Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Mechanical System Lifetime Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

Approximate Probability Density Function Solution of Multi-Degree-of-Freedom Coupled Systems Under Poisson Impulses

verfasst von : H. T. Zhu

Erschienen in: Numerical Methods for Reliability and Safety Assessment

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

A solution procedure is proposed to approximate the probability density function (PDF) solution of high-dimensional non-linear systems under Poisson impulses. The PDF solution yields the generalized Fokker–Planck–Kolmogorov (FPK) equation. First a state-space-split method is proposed to reduce the high-dimensional generalized FPK equation to a low dimensional equation. After that, the exponential–polynomial closure method is further adopted to solve the reduced FPK equation for the PDF solution. In order to show the effectiveness of the proposed solution procedure, a two-degree-of-freedom coupled pitch–roll ship motion system and a 10-degree-of-freedom mass–spring–damper system are investigated, respectively. Compared to the simulated results, the proposed solution procedure is effective to obtain the PDF solution, especially in the tail region which is very important for reliability analysis.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Multicut-High Dimensional Model Representation for Reliability Bounds Estimation
Nächstes Kapitel Evaluate Reliability of Morgenstern–Price Method in Vertical Excavations
Literatur
Atalik TS, Utku S (1976) Stochastic linearization of multi-degree-of-freedom non-linear systems. Earthquake Eng Struct Dyn 4:411–420CrossRef
Cai GQ, Lin YK (1992) Response distribution of non-linear systems excited by non-Gaussian impulsive noise. Int J Nonlinear Mech 27:955–967MathSciNetCrossRefMATH
Cai GQ, Lin YK (1996) Exact and approximate solutions for randomly excited MDOF non-linear systems. Int J Nonlinear Mech 31:647–655MathSciNetCrossRefMATH
Caughey TK, Ma F (1982) The exact steady-state solution of a class of nonlinear stochastic systems. Int J Nonlinear Mech 17:137–142MathSciNetCrossRefMATH
Di Paola M, Santoro R (2008) Non-linear systems under Poisson white noise handled by path integral solution. J Vib Control 14:35–49MathSciNetCrossRefMATH
Er GK (2011) Methodology for the solutions of some reduced Fokker–Planck equations in high dimensions. Ann Phys (Berlin) 523:247–258MathSciNetCrossRef
Er GK, Iu VP (2011) A new method for the probabilistic solutions of largescale nonlinear stochastic dynamic systems. In: Zhu WQ, Lin YK, Cai GQ (eds) IUTAM symposium on nonlinear stochastic dynamics and control, vol 29, IUTAM book series. Springer, New York, pp 25–34
Köylüoğlu HU, Nielsen SRK, Iwankiewicz R (1994) Reliability of nonlinear oscillators subject to Poisson driven impulses. J Sound Vib 176:19–33CrossRefMATH
Köylüoğlu HU, Nielsen SRK, Çakmak AŞ (1995) Fast cell-to-cell mapping (path integration) for nonlinear white noise and Poisson driven systems. Struct Saf 17:151–165CrossRef
Langley RS (1985) A finite element method for the statistics of non-linear random vibration. J Sound Vib 101:41–54CrossRefMATH
Lin YK, Cai GQ (1988) Exact stationary response solution for second order nonlinear systems under parametric and external white noise excitations: Part II. ASME J Appl Mech 55:702–705MathSciNetCrossRefMATH
Muscolino G, Ricciardi G (1999) Probability density function of MDOF structural systems under non-normal delta-correlated inputs. Comput Methods Appl Mech Eng 168:121–133CrossRefMATH
Muscolino G, Ricciardi G, Cacciola P (2003) Monte Carlo simulation in the stochastic analysis of non-linear systems under external stationary Poisson white noise input. Int J Nonlinear Mech 38:1269–1283MathSciNetCrossRefMATH
Proppe C (2002a) The Wong-Zakai theorem for dynamical systems with parametric Poisson white noise excitation. Int J Eng Sci 40:1165–1178MathSciNetCrossRefMATH
Proppe C (2002b) Equivalent linearization of MDOF systems under external Poisson white noise excitation. Prob Eng Mech 17:393–399CrossRef
Proppe C (2003) Exact stationary probability density functions for non-linear systems under Poisson white noise excitation. Int J Nonlinear Mech 38:557–564MathSciNetCrossRefMATH
Proppe C, Pradlwarter HJ, Schuëller GI (2003) Equivalent linearization and Monte Carlo simulation in stochastic dynamics. Prob Eng Mech 18:1–5CrossRef
Roberts JB, Spanos PD (2003) Random vibration and statistical linearization. Dover, Mineola, NYMATH
Shinozuka M (1972) Monte Carlo solution of structural dynamics. Comput Struct 2:855–874CrossRef
Socha L (2008) Linearization methods for stochastic dynamic systems. Springer, BerlinMATH
Spanos PD (1981) Stochastic linearization in structural dynamics. ASME Appl Mech Rev 34:1–8MathSciNet
Vasta M (1995) Exact stationary solution for a class of non-linear systems driven by a non-normal delta-correlated process. Int J Nonlinear Mech 30:407–418MathSciNetCrossRefMATH
Wojtkiewicz SF, Johnson EA, Bergman LA, Grigoriu M, Spencer BF Jr (1999) Response of stochastic dynamical systems driven by additive Gaussian and Poisson white noise: solution of a forward generalized Kolmogorov equation by a spectral finite difference method. Comput Methods Appl Mech Eng 168:73–89CrossRefMATH
Wu Y, Zhu WQ (2008a) Stationary response of MDOF dissipated Hamiltonian systems to Poisson white noises. ASME J Appl Mech 75:044502CrossRef
Wu Y, Zhu WQ (2008b) Stationary response of multi-degree-of-freedom vibroimpact systems to Poisson white noises. Phys Lett A 372:623–630MathSciNetCrossRefMATH
Zhu HT, Er GK, Iu VP, Kou KP (2009) EPC procedure for PDF solution of non-linear oscillators excited by Poisson white noise. Int J Nonlinear Mech 44:304–310CrossRef
Metadaten
Titel
Approximate Probability Density Function Solution of Multi-Degree-of-Freedom Coupled Systems Under Poisson Impulses
verfasst von
H. T. Zhu
Copyright-Jahr
2015
Buch
Numerical Methods for Reliability and Safety Assessment

Print ISBN: 978-3-319-07166-4

Electronic ISBN: 978-3-319-07167-1

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-319-07167-1_19

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise