On a nonlinear single-mass two-frequency pendulum tuned mass damper to reduce horizontal vibration

This paper considers a nonlinear single-mass two-frequency pendulum tuned mass damper (TMD) to reduce horizontal vibration. The proposed TMD contains one mass moving along a bar while the bar can rotate around the fulcrum point attached with the controlled structure. Under a horizontal excitation, the single TMD mass has two motions (swing and translation) at the same time and the proposed TMD has two natural frequencies. In comparison with the optimal linear single mass TMD, because of the inherent nonlinearity of the proposed TMD, it has good performance for large vibration. Moreover, the proposed TMD is also less sensitive to the parameter mistuning. The problem is expressed in the non-dimensional equation form. The approximated vibration amplitudes can be obtained by solving a scalar algebraic equation. The numerical simulation is carried out to verify the approximate analysis.