Nonlinear mathematical modeling and optimum design of tuned mass dampers using adaptive dynamic harmony search algorithm

Abstract

A novel adaptive dynamic harmony search (ADHS) algorithm is proposed based on the dynamical parameters that are adjusted using the previous results of the harmony memory with a simple formulation. The accuracy and efficiency of ADHS algorithm are compared with the several improved versions of harmony search through mathematical benchmark examples. The optimum design database of tuned mass damper (TMD) parameters for a damped main system under white-noise base excitation is extracted by the ADHS algorithm for applicable engineering problem. Four mathematical models are calibrated using the nonlinear training approach-based ADHS for approximating the optimum tuning TMD parameters. By considering the root mean square error and confidence index, a best nonlinear model is selected among the proposed models using ADHS training scheme and several existing empirical models. A 10-story benchmark structural example under earthquake excitation is considered for validation of the proposed nonlinear model. The simulation results demonstrate that the ADHS provides more accurate and efficient results than the improved harmony search algorithms for mathematical benchmark examples. The proposed nonlinear model also performs with the efficient computational burdens compared with the optimization algorithms for optimum tuning of TMD parameters of a 10-story structure, more accurately. KEYWORDSadaptive dynamic harmony search algorithm, mathematical models, optimum tuning, seismic applications, tuned mass damper | INTRODUCTIONTuned mass dampers (TMDs) are widely used to suppress or absorb vibration of mechanical and structural systems. A typical TMD system consists of a mass, spring, and dashpot, which installed on mechanical and structural main systems. Tuning the TMD parameters has a key role in its performance in reducing the vibration amplitudes of the main system. Considering the elastic structures equipped with TMD, the possibility and accuracy in assuming multidegree-of-freedom main system as a single-degree-of-freedom (SDOF) system are confirmed in Warburton and Ayorinde [1] and Ayorinde and Warburton. [2] Several closed-form expressions have been introduced to tune the TMD parameters for damped SDOF main system. [3][4][5][6] Chang [7] proposed formulas for designing TMDs subjected /journal/stc 1 of 20 to both wind and earthquake loadings. An analytical approach was used by Asami et al. [8] to derive formulas for tuning TMD subjected to several loadings. Bakre and Jangid [9] applied a numerical search technique for optimum tuning of TMD in base-excited undamped and damped main systems. On the basis of the "fixed-point" theory of Den Hartog for undamped main system, Ghosh and Basu [10] proposed a closed-form optimal tuning criterion for the damped main system. A wide-range numerical tuning procedure on the basis of particle swarm optimization method was carried by Leung and Zhang [11] to suggest new explicit expressions for optimum estimation of TMD parameters. Salvi and Rizzi [12] used a tuning method on the basis of minimax ...

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