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A probabilistic linearization method for non-linear systems subjected to additive and multiplicative excitations
15 references·1 citing·30 second hop
A probabilistic linearization method for non-linear systems subjected to additive and multiplicative excitations (2006)A probabilistic linearization method for …A non-Gaussian stochastic linearization method (2006)A non-Gaussian stochastic lin…Linearization in Analysis of Nonlinear Stochastic Systems: Recent Results—Part I: Theory (2005)Linearization in Analysis of …Stochastic Linearization Technique: A New Interpretation and a Selective Review (2000)Stochastic Linearization Tech…Approximate solutions for non-linear random vibration problems (1996)Approximate solutions for non…Stochastic linearization of MDOF systems under parametric excitations (1992)Stochastic linearization of M…Non-Gaussian Linearization Method for Stochastic Parametrically and Externally Excited Nonlinear Systems (1992)Non-Gaussian Linearization Me…A new approximate solution technique for randomly excited non-linear oscillators—II (1992)A new approximate solution te…Non-Gaussian linearization — an efficient tool to analyse nonlinear MDOF-systems (1991)Non-Gaussian linearization — …Linearization in Analysis of Nonlinear Stochastic Systems (1991)Linearization in Analysis of …Random vibration and statistical linearization (1990)Random vibration and statisti…Random vibration and statistical linearization (1990)Random vibration and statisti…Methods and Gaussian Criterion for Statistical Linearization of Stochastic Parametrically and Externally Excited Nonlinear Systems (1989)Methods and Gaussian Criterio…Comparison of Gaussian closure technique and equivalent linearization method (1987)Comparison of Gaussian closur…Probabilistic Structural Dynamics: Advanced Theory and Applications (1967)Probabilistic Structural Dyna…On the relation between ordinary and stochastic differential equations (1965)On the relation between ordin…A sampling-variability-free dimension-reduced probability density evolution equation method for high-dimensional nonlinear stochastic dynamic analysis (2025)A sampling-variability-free d…Probabilistic Theory of Structural Dynamics (1976)Exact and approximate solutions for randomly excited MDOF non-linear systems (1996)Multi-Gaussian closure method for randomly excited non-linear systems (1998)Polynomial Correlated Function Expansion for Nonlinear Stochastic Dynamic Analysis (2014)Stochastic Differential Equations: Theory and Applications. (1976)Modified stochastic linearization technique for colored noise excitation of Duffing oscillator (1994)Influences of system uncertainties on the numerical transfer path analysis of engine systems (2017)Efficient stochastic response analysis of high-dimensional nonlinear systems subject to multiplicative noise via the DR-PDEE (2025)Applied non-Gaussian processes : examples, theory, simulation, linear random vibration, and MATLAB solutions (1995)Stochastic Analysis (1997)The Duffing oscillator under combined periodic and random excitations (2012)Method for Random Vibration of Hysteretic Systems (1976)Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations (1984)Stochastic Linearization in Structural Dynamics (1988)Comparison between equivalent linearization and Gaussian closure for random vibration analysis of several nonlinear systems (1990)Probability density equivalent linearization technique for nonlinear oscillator with stochastic excitations (1998)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)Linearization in Analysis of Nonlinear Stochastic Systems, Recent Results—Part II: Applications (2005)Sixty years of stochastic linearization technique (2016)A novel local stochastic linearization method via two extremum entropy principles (2002)Application and extension of the stochastic linearization by Anh and Di Paola (2008)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)Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation (2004)Applications of Hilbert–Huang transform to non‐stationary financial time series analysis (2003)The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain parameters (2006)The principle of preservation of probability and the generalized density evolution equation (2006)
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References

  • 1990Random vibration and statistical linearization995 cited
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  • 1967Probabilistic Structural Dynamics: Advanced Theory and Applications629 cited
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  • 2005Linearization in Analysis of Nonlinear Stochastic Systems: Recent Results—Part I: Theory86 cited
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  • 2000Stochastic Linearization Technique: A New Interpretation and a Selective Review38 cited
  • 1987Comparison of Gaussian closure technique and equivalent linearization method27 cited
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  • 1989Methods and Gaussian Criterion for Statistical Linearization of Stochastic Parametrically and Externally Excited Nonlinear Systems20 cited
  • 1992Non-Gaussian Linearization Method for Stochastic Parametrically and Externally Excited Nonlinear Systems15 cited

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1991
Non-Gaussian linearization — an efficient tool to analyse nonlinear MDOF-systems
12 cited

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  • 2025A sampling-variability-free dimension-reduced probability density evolution equation method for high-dimensional nonlinear stochastic dynamic analysis8 cited