Design of Nonlinear Tuned Mass Damper by Using the Harmonic Balance Method

Abstract

As a passive control device, tuned mass dampers (TMDs) are widely used in structural vibration control. Due to the nonlinear characteristics of a TMD, it is important to consider nonlinearity in the design process. In this study, the authors analyzed the control results for the traditional design method of a TMD and concluded that the traditional design method is not sufficiently effective when considering the nonlinear behavior of TMDs. Furthermore, it is demonstrated that the improved design method proposed previously by researchers may not provide the best control effect in some cases. To accurately incorporate the nonlinearities in the design process, the harmonic balance method (HBM) is used to determine the steady-state amplitude of a single-degree-of-freedom structure controlled by a nonlinear TMD. The result of the analysis is used to calculate the optimal frequency ratio of the TMD, which is subsequently used in the design. Finally, the calculated optimal frequency is compared with the numerically obtained optimal result. Through the simulation, it can be shown that the proposed method can effectively incorporate both hardening and softening nonlinearity.