Optimal Pendulum Tuned Mass Damper Design Applied to High Towers Using Genetic Algorithms: Two-DOF Modeling

High and slender towers may experience excessive vibrations caused by both wind and seismic loads. To avoid excessive vibrations in towers, tuned mass dampers (TMDs) are often used as passive control devices due to their low cost. The TMDs can absorb part of the energy of vibration transmitted from the main structure. These devices need to be finely tuned in order to work as efficient dampers; otherwise, they can adversely amplify structural vibrations. This paper presents the optimal parameters of a pendulum TMD (PTMD) to control the vibrations of slender towers subjected to an external random force. The tower is modeled as a single-degree-of-freedom (SDOF) mass-spring system via an assumed-mode procedure with a pendulum attached. A genetic algorithm (GA) toolbox developed by the authors is used to find the optimal parameters of the PTMD, such as the support flexural stiffness/damping, the mass ratio and the pendulum length. The chosen fitness function searches for a minimization of the maximum frequency peaks. The results are compared with a sensibility map that contains the information of the maximum amplitude as a function of the pendulum length and the mass ratio between the pendulum and the tower. The optimal parameters can be expressed as a power-law function of the supporting flexural stiffness. In addition, a parametric analysis and a time-history verification are performed for several combinations of mass ratio and pendulum length.