Abstract
This paper introduces higher-order solutions of the quadratic nonlinear stochastic oscillatory equation. Solutions with different orders and different number of corrections are obtained with the WHEP technique which uses the WienerHermite expansion and perturbation technique. The equivalent deterministic equations are derived for each order and correction. The solution ensemble average and variance are estimated and compared for different orders, different number of corrections and different strengths of the nonlinearity. The solutions are simulated using symbolic computation software such as Mathematica. The comparisons between different orders and different number of corrections show the importance of higher-order and higher corrected WHEP solutions for the nonlinear stochastic differential equations.
Highlights
Analysis of the response of linear and nonlinear systems subjected to random excitations is of considerable interest to the fields of mechanical and structural engineering [1]
This paper introduces higher-order solutions of the quadratic nonlinear stochastic oscillatory equation
Solutions with different orders and different number of corrections are obtained with the WHEP technique which uses the WienerHermite expansion and perturbation technique
Summary
Analysis of the response of linear and nonlinear systems subjected to random excitations is of considerable interest to the fields of mechanical and structural engineering [1]. According to [3], the solution of stochastic partial differential equations (SPDEs) using Wiener-Hermite expansion (WHE) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. Since Cameron and Martin’s work, WHE has become a useful tool in stochastic analysis involving white noise (Brownian motion) [3] Another formulation was suggested and applied by Meecham and his co-workers [13, 14]. In the current work the generalized WHEP technique developed in [22] is used to derive higher-order with higher corrections system of equations for the quadratic nonlinear stochastic oscillatory equation and solve them.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
