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A new approximate solution technique for randomly excited non-linear oscillators—II
9 references·8 citing·28 second hop
A new approximate solution technique for randomly excited non-linear oscillators—II (1992)A new approximate solution technique for …Random vibration and statistical linearization (1990)Random vibration and statisti…Random vibration and statistical linearization (1990)Random vibration and statisti…Stochastic averaging: An approximate method of solving random vibration problems (1986)Stochastic averaging: An appr…Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations (1984)Cumulant-neglect closure for …Non-gaussian closure for random vibration of non-linear oscillators (1980)Non-gaussian closure for rand…Probabilistic Theory of Structural Dynamics (1976)Probabilistic Theory of Struc…Approximate analysis of non-linear stochastic systems (1976)Approximate analysis of non-l…On the relation between ordinary and stochastic differential equations (1965)On the relation between ordin…On a Formula Concerning Stochastic Differentials (1951)On a Formula Concerning Stoch…Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process (2020)Path Integral Methods for the…Nonlinear system stochastic response determination via fractional equivalent linearization and Karhunen–Loève expansion (2017)Nonlinear system stochastic r…Polynomial Correlated Function Expansion for Nonlinear Stochastic Dynamic Analysis (2014)Polynomial Correlated Functio…Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization (2002)Some properties of multi-degr…A new stationary PDF approximation for non-linear oscillators (2000)A new stationary PDF approxim…Multi-Gaussian closure method for randomly excited non-linear systems (1998)Multi-Gaussian closure method…Exact and approximate solutions for randomly excited MDOF non-linear systems (1996)Exact and approximate solutio…Approximate solution for nonlinear random vibration problems by partial stochastic linearization (1993)Approximate solution for nonl…Probabilistic Structural Dynamics: Advanced Theory and Applications (1967)Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations (2022)Physically Driven Exact Dimension Reduction of a Class of Nonlinear Multidimensional Systems Subjected to Additive White Noise (2022)Reliability of dynamical systems with combined Gaussian and Poisson white noise via path integral method (2022)On stochastic differential equations (1951)Developments in stochastic structural mechanics (2006)Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects (2006)Solution of Fokker-Planck equation by finite element and finite difference methods for nonlinear systems (2006)Stochastic Differential Equations (2014)On stationary solutions of a stochastic differential equation (1964)Diffusion processes with continuous coefficients, I (1969)Itô’s stochastic calculus: Its surprising power for applications (2010)Random field finite elements (1986)Nonlinear Vibration Models for Extremes and Fatigue (1988)A nonparametric model of random uncertainties for reduced matrix models in structural dynamics (2000)Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Stochastic Dynamics of Marine Structures (2012)The dynamics of speculative behaviour (1992)Response statistics of nonlinear, compliant offshore structures by the path integral solution method (1993)Stochastic analysis, rough path analysis and fractional Brownian motions (2002)Approaching complexity by stochastic methods: From biological systems to turbulence (2011)A Wong-Zakai theorem for stochastic PDEs (2015)Non-Gaussianclosure techniques for stationary random vibration (1985)An Improved Closure Method for Analysis of Nonlinear Stochastic Systems (1998)Stochastic dynamic response analysis and reliability assessment of non-linear structures under fully non-stationary ground motions (2019)Dynamic response of non-linear systems to poisson-distributed random impulses (1992)A reliability analysis method based on analytical expressions of the first four moments of the surrogate model of the performance function (2018)Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation (2004)
this work references cited by second hop

References

  • 1976Probabilistic Theory of Structural Dynamics1,398 cited
  • 1990Random vibration and statistical linearization995 cited
  • 1990Random vibration and statistical linearization822 cited
  • 1965On the relation between ordinary and stochastic differential equations697 cited
  • 1986Stochastic averaging: An approximate method of solving random vibration problems577 cited
  • 1951On a Formula Concerning Stochastic Differentials369 cited
  • 1984Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations234 cited
  • 1980Non-gaussian closure for random vibration of non-linear oscillators153 cited
  • 1976Approximate analysis of non-linear stochastic systems75 cited

Cited by

  • 1996Exact and approximate solutions for randomly excited MDOF non-linear systems51 cited
  • 1998Multi-Gaussian closure method for randomly excited non-linear systems39 cited
  • 2014Polynomial Correlated Function Expansion for Nonlinear Stochastic Dynamic Analysis30 cited
  • 2020Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process30 cited
  • 1993Approximate solution for nonlinear random vibration problems by partial stochastic linearization20 cited

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2002
Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization
17 cited
  • 2017Nonlinear system stochastic response determination via fractional equivalent linearization and Karhunen–Loève expansion14 cited
  • 2000A new stationary PDF approximation for non-linear oscillators13 cited