# Damping of Beam Vibrations Using Tuned Particles Impact Damper
## 1 Introduction  
Devices that are able to attenuate unwanted mechanical vibrations have interested researches and engineers for several decades. In the everyday engineering applications we can distinguish various types of vibration damper designs. The most popular passive shock absorbers constructions consist of viscous properties of elastomers or more or less sophisticated fluids or gels. Nowadays, it seems that so called Particles Impact Dampers (PID) start to play an increasingly important role in the field of vibrations damping. The classical PID principle of operation lies in inelastic collisions of loose particles enclosed in the specially designed container or cavities. The Energy dissipation mechanism is additionally related to the frictional contact of grains and the container casing. The PID device connected to the vibrating element or structure absorbs a part of global kinetic energy of the investigated system and reduces its vibrations amplitudes. The effectiveness of such a damping strategy mainly results from coupling of friction and impact phenomenon. The energy dissipation process in the most commonly used damping devices is generally related either to the friction phenomenon or previously mentioned visco-elastic material deformations. Such mechanisms increase the operating temperature and also the wear of material resulting in decreasing of damping properties. Considering the aforementioned limitations, the use of granular dampers in which the influence of temperature and material degradation is less important seems to be particularly interesting. The additional advantages of PIDs are: they can perform in a very wide range of frequencies, they can be made of recycled materials, economical aspect, the global mass of the system with grains moving in the internal cavity is generally lower than the initial. All the previously mentioned features of PIDs cause that such devices are very often applied in dynamic systems working in harsh environments. The adjustment of damping properties in a considered group of shock absorbers is limited and consists of choosing the right kind, consistency, shape and size of grains for the given application. In world literature a significant number of studies have been carried out in the field of granular dampers analysis. They are mainly focused on efficiency ([1; 2; 3; 4]), optimization ([5; 6; 7]),applications ([8; 9; 10; 11]) and modeling ([12; 13; 14]). An interesting problem is discussed in Reference [15] where Particles Impact Damper is treated as a double pendulum striking element. It is confirmed that such an object is especially effective to attenuate vibrations of various slender elements. Various excitation rules and PID parameters are taken into account in experimental studies. Other papers suggest, that the PID can be a part of alternative energy harvesting device [16]. In this case the classical grains are replaced by a moving magnet forming the previously mentioned original energy harvester. Taking into account damping of vibrations of elements operating in an extreme environment, the reliability and durability of devices are extremely important. The typical example of such an environment is aerospace engineering, where PIDs are especially popular. It is presented in Reference [17] that attenuation of vibrations of highly sensitive electric circuits can be achieved by PIDs. Application of granular damping seems to also be optimal solution in the case of taking-off or landing of spacecrafts. Various modifications of classical PID designs are also investigated in recently published papers. In Reference [18], the authors propose an innovative solution for the semi-active Tuned Liquid Column Damper (sTLCD). Such a device is connected to the base structure using the spring with controlled stiffness. The efficiency of the considered system is discussed and different control algorithms are taken into consideration in the paper. Applied control strategies enabled the authors to effectively tune the frequency of a structure.