and are the mass, stiffness, and damping of the i -th floor ( i =1, 2, …, N) respectively; and , and are the tuned mass damper's mass, stiffness, and damping, respectively. Also, represent the lateral displacement of i -th floor. The state-space equation can solve the equation of motion as: