Solutions to Stochastic Dynamical Systems with Fractional Derivative Damping
Апстракт
In this paper, the Galerkin method is presented to estimate the approximate stationary and non-stationary responses of nonlinear random dynamical systems with fractional derivative damping. Based on equivalent linearization method, the equation of motion is reverted to a linear equation in terms of envelope and phase process at first. After that, stochastic averaging method is used to get an averaged Ito differential equation with fractional derivative approximated by a periodic function. Finally, the approximate non-stationary probability density function solution of the associated Fokker-Planck equation is obtained by applying the Galerkin method. The application on a Rayleigh oscillator shows that the methods we utilized in this paper are efficient and reliable by comparing the stationary solution between the exact and approximated one.
Извор:
Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of th, 2014, 1949-1963Издавач:
- American Society of Civil Engineers (ASCE)
Колекције
Институција/група
Mašinski fakultetTY - CONF AU - Li, Wei AU - Zhao, Junfeng AU - Trišović, Nataša AU - Zhang, Y. PY - 2014 UR - https://machinery.mas.bg.ac.rs/handle/123456789/1981 AB - In this paper, the Galerkin method is presented to estimate the approximate stationary and non-stationary responses of nonlinear random dynamical systems with fractional derivative damping. Based on equivalent linearization method, the equation of motion is reverted to a linear equation in terms of envelope and phase process at first. After that, stochastic averaging method is used to get an averaged Ito differential equation with fractional derivative approximated by a periodic function. Finally, the approximate non-stationary probability density function solution of the associated Fokker-Planck equation is obtained by applying the Galerkin method. The application on a Rayleigh oscillator shows that the methods we utilized in this paper are efficient and reliable by comparing the stationary solution between the exact and approximated one. PB - American Society of Civil Engineers (ASCE) C3 - Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of th T1 - Solutions to Stochastic Dynamical Systems with Fractional Derivative Damping EP - 1963 SP - 1949 DO - 10.1061/9780784413609.195 ER -
@conference{ author = "Li, Wei and Zhao, Junfeng and Trišović, Nataša and Zhang, Y.", year = "2014", abstract = "In this paper, the Galerkin method is presented to estimate the approximate stationary and non-stationary responses of nonlinear random dynamical systems with fractional derivative damping. Based on equivalent linearization method, the equation of motion is reverted to a linear equation in terms of envelope and phase process at first. After that, stochastic averaging method is used to get an averaged Ito differential equation with fractional derivative approximated by a periodic function. Finally, the approximate non-stationary probability density function solution of the associated Fokker-Planck equation is obtained by applying the Galerkin method. The application on a Rayleigh oscillator shows that the methods we utilized in this paper are efficient and reliable by comparing the stationary solution between the exact and approximated one.", publisher = "American Society of Civil Engineers (ASCE)", journal = "Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of th", title = "Solutions to Stochastic Dynamical Systems with Fractional Derivative Damping", pages = "1963-1949", doi = "10.1061/9780784413609.195" }
Li, W., Zhao, J., Trišović, N.,& Zhang, Y.. (2014). Solutions to Stochastic Dynamical Systems with Fractional Derivative Damping. in Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of th American Society of Civil Engineers (ASCE)., 1949-1963. https://doi.org/10.1061/9780784413609.195
Li W, Zhao J, Trišović N, Zhang Y. Solutions to Stochastic Dynamical Systems with Fractional Derivative Damping. in Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of th. 2014;:1949-1963. doi:10.1061/9780784413609.195 .
Li, Wei, Zhao, Junfeng, Trišović, Nataša, Zhang, Y., "Solutions to Stochastic Dynamical Systems with Fractional Derivative Damping" in Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management - Proceedings of th (2014):1949-1963, https://doi.org/10.1061/9780784413609.195 . .