Establishment of theoretical models for beam structures with particle impact damper

Over the past few decades, research on impact dampers has grown significantly, leading to numerous analytical and experimental investigations in that field. Vibrations can harm industrial equipment and cause process errors. Particle impact damper has a significant impact on lowering vibration and has been broadly implemented in various engineering applications. This work deals with the theoretical modeling for cantilever beam and fixed-fixed beam attached with a cylindrical enclosure filled with particles. Transient and forced excitations are considered to trace the motion of the primary mass with respect to time. Also, theoretical modeling of particle arrangement in enclosure, condition for particles to detach from base or ceiling of enclosure, motion of particle after detachment from enclosure, and mechanism of collision and friction of particles are discussed and presented in detail. Theoretical models proposed in this study can be used to generate theoretical readings for practical engineering applications.