Citation map · Study

SZodixStudyAcademic Library

Shelves Open access

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

Wiener Path Integral based response determination of nonlinear systems subject to non-white, non-Gaussian, and non-stationary stochastic excitation

16 references·16 citing·26 second hopsampled

FromToDepth

this work references cited by second hop· second hop is a sample of the most-cited connections

References

2003Stochastic Differential Equations2,978 cited
2007Simulation and the Monte Carlo Method2,454 cited
1976Stochastic Differential Equations: Theory and Applications.2,351 cited
1976Probabilistic Theory of Structural Dynamics1,398 cited
1991Simulation of Stochastic Processes by Spectral Representation1,379 cited
2006Stochastic Differential Equations1,269 cited
1990Random vibration and statistical linearization995 cited
2009Stochastic Dynamics of Structures923 cited
2007Stochastic Differential Equations: Theory and Applications588 cited
1986Stochastic averaging: An approximate method of solving random vibration problems577 cited
1992Random Vibration of Mechanical and Structural Systems493 cited
1993Random vibration of mechanical and structural systems464 cited
2002Stochastic Calculus: Applications in Science and Engineering345 cited
1998Monte Carlo Treatment of Random Fields: A Broad Perspective225 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

Cited by

2020Addressing the curse of dimensionality in stochastic dynamics: a Wiener path integral variational formulation with free boundaries54 cited
2019Wiener path integrals and multi-dimensional global bases for non-stationary stochastic response determination of structural systems47 cited
2020Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process30 cited
2020Stochastic Response Analysis and Reliability-Based Design Optimization of Nonlinear Electromechanical Energy Harvesters With Fractional Derivative Elements29 cited
2019Reliability analysis of nonlinear vibro-impact systems with both randomly fluctuating restoring and damping terms28 cited
2020Stochastic response determination of nonlinear structural systems with singular diffusion matrices: A Wiener path integral variational formulation with constraints27 cited
2020An exact closed-form solution for linear multi-degree-of-freedom systems under Gaussian white noise via the Wiener path integral technique27 cited
2020Functional Series Expansions and Quadratic Approximations for Enhancing the Accuracy of the Wiener Path Integral Technique25 cited
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
2024An extrapolation approach within the Wiener path integral technique for efficient stochastic response determination of nonlinear systems24 cited
2021Survival probability of nonlinear oscillators endowed with fractional derivative element and subjected to evolutionary excitation: A stochastic averaging treatment with path integral concepts21 cited
2020Wiener path integral most probable path determination: A computational algebraic geometry solution treatment18 cited
2020An exact and efficient time-domain method for random vibration analysis of linear structures subjected to uniformly modulated or fully non-stationary excitations17 cited
2019Nonlinear 6D response statistics of a rotating shaft subjected to colored noise by path integration on GPU17 cited
2022A Wiener Path Integral Formalism for Treating Nonlinear Systems with Non-Markovian Response Processes16 cited
2022Exploiting expansion basis sparsity for efficient stochastic response determination of nonlinear systems via the Wiener path integral technique15 cited