# Damping of Beam Vibrations Using Tuned Particles Impact Damper
## 1 Introduction
The proposed solution is especially interesting in civil engineering where the increased danger of earthquakes exists. A lot of papers dealing with granular damping discuss various modeling approaches and problems encountered in the laboratory tests. Also experimentally determined damping characteristics are presented and discussed in detail ([19; 20; 21]). Despite the apparent simplicity of the PIDs fundamental working rule it can be concluded, that capturing the real behavior of the discussed group of devices is rather complex. Previously mentioned papers generally simplify the PIDs modelling process to the 1 or 2 Degrees of Freedom (DOF) problems incorporating additionally external forces or equivalent damping parameters. In Reference [22] or Reference [23] the complex dynamics of vibrating sphere particles is compared to the dense gas flow. Such a solution allows to represent the damping characteristics by formulas dependent on: a mass ratio, volume ratio, restitution coefficient and excitation frequency. The different approach to the PIDs modelling problems can be observed in Reference [24] or Reference [25], where the sophisticated numerical software is used to capture the real laboratory test results. In Reference [24] an interesting original technique to predict the harmonic response of particle damping structure based on ANSYS software is discussed. Other approach basing on Discreet Element Method (DEM) is investigated in Reference [25] where the energy dissipation problems of harmonically excited elements are solved numerically. To solve the classical inverse problem consisting of calibrating the selected model parameters basing on the real response of the PID device various numerical optimization techniques are taken into consideration. In Reference [26] the damper parameters are captured using Artificial Neural Networks. The efficiency of proposed methodology was compared with two other popular parameters identification methods - Feed Forward Back Propagation Network and Radial Basis Function. An interesting practical engineering application of PIDs in the automotive industry is presented in Reference [27] where a granular damper is used as a sound absorber. It is confirmed that such a device is also suitable for increasing the driving comfort of the passengers. Granular dampers are also used in suppression of vibrations in centrifugal field of gear transmission ([28]). In such a case the tightly packed loose material is placed in specially designed holes in the gears. The reliability of PIDs is validated by the comparison of real response of the system with the numerical DEM simulations. The other grain based damping of vibration techniques being the alternative to the discussed PIDs are so called Chain Dampers ([29; 30]) or Vibro-Impact Nonlinear Energy Sinks ([31; 32; 33]). Application of various PIDs seems to be especially interesting in the controlling nonlinear dynamics of slender and light objects resulted from the unknown disturbances. Typical examples of such structures are wind turbines ([34; 35]). Reference [36] describes the effective damping of rail vibrations by adding a TPID consisting of Tuned Absorber Mass and Impact Ball. The mathematical model, experiments and simulations are introduced to establish the optimal damping parameters for the system. In the mentioned paper, the authors analyze the effectiveness of the structure by separating the components of the damper. Reference [37] provides the literature review over PID dampers. It presents various technical solutions and modelling methods. They describe typical applications of the TPIDs, which however allow to change the parameters of the attenuator, but require a significant human involvement aspect. In Reference [38] a simple mathematical model of the vibrating system including TPID damper described as a 2-DOF system is presented. The shock absorber model is mainly described by two coupled parameters: equivalent damping and equivalent mass. Reference [39] presents the construction of a damper named TPID.