Frequency Response Design of Uncertain Vibration Systems  
Author G. J. Savage


Co-Author(s) Y. K. Son


Abstract When components of a system are described by random variables, performance measures such as modal frequencies and modal shapes or amplitudes and phases, are also random variables and the frequency response (FR) requires the solution of a frequency-variant probability problem. This paper presents a new metric to assess the frequency response of uncertain systems and ensure performance measures best meet their limit specifications over the frequency band of interest. The novelty of the approach is the creation of a frequency-invariant probability problem through: a) the discretization of the frequency band of interest into multiple contiguous point frequencies, b) the introduction of new performance indices that measure the probability of failure over the entire frequency band, and c) the introduction of explicit metamodels to provide extremely fast probability evaluations through Monte Carlo simulation. The key to the performance indices are limit-state functions formed at all discrete, contiguous, frequencies. Each limit-state function establishes a non-conformance region in terms of the random design variables. The probabilities of the nonconformance regions are correctly combined to provide a single series-system index to be maximized by adjusting distribution parameters. The simple explicit meta- model is based on Kriging and performance measures at arbitrary design sets are efficiently calculated. Error analysis suggests ways to predict and control the errors. A case study of a vibration absorber mechanism shows how the new methodology provides an improved and timely design.


Keywords Vibratory Systems, Probability, Design of Experiments, Meta-models, Performance Indices, Monte Carlo
    Article #:  1945
Proceedings of the 19th ISSAT International Conference on Reliability and Quality in Design
August 5-7, 2013 - Honolulu, Hawaii, U.S.A.