Path integral solution for nonlinear systems under parametric Poissonian white noise input |
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| Affiliation: | 1. Dipartimento di Ingegneria Civile, Ambientale, Aerospaziale, dei Materiali (DICAM), Università degli Studi di Palermo, Viale delle Scienze, I-90128 Palermo, Italy;2. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK;1. SEMTE, Faculties of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287-6106, USA;2. Gyeongsang National University, Department of Energy and Mechanical Engineering, Institute of Marine Industry, Tongyoung, Gyeongnam 650-160, South Korea;3. Laboratoire Modélisation et Simulation Multi Echelle, Université Paris-Est, 5, Bd Descartes, 77454 Marne-la-Vallée Cedex 02, France;1. Center for Optimization and Reliability in Engineering (CORE), Department of Civil Engineering, Federal University of Santa Catarina, Florianópolis, SC, Brazil;2. Department of Structural Engineering, University of São Paulo, São Carlos, SP, Brazil;1. Calatrava Family Endowed Chair, Columbia University, New York, NY, USA;2. Professore Ordinario, University of Palermo, Palermo, Italy;3. Cheung Kong Scholar of Structural Engineering, Tongji University, Shanghai, China;4. LB Ryon Endowed Chair in Engineering, Rice University, Houston, Texas, USA;1. Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, NY 10027, USA;2. Rice University, MS 321, P.O. Box 1892, Houston, TX 77251, USA;1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072,China;2. Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China |
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| Abstract: | In this paper the problem of the response evaluation in terms of probability density function of nonlinear systems under parametric Poisson white noise is addressed. Specifically, extension of the Path Integral method to this kind of systems is introduced. Such systems exhibit a jump at each impulse occurrence, whose value is obtained in closed form considering two general classes of nonlinear multiplicative functions. Relying on the obtained closed form relation liking the impulses amplitude distribution and the corresponding jump response of the system, the Path Integral method is extended to deal with systems driven by parametric Poissonian white noise. Several numerical applications are performed to show the accuracy of the results and comparison with pertinent Monte Carlo simulation data assesses the reliability of the proposed procedure. |
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| Keywords: | Nonlinear systems Parametric input Path integral solution Poisson white noise |
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