Optimization of multiple tuned mass dampers for vibration control of system under external excitation

Abstract

Using a numerical searching technique the optimum parameters of multiple tuned mass dampers (MTMD) for suppressing the dynamic response of a damped main system subjected to external excitation are investigated. The criteria selected for the optimality is the minimization of the steady-state displacement of the main system under external harmonic excitation. The parameters of the MTMD that are optimized include: the damping ratio, the tuning frequency ratio and the frequency band-width. The optimum parameters of the MTMD system and corresponding steady-state displacement are obtained for different damping ratios of the main system and the mass ratios of the MTMD system. The explicit formulae for the optimum parameters of MTMD (i.e. damping ratio, band-width and tuning frequency) are then derived using a curve-fitting scheme that can readily be used for engineering applications. The error in the proposed explicit expressions is investigated and found to be quite negligible. The effectiveness of optimally designed MTMD system is also compared with that of the optimum single tuned mass damper and it is observed that the optimally designed MTMD system is found to be more effective for vibration control than the single tuned mass damper. Further, the damping in the main system significantly influences the optimum parameters and the effectiveness of the MTMD system. Finally, a sensitivity analysis of optimally designed MTMD system to study its performance under uncertainty in the parameter is also carried out.