MINIMIZING HANKEL’S NORM AS DESIGN CRITERION OF MULTIPLE TUNED MASS DAMPERS

Tuned mass damper (TMD) have been studied and installed in structures extensively to protect the structures against lateral loads. Multiple tuned mass dampers (MTMDs) which include a number of TMDs with different parameters have been proposed for improving the performance of single TMDs. When the structural system is considered as multiple degrees of freedom (MDOF) and implemented with MTMDs, there is no effective closed-form solution to determine the optimal parameters of MTMDs. On the other hand designing optimal MTMDs include a large number of variables. For optimal design of MTMDs, in this research an effective method has been proposed in which the parameters of TMDs are determined based on minimizing the Hankel’s norm of structure. Since the optimization procedure includes a large number of variables, hence it has been decided to use Genetic Algorithms (GAs) for determining the variables. For numerical simulation, the method has been utilized on an eight-storey shear frame modeled as MDOF, and optimal MTMDs have been designed. The results show that using the Hankel’s norm of structure as objective function has led to design effective MTMDs which could be effective in reducing the response of structure, especially the average value, under different far-field and near-field earthquakes. Also it has been found that the method is effective regarding its simplicity and convergence in solving complex optimization problem. Through extensive numerical analysis the effect of MTMDs mass ratio and TMDs number in MTMDs has been studied.

Keywords:

passive control , tuned mass damper , multiple tuned mass damper , hankel’s norm , optimization