Closed-form solutions for the optimal design of inerter-based dynamic vibration absorbers

This paper is concerned with the development of novel closed-form solutions for the optimal design of inerter-based dynamic vibration absorbers by extending the Den Hartog's technique. Furthermore, in order to validate the closed solutions, an optimization problem for minimizing the standard deviation of difference among vibration amplitudes under an excitation frequencies range is formulated. Additionally, the numerical simulations showed that the extended fixed-points technique produces similar results than the H-infinity optimization technique. The mechanical impedances studied in this research showed the best performance by minimizing the vibration amplitudes and maximizing the effective bandwidth of the classic Dynamic Vibration Absorber. The results showed that, by extending the fixed-points technique, a simplest alternative for the optimal design of IDVAs regardless of numerical methods, such as the sequential quadratic programing (SQP) or non-linear optimization techniques, was obtained.