A computational framework for mean square responses of bidirectional nonlinear systems under correlated stochastic excitation. (14th April 2022)

• Record Type: Journal Article
• Authors: Gogoi, Ankush; Panda, Satyam; Hazra, Budhaditya
• Is Part Of: Journal of sound and vibration. Volume 523(2022)
• Publication Date: 2022-04-14
• Subjects: Correlated Wiener process -- Stochastic integration scheme -- Bidirectional system -- Nonlinear system -- Mean square response -- Torsionally coupled systems; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2021.116689
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: A mathematical framework using Ito–Taylor expansion based stochastic integration scheme for planar structural systems subjected to correlated bidirectional excitation at the base is presented. The bidirectional excitation is modeled using correlated Wiener processes. Instead of simple lumped mass representation of structural systems, a more realistic planar multidirectional model is adopted here. Such assumption adequately captures the behavior of systems under real ground excitation which are often multidimensional in nature. The bidirectional excitation model is developed using a mathematically rigorous framework of correlated Wiener derivatives, exploiting the relationship between Wiener and white noise processes, something that is rarely adopted in literature. An Ito–Taylor expansion based Taylor 1.5 integration scheme is developed first for generating system responses, and, the same Ito–Taylor based scheme is utilized to create an automated framework for the evolution of mean-square responses, a manually difficult exercise otherwise. The proposed framework facilitates the development and simultaneous evaluation of n + n C 2 (where, n is the number of system states) mean square equations after obtaining the mean square terms using Kronecker product. Extensive simulation studies are carried out for a torsionally coupled linear bidirectional frame, stochastic bidirectional duffing system and a Bouc–Wen hysteretic system at the base. The results for each of the case studies show that non-accounting of correlation in the bidirectional excitation leads to as much as 30% error in the estimation of displacement mean square responses. Highlights: An Ito-calculus based framework for bidirectional correlated stochastic excitation is proposed. Bidirectional excitation is modeled using correlated Wiener process. Torsionally coupled linear and nonlinear planar structural systems are considered. Automated framework for mean square response estimation is developed. Effect of correlation on response statistics is demonstrated.