H2, Mixed H2/H∞ and H2/L1 Optimally Tuned Passive Isolators and Absorbers

Abstract

In many practical applications, unbalanced rotating machinery cause vibrations that transmit large oscillatory forces to the system foundation. Using ad hoc optimization schemes tuned isolators and absorbers have traditionally been designed to suppress system vibration levels by attempting to minimize the peak frequency response of the force/displacement transmissibility system transfer function. In this paper, we formulate the classical isolator and absorber vibration suppression problems in terms of modern system theoretic criteria involving H2 (shock response), mixed H2 /H∞ (worst-case peak frequency response), and mixed H2 /L1 (worst-case peak amplitude response) performance measures. In particular, using a quasi-Newton optimization method we design H2 , mixed H2 /H∞ and mixed H2 /L1 optimally tuned isolators and absorbers for multi-degree-of-freedom vibrational systems. Finally, we compare our results to the classical Snowdon and Den Hartog absorbers.