S. Sartori-junior, J. M. Balthazar, and B. R. Junior, Non-linear dynamics of a tower orchard sprayer based on an inverted pendulum model, Biosystems Engineering, vol.103, issue.4, pp.417-426, 2009.
DOI : 10.1016/j.biosystemseng.2008.09.003

S. and S. Junior, Mathematical modeling and dynamic analysis of a orchards spray tower, M.Sc. Dissertation, 2008.

S. Sartori-junior, M. Balthazar, and B. R. Pontes, Nonlinear dynamics of an orchard tower sprayer based on a double inverted pendulum model, In: Proceedings of COBEM, 2007.

C. Soize, Stochastic Models of Uncertainties in Computational Mechanics
DOI : 10.1061/9780784412237

URL : https://hal.archives-ouvertes.fr/hal-00749201

C. Soize, Stochastic modeling of uncertainties in computational structural dynamics???Recent theoretical advances, Journal of Sound and Vibration, vol.332, issue.10, pp.2379-2395, 2013.
DOI : 10.1016/j.jsv.2011.10.010

URL : https://hal.archives-ouvertes.fr/hal-00743699

A. C. Jr, C. Soize, and R. Sampaio, Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings, Computational Mechanics, pp.849-878, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01194190

A. C. Jr and R. Sampaio, On the nonlinear stochastic dynamics of a continuous system with discrete attached elements, Applied Mathematical Modelling, vol.39, pp.809-819, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01438635

G. Perrin, D. Duhamel, C. Soize, and C. Funfschilling, Quantification of the influence of the track geometry variability on the train dynamics, Mechanical Systems and Signal Processing, vol.60, issue.61, pp.945-957, 2015.
DOI : 10.1016/j.ymssp.2015.01.004

URL : https://hal.archives-ouvertes.fr/hal-01137530

T. G. Ritto and L. C. Nunes, Bayesian model selection of hyperelastic models for simple and pure shear at large deformations, Computers & Structures, vol.156, pp.101-109, 2015.
DOI : 10.1016/j.compstruc.2015.04.008

A. T. Beck, W. J. Gomes, R. H. Lopez, and L. F. , A comparison between robust and risk-based optimization under uncertainty, Structural and Multidisciplinary Optimization, pp.52-479, 2015.
DOI : 10.1007/s00158-015-1253-9

A. Cunha-jr, J. L. Felix, and J. M. Balthazar, On the nonlinear dynamics of an inverted double pendulum over a vehicle suspension subject to random excitations, Proceedings of COBEM 2015, 2015.

A. Cunha-jr, J. L. Felix, and J. M. Balthazar, Effects of a random loading emulating an irregular terrain in the nonlinear dynamics of a tower sprayer, Procedings of The 3rd International Symposium on Uncertainty Quantification and Stochastic Modeling, 2016.
DOI : 10.20906/CPS/USM-2016-0008

URL : https://hal.archives-ouvertes.fr/hal-01471293

E. Fehlberg, Low-order classical Runge-Kutta formulas with step size control and their application to some heat transfer problems, 1969.

U. Ascher and C. Greif, A First Course in Numerical Methods, Society for Industrial and Applied Mathematics, 2011.
DOI : 10.1137/9780898719987

D. Xiu, Numerical Methods for Stochastic Computations: A Spectral Method Approach, 2010.

R. Ghanem and P. Spanos, Stochastic Finite Elements: A Spectral Approach, 2003.
DOI : 10.1007/978-1-4612-3094-6

S. Bellizzi and R. Sampaio, POMs analysis of randomly vibrating systems obtained from Karhunen???Lo??ve expansion, Journal of Sound and Vibration, vol.297, issue.3-5, pp.774-793, 2006.
DOI : 10.1016/j.jsv.2006.04.023

R. Sampaio and C. Soize, Remarks on the efficiency of POD for model reduction in non-linear dynamics of continuous elastic systems, International Journal for Numerical Methods in Engineering, vol.45, issue.3, pp.22-45, 2007.
DOI : 10.1002/nme.1991

URL : https://hal.archives-ouvertes.fr/hal-00686148

G. Stefanou and M. Papadrakakis, Assessment of spectral representation and Karhunen???Lo??ve expansion methods for the simulation of Gaussian stochastic fields, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.21-24, pp.2465-2477, 2007.
DOI : 10.1016/j.cma.2007.01.009

S. Bellizzi and R. Sampaio, Smooth Karhunen???Lo??ve decomposition to analyze randomly vibrating systems, Journal of Sound and Vibration, vol.325, issue.3, pp.491-498, 2009.
DOI : 10.1016/j.jsv.2009.03.044

S. Bellizzi and R. Sampaio, Karhunen???Lo??ve modes obtained from displacement and velocity fields: Assessments and comparisons, Mechanical Systems and Signal Processing, vol.23, issue.4, pp.1218-1222, 2009.
DOI : 10.1016/j.ymssp.2008.10.005

S. Bellizzi and R. Sampaio, Smooth decomposition of random fields, Journal of Sound and Vibration, vol.331, issue.15, pp.3509-3520, 2012.
DOI : 10.1016/j.jsv.2012.03.030

URL : https://hal.archives-ouvertes.fr/hal-00700018

S. Bellizzi and R. Sampaio, The smooth decomposition as a nonlinear modal analysis tool, Mechanical Systems and Signal Processing, pp.64-65, 2015.
DOI : 10.1016/j.ymssp.2015.04.015

M. Trindade, C. Wolter, and R. Sampaio, Karhunen???Lo??ve decomposition of coupled axial/bending vibrations of beams subject to impacts, Journal of Sound and Vibration, vol.279, issue.3-5, pp.1015-1036, 2005.
DOI : 10.1016/j.jsv.2003.11.057

D. P. Kroese, T. Taimre, and Z. I. Botev, Handbook of Monte Carlo Methods, 2011.
DOI : 10.1002/9781118014967

A. C. Jr, R. Nasser, R. Sampaio, H. Lopes, and K. Breitman, Uncertainty quantification through Monte Carlo method in a cloud computing setting, Computer Physics Communications, vol.185, pp.1355-1363, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01438643

C. Soize, A comprehensive overview of a non-parametric probabilistic approach of model uncertainties for predictive models in structural dynamics, Journal of Sound and Vibration, vol.288, issue.3, pp.623-652, 2005.
DOI : 10.1016/j.jsv.2005.07.009

URL : https://hal.archives-ouvertes.fr/hal-00686182

A. V. Oppenheim and R. W. Schafer, Discrete-Time Signal Processing, 2009.

C. Soize, Fundamentals of random signal analysis: Application to modal identification in structural dynamics, Lecture Notes, 1997.