472 X.Q. Wang and M.P. Mignolet D(F0) (lb in) 102 10−4 10−3 10−2 Unc. Band 5th perc. 95th perc. F0 (lb) F 0 (lb) K(F0) (lb/in) 100 150 200 250 300 350 400 450 500 0 2 4 6 8 10 12 14 16 18 x 106 Unc. Band 5th perc. 95th perc. a b Fig. 44.9 5th–95th percentiles bands of uncertainty on (a) dissipation per cycle and (b) stiffness vs. amplitude of harmonic force for the split 4-parameter Iwan model with parameters determined from Table 44.2. Also shown are the nine measurement sets The randomization of this split Iwan model was next discussed and the selection of statistical distributions and identification of the parameters from the available experimental data were described in details. The availability of such a stochastic model permits the prediction of the statistics, including band of uncertainty, on the predicted behavior, dissipation and stiffness, of the joints. References 1. Ibrahim RA, Pettit CL (2005) Uncertainties and dynamic problems of bolted joints and other fasteners. J Sound Vib 279:857–936 2. Dohnal F, Mace BR, Ferguson NS (2009) Joint uncertainty propagation in linear structural dynamics using stochastic reduced basis methods. AIAA J 47:961–969 3. Segalman DJ, Gregory DL, Starr MJ, Resor BR, Jew MD, Lauffer JP, Ames NM (2009) Handbook on dynamics of jointed structures. Sandia Report SAND2009-4164 4. Bowman AW, Azzalini A (1997) Applied smoothing techniques for data analysis. Oxford University Press, Oxford 5. Terrell GR, Scott DW (1992) Variable kernel density estimation. Ann Stat 20:1236–1265 6. Soize C (2011) A computational inverse method for identification of non-Gaussian random fields using the Bayesian approach in very high dimension. Comput Meth Appl Mech Eng 200:3083–3099 7. Soize C, Ghanem R (2004) Physical systems with random uncertainties: chaos representation with arbitrary probability measure. SIAM J Sci Comput 26:395–410 8. Sakamoto S, Ghanem R (2002) Polynomial chaos decomposition for the simulation of non-Gaussian nonstationary stochastic processes. J Eng Mech 128:190–201 9. Soize C (2005) A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics. J Sound Vib 288:623–652
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