Dynamic performance optimization of a vibration absorber for an uncertain system using a probabilistic design approach

This paper presents a probabilistic approach to optimize dynamic performance of a vibration absorber when the main system is described by random variables. The sinusoidal steady-state amplitude of the main mass is considered as the dynamic performance measure of a vibration absorber. The design goal is to reduce both the mean and variance of the dynamic performance measure over the excitation frequency range. The design process is complicated because the resonance frequency of the main system is also a random variable. In order to address these difficulties, critical amplitudes according to three critical frequencies capable of representing the excitation frequency range are established. Then limit-state functions are formed at each of the critical frequencies by subtracting the respective dynamic performance measure from the critical amplitude. Each limit-state function establishes a non-conformance region in terms of the random variables. The probability of the union of the non-conformance regions provides a single objective to be minimized by adjusting the design parameters in the vibration absorber for performance optimization of the absorber. A first-order reliability method is implemented to efficiently estimate probabilities. Monte-Carlo sampling is invoked to verify the proposed approach. The proposed approach for the absorber design is compared with a deterministic approach and other approaches available in the open literature.