General routine of suppressing single vibration mode by multi-DOF tuned mass damper: Application of three-DOF

Abstract

Abstract The multi-degree-of-freedom (MDOF) tuned mass damper (TMD) has demonstrated a more effective performance than single-DOF and multiple SDOF TMDs. For a damping mass in the space, there are maximum six DOFs; however, only along the vibration direction of the main structure can the motion of the TMD be utilized to control the vibration mode. Therefore, the maximum available DOFs of a TMD for mitigating single translational mode are three (i.e. one translational DOF and two rotational DOFs). A general routine of suppressing single vibration mode by multi-DOF TMD is presented, especially, a three-DOF TMD is used for example. Based on the non-dimensional dynamic model, the design parameters of the TMD are optimized via the simulated annealing algorithm according to the H∞ criterion. The graphical approach is utilized to design the configuration of the TMD with prescribed DOFs. Stiffness and natural frequencies are formulated analytically by the compliance matrix method, based on which the dimensions of the TMD are determined. It is demonstrated that the SDOF and two-DOF TMDs are special cases of the three-DOF TMD from the point of mathematical modeling, numerical optimization and design methodology. Theoretical formulation is verified by conducting hammer tests on the TMD under various geometry configurations. After employing the three-DOF TMD, 86.5% reduction of the amplitude of the frequency response function (FRF) of an I-shaped part is achieved, which shows 29.5% improvement than previous two-DOF TMD.