Enhanced motion control performance of the tuned mass damper inerter through primary structure shaping

Abstract

The tuned mass-damper-inerter (TMDI) is a linear passive dynamic vibration absorber widely considered in the literature to mitigate the motion of dynamically excited primary structures. Previous studies focused on optimal TMDI tuning approaches and connectivity arrangements to improve motion control efficiency for some given primary structure. This paper investigates the influence of the elastic and mass properties of the primary structure to the TMDI motion control performance. This is pursued through an innovative parametric study involving a wide range of tapered beam-like cantilevered primary structures with different continuously varying flexural rigidity and mass distributions equipped with TMDIs optimally tuned for resonant harmonic and for white noise excitations. Optimal TMDI tuning and performance assessment are expedited through a novel simplified two-degree-of-freedom dynamic model which accounts for the properties of the primary structure. It is found that reduced free-end displacement and TMDI stroke are achieved for primary structures in which the ratio of flexural rigidity over mass decreases faster with height resulting in vibration modal shapes with higher convexity. The latter is quantified though the average modal curvature shown to be well-correlated with TMDI motion control improvement. It is concluded that judicial shaping of the primary structure extends the applicability of the TMDI to structures where connecting the inerter away from the free-end is practically challenging while contains the magnitude of the inerter and damping forces exerted to the primary structure. Therefore, this study paves the way towards combining optimal TMDI tuning with primary structure design for improved performance to dynamic loads.