Search results for "Wiener path integral"

showing 3 items of 3 documents

An Efficient Wiener Path Integral Technique Formulation for Stochastic Response Determination of Nonlinear MDOF Systems

2015

The recently developed approximate Wiener path integral (WPI) technique for determining the stochastic response of nonlinear/hysteretic multi-degree-of-freedom (MDOF) systems has proven to be reliable and significantly more efficient than a Monte Carlo simulation (MCS) treatment of the problem for low-dimensional systems. Nevertheless, the standard implementation of the WPI technique can be computationally cumbersome for relatively high-dimensional MDOF systems. In this paper, a novel WPI technique formulation/implementation is developed by combining the “localization” capabilities of the WPI solution framework with an appropriately chosen expansion for approximating the system response PDF…

Mechanical EngineeringReliability (computer networking)Monte Carlo methodnonlinear systemCondensed Matter PhysicsDisplacement (vector)Nonlinear systemStochastic dynamicsOrders of magnitude (time)Variational formulationMechanics of MaterialsControl theorystochastic dynamicPath integral formulationBoundary value problemWiener path integralMathematics
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Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral

2014

A novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators endowed with fractional derivatives elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes which rely on a discrete version of the…

Euler-Lagrange equationMechanical EngineeringMonte Carlo methodMathematical analysisAerospace EngineeringOcean EngineeringStatistical and Nonlinear PhysicsProbability density functionFractional derivativeCondensed Matter PhysicsFractional calculusEuler–Lagrange equationNonlinear systemNuclear Energy and EngineeringPath integral formulationNonlinear systemWiener Path IntegralStochastic dynamicFunctional integrationFractional variational problemFractional quantum mechanicsCivil and Structural EngineeringMathematicsProbabilistic Engineering Mechanics
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A Wiener Path Integral Technique for Non-Stationary Response Determination of Nonlinear Oscillators with Fractional Derivative Elements

2014

In this paper a novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators with fractional derivative elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes. In this manner, the analytical Wi…

Hybrid Monte CarloMathematical analysisMonte Carlo methodAnalytical techniquePath integral formulationfractional derivativeProbability density functionFunctional integrationstochastic responseClosed-form expressionWiener path integralMathematicsFractional calculusVulnerability, Uncertainty, and Risk
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