On a nonlinear single-mass two-frequency pendulum tuned mass damper to reduce horizontal vibration L. D. Viet a, *, N. B. Nghi a a Institute of Mechanics, 264 Doi Can, Hanoi, Vietnam; Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, Vietnam Abstract: 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. Keywords: Pendulum tuned mass damper, frequency response, nonlinear tuned mass damper, Coriolis force 1. Introduction A TMD, which consists of a moving mass attached to the main structure through springs and dampers, is a well-known device to suppress vibration. The classical linear single mass TMD is simple but still has some limitations such as the narrow band of suppression frequency and the sensitivity problems due to mistuning. There are a lot of efforts to improve the linear single mass TMD by considering multiple TMD, nonlinear TMD or by adding control. In [1-4] and references herein, one can find several methods to optimize the multiple TMD. The multiple TMD is proved to be more effective and less sensitive to mistuning than the single TMD. Adding control to the TMD leads to the concepts of active TMD, hybrid TMD or semi-active TMD. However, this problem is too big to introduce here. The readers can find a good overview in [5]. Other studies consider the nonlinear TMD [6-9]. The nonlinearity can be added by the cubic spring or by the impact. Pendulum behavior is another source of nonlinearity. In fact, as the natural frequency of a pendulum depends only on its length, it is easier to tune pendulum TMD frequency in practical applications. The three-dimensional motions of the pendulum TMD has been studied in [11- 13]. Some other types of pendulum TMD were presented in [14, 15]. The nonlinearity of the pendulum also reveals a new type of TMD called Coriolis TMD or Coriolis vibration absorber [16]. In a structure vibrating in one direction, a linear single mass TMD attached to this structure has only one degree of freedom (DOF) and one natural frequency. Increasing the number of DOF of the TMD can improve its performance. An evident approach is to use the multiple TMD. There are a lot of publications on the multiple TMD. However, because the TMD mass has to be divided into many smaller ones, * Corresponding author. E-mail address: laviet80@yahoo.com, ldviet@imech.ac.vn (L.D.Viet)