New formulas for optimal design of TMD using genetic programming method and their application to control of seismic-excited structures

The purpose of this paper is to propose new formulas for optimal tuning of tuned mass damper (TMD) parameters using the genetic programming (GP) method with the aim of its application in seismic-excited structures. For this purpose, the optimal TMD parameters in the main structure under white-noise base acceleration are determined using the teaching-learning-based optimization (TLBO) algorithm for a wide range of TMD mass ratios and structural damping ratios. The outcome database is then applied to derive formulas based on the GP technique. The proposed formulas have high accuracy and efficiency while eliminating computational costs. Considering two 10-story and 40-story structures, the efficiency of the proposed formulas is then evaluated for seismic control applications of structures. For this purpose, their results are compared with those given by the TLBO algorithm. The numerical studies show that the optimal tuning of TMD parameters using the proposed formulas, while eliminating the computational cost due to the use of meta-heuristic optimization algorithms, provides better performance in reducing the floor displacement and absolute acceleration of the studied structures. Consequently, they can be efficient for seismic control applications of structures by presenting a simple and fast optimal tuning. The TMD tuned using the TLBO results in a reduction of 18.03%, 6.72% in the maximum displacement and acceleration of the 10-story structure, while the TMD adjusted using the proposed formulas gives a reduction of 18.47% and 11.23% in the above-mentioned responses. The results given for the 40-story structure show a reduction of 9.46% and 0.98% for the TMD tuned by the TLBO, while it is found a reduction of 11.58% and 5.1%% in the maximum displacement and acceleration for the TMD tuned by the suggested formulas.