Optimal design of particle dampers for structures with low first eigenfrequency under forced vibration

Abstract

Recently, the rolling attribute of spheres has been used to develop efficient particle dampers for horizontal low amplitude vibrations. As long as the particle container’s acceleration stays below the gravitational acceleration, this rolling effect of spheres can be used. Hereby, the estimation of the damper’s energy dissipation is accurately possible using analytical formulas. In this paper, the workflow for a systematic damper design for an underlying structure of low first eigenfrequency under forced vibration is presented. The analytical formulas describing the dampers energy dissipation are coupled to a modal reduced model of the utilized vibrating structure. Then an analytical expression for an optimal damper design is derived. Also, the calculation scheme to obtain the frequency response function of the system is presented. As application example, a simple beam-like structure is used, whereby its base point is subjected to a harmonic motion of variable frequency using a linear drive. The particle damper is mounted at the tip of the beam and its velocity is measured using a laser scanning vibrometer. Thus, the frequency response function is obtained experimentally. A good agreement between analytical and experimental obtained frequency response function is achieved for the optimized particle damper, validating the presented approach.