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Research Papers

An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems

[+] Author and Article Information
Ioannis A. Kougioumtzoglou

Department of Civil Engineering
and Engineering Mechanics,
Columbia University,
New York, NY 10027
e-mail: ikougioum@columbia.edu

Alberto Di Matteo

Dipartimento di Ingegneria Civile,
Ambientale e dei Materiali (DICAM),
Università degli Studi di Palermo,
Viale delle Scienze,
Palermo 90128, Italy
e-mail: alberto.dimatteo@unipa.it

Pol D. Spanos

Honorary Mem. ASME
Department of Mechanical Engineering
and Materials Science,
Rice University,
6100 Main Street,
Houston, TX 77005-1827
e-mail: spanos@rice.edu

Antonina Pirrotta

Dipartimento di Ingegneria Civile,
Ambientale e dei Materiali (DICAM),
Università degli Studi di Palermo,
Viale delle Scienze,
Palermo 90128, Italy
e-mail: antonina.pirrotta@unipa.it

Mario Di Paola

Dipartimento di Ingegneria Civile,
Ambientale e dei Materiali (DICAM),
Università degli Studi di Palermo,
Viale delle Scienze,
Palermo 90128, Italy
e-mail: mario.dipaola@unipa.it

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 1, 2015; final manuscript received June 18, 2015; published online July 10, 2015. Editor: Yonggang Huang.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Appl. Mech 82(10), 101005 (Jul 10, 2015) (7 pages) Paper No: JAM-15-1281; doi: 10.1115/1.4030890 History: Received June 01, 2015

The recently developed approximate Wiener path integral (WPI) technique for determining the stochastic response of nonlinear/hysteretic multi-degree-of-freedom (MDOF) systems has proven to be reliable and significantly more efficient than a Monte Carlo simulation (MCS) treatment of the problem for low-dimensional systems. Nevertheless, the standard implementation of the WPI technique can be computationally cumbersome for relatively high-dimensional MDOF systems. In this paper, a novel WPI technique formulation/implementation is developed by combining the “localization” capabilities of the WPI solution framework with an appropriately chosen expansion for approximating the system response PDF. It is shown that, for the case of relatively high-dimensional systems, the herein proposed implementation can drastically decrease the associated computational cost by several orders of magnitude, as compared to both the standard WPI technique and an MCS approach. Several numerical examples are included, whereas comparisons with pertinent MCS data demonstrate the efficiency and reliability of the technique.

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Figures

Grahic Jump Location
Fig. 1

Marginal response displacement PDF p(x,t) for the Duffing oscillator with β = 1, k0 = 0.3, ɛ = 1, and S0 = 0.0637 via the developed technique; comparison with MCS data (20,000 samples) and exact marginal stationary distribution

Grahic Jump Location
Fig. 2

Marginal response displacement PDF p(x,t) for the bimodal Duffing oscillator with β = 1, k0 = -0.3, ɛ = 1, and S0 = 0.0637 via the developed technique; comparison with MCS data (40,000 samples) and exact marginal stationary distribution

Grahic Jump Location
Fig. 3

Marginal response displacement PDF p(y1,t) for 2DOF nonlinear building structure with k = 1, c = 0.1, ɛ = 0.1, and S0 = 0.0637 via the developed technique; comparison with MCS data (30,000 samples)

Grahic Jump Location
Fig. 4

Marginal response displacement PDF p(y2,t) for 2DOF nonlinear building structure with k = 1, c = 0.1, ɛ = 0.1, and S0 = 0.0637 via the developed technique; comparison with MCS data (30,000 samples)

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