Citation map · Study

SZodixStudyAcademic Library

Shelves Open access

Study · an open academic library·Metadata from OpenAlex (CC0)·Shelves·OpenAlex metadata, de-duplicated

Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process

16 references·7 citing·30 second hop

FromToDepth

this work references cited by second hop

References

1976Probabilistic Theory of Structural Dynamics1,398 cited
1990Random vibration and statistical linearization995 cited
2009Stochastic Dynamics of Structures923 cited
1951On stochastic differential equations832 cited
2014Stochastic Differential Equations574 cited
1997A state-of-the-art report on computational stochastic mechanics424 cited
1951On a Formula Concerning Stochastic Differentials369 cited
2004Probability density evolution method for dynamic response analysis of structures with uncertain parameters368 cited
1995Applied non-Gaussian processes : examples, theory, simulation, linear random vibration, and MATLAB solutions288 cited
2000Efficient path integration methods for nonlinear dynamic systems250 cited
1984Cumulant-neglect closure for non-linear oscillators under random parametric and external excitations234 cited
2005The probability density evolution method for dynamic response analysis of non‐linear stochastic structures219 cited
2019Direct probability integral method for stochastic response analysis of static and dynamic structural systems201 cited
1993Response statistics of nonlinear, compliant offshore structures by the path integral solution method187 cited
2011

Only edges whose both ends are imported exist here. Widen the year window, or show the whole map. Back to the work

An analytical Wiener path integral technique for non-stationary response determination of nonlinear oscillators

181 cited

1970First-crossing probabilities of the linear oscillator168 cited

Cited by

2023A Wiener path integral technique for determining the stochastic response of nonlinear oscillators with fractional derivative elements: A constrained variational formulation with free boundaries24 cited
2022Stochastic dynamic analysis of nonlinear MDOF systems under combined Gaussian and Poisson noise excitation based on DPIM19 cited
2022A Wiener Path Integral Formalism for Treating Nonlinear Systems with Non-Markovian Response Processes16 cited
2022Response Statistics of Single-Degree-of-Freedom Systems with Lévy Noise by Improved Path Integral Method14 cited
2023Response and reliability of suspension system under stochastic and periodic track excitations by path integral method13 cited
2024Stochastic dynamics of mechanical systems with impacts via the Step Matrix multiplication based Path Integration method12 cited
2022Systematic matrix formulation for efficient computational path integration12 cited