Attenuation of a linear oscillator using a nonlinear and a semi-active tuned mass damper in series

In this paper, the behavior of a three degrees-of-freedom system is examined, consisting of a linear primary structure (PS), a tuned mass damper with a small cubic stiffness nonlinearity and a semi-active tuned mass damper (STMD) connected in series—each element with a mass approximately two orders of magnitude smaller than the previous. Using numerical simulations, it is determined that an STMD with a mass four orders of magnitude smaller than the PS is able to greatly reduce the amplitude of the PS response by acting to keep the nonlinear tuned mass damper within its linear range. Effective attenuation is dependent on appropriate selection of design parameters—selecting an appropriate STMD mass ratio given its damping, the strength of the stiffness nonlinearity, and the largest forcing amplitude expected. Using a standard tuning approach for the STMD (modulating its stiffness to match the natural frequency of the STMD to the excitation frequency) and comparing its performance with an optimal passive linear tuned mass damper (TMD), the STMD provides a wider-band frequency-response amplitude reduction but often increases the response amplitude slightly above the resonance frequency. A piecewise linear tuning approach for the STMD is proposed which combines the performance benefits of the STMD and the TMD to improve performance and further reduce power requirements.