Vibration reduction by using two tuned mass dampers with dry friction damping

Vibration reduction of a single-degree-of-freedom system connected to two tuned mass dampers (TMDs) equipped with dry friction dampers is considered in this work. The system is subjected to sinusoidal base excitation. Parameters of TMDs are optimized to minimize the peak values of the response of the primary system. Harmonic balance method (HBM) is used to obtain the steady state solution of the three-degrees-of-freedom nonlinear system in frequency domain. Newton’s method with arc length continuation is utilized to solve the resulting nonlinear algebraic equation set. In addition to that, optimum linear system and other nonlinear elements are investigated. Genetic algorithm is used to optimize parameters of TMDs