MOTION CONTROL PERFORMANCE OF TUNED MASS DAMPER INERTER (TMDI) IN CONTINUOUS WHITE-NOISE EXCITED CANTILEVERED BEAMS WITH VARIOUS SHAPES

Abstract

The tuned mass‐damper‐inerter (TMDI) is a linear passive dynamic vibration absorber for motion control of dynamically excited building (primary) structures. It couples the classical tuned mass damper (TMD), comprising a secondary mass attached to the top building floor via a spring and dashpot, with an inerter, a mechanical element resisting relative acceleration, which links the secondary mass to a lower floor. Recent studies demonstrate that TMDI motion control effectiveness is influenced by the vibration modes of the uncontrolled primary structure. Herein, this influence is quantified through a parametric investigation considering a wide range of white-noise excited primary structures modelled as cantilevered continuous beams with various shapes and, therefore, different vibration modes. This quantification is facilitated by considering a low-order model of TMDI-equipped flexural cantilever which accounts for the effect of flexural rigidity and mass distribution of the primary structure as well as the influence of the fundamental mode shape to the location that the inerter connects the secondary mass to the primary structure. The investigation is further supported by optimal H2 tuning of TMDI aiming to minimize the free-end primary structure displacement under white noise excitation. It is shown that the TMDI achieves enhanced structural performance as the inerter links the secondary mass further away from the top of the primary structure where the mass is attached to for all primary structure shapes. Moreover, it is found that improved TMDI performance and reduced stroke (relative secondary mass displacement with respect to the primary structure) are achieved for primary structure shapes with stiffness and mass distribution weighted heavier towards the base of the structure (i.e., when most of material is concentrated towards the bottom end of the structure) either through appropriate shaping or through increase of base to free-end depth ratio for fixed non-uniform shapes.