Optimal design of a novel tuned mass-damper–inerter (TMDI) passive vibration control configuration for stochastically support-excited structural systems

This paper proposes a novel passive vibration control configuration, namely the tuned mass-damper–inerter (TMDI), introduced as a generalization of the classical tuned mass-damper (TMD), to suppress the oscillatory motion of stochastically support excited mechanical cascaded (chain-like) systems. The TMDI takes advantage of the “mass amplification effect” of the inerter, a two-terminal flywheel device developing resisting forces proportional to the relative acceleration of its terminals, to achieve enhanced performance compared to the classical TMD. Specifically, it is analytically shown that optimally designed TMDI outperforms the classical TMD in minimizing the displacement variance of undamped single-degree-of-freedom (SDOF) white-noise excited primary structures. For this particular case, optimal TMDI parameters are derived in closed-form as functions of the TMD mass and the inerter constant. Furthermore, pertinent numerical data are furnished, derived by means of a numerical optimization procedure, for a 3-DOF classically damped primary structure base excited by stationary colored noise, which exemplify the effectiveness of the TMDI over the classical TMD to suppress the fundamental mode of vibration for MDOF structures. It is concluded that the incorporation of the inerter in the proposed TMDI configuration can either replace part of the TMD vibrating mass to achieve lightweight passive vibration control solutions, or improve the performance of the classical TMD for a given TMD mass.