Optimal probabilistic design of the dynamic performance of a vibration absorber

This paper presents a non-sample-based probabilistic approach to determine the parameters in 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. 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, system-specified, maximum, 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. A first-order reliability method is implemented to efficiently estimate probabilities. Monte-Carlo sampling is invoked to verify our method. The proposed approach for the absorber design is compared with a deterministic approach and a second-order transmission of moments approach available in the open literature. The proposed approach is found to be robust, expandable and flexible.