Wiener Path Integral based response determination of nonlinear systems subject to non-white, non-Gaussian, and non-stationary stochastic excitation

The recently developed Wiener Path Integral (WPI) technique for determining the joint response probability density function of nonlinear systems subject to Gaussian white noise excitation is generalized herein to account for non-white, non-Gaussian, and non-stationary excitation processes. Specifica...

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Veröffentlicht in:Journal of sound and vibration Jg. 433; S. 314 - 333
Hauptverfasser: Psaros, Apostolos F., Brudastova, Olga, Malara, Giovanni, Kougioumtzoglou, Ioannis A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier Ltd 27.10.2018
Elsevier Science Ltd
Schlagworte:
Computer simulation
Excitation
Excitation spectra
Gaussian beams (optics)
Gaussian process
Integrals
Mathematical analysis
Mathematical models
Mechanical engineering
Modulus of elasticity
Monte Carlo simulation
Non-white and non-Gaussian stochastic processes
Nonlinear response
Nonlinear system
Nonlinear systems
Normal distribution
Path integral
Probability density functions
Stochastic dynamics
Stochastic models
White noise
Stochastic dynamics
Path integral
Non-white and non-Gaussian stochastic processes
Nonlinear system
ISSN:0022-460X, 1095-8568
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Zusammenfassung:The recently developed Wiener Path Integral (WPI) technique for determining the joint response probability density function of nonlinear systems subject to Gaussian white noise excitation is generalized herein to account for non-white, non-Gaussian, and non-stationary excitation processes. Specifically, modeling the excitation process as the output of a filter equation with Gaussian white noise as its input, it is possible to define an augmented response vector process to be considered in the WPI solution technique. A significant advantage relates to the fact that the technique is still applicable even for arbitrary excitation power spectrum forms. In such cases, it is shown that the use of a filter approximation facilitates the implementation of the WPI technique in a straightforward manner, without compromising its accuracy necessarily. Further, in addition to dynamical systems subject to stochastic excitation, the technique can also account for a special class of engineering mechanics problems where the media properties are modeled as stochastic fields. Several numerical examples pertaining to both single- and multi-degree-of-freedom systems are considered, including a marine structural system exposed to flow-induced non-white excitation, as well as a bending beam with a non-Gaussian and non-homogeneous Young's modulus. Comparisons with Monte Carlo simulation data demonstrate the accuracy of the technique.
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ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2018.07.013