Stability of a nonlinear second order equation under parametric bounded noise excitation

13th International Conference on Motion and Vibration Control; 12th International Conference on Recent Advances in Structural Dynamics

Wiebe, Richard^1 ; Xie, Wei-Chau^2

Department of Civil and Environmental Engineering, University of Washington, Seattle

WA, United States^1

Department of Civil and Environmental Engineering, University of Waterloo, Waterloo

ON, Canada^2

关键词: Analytical approximation;    Axially loaded columns;    Bounded noise excitations;    Process deviations;    Second order nonlinear equations;    Second-order equation;    Stability equations;    Stationary solutions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/744/1/012173/pdf
DOI  :  10.1088/1742-6596/744/1/012173

来源: IOP

【 摘 要 】

The motivation for the following work is a structural column under dynamic axial loads with both deterministic (harmonic transmitted forces from the surrounding structure) and random (wind and/or earthquake) loading components. The bounded noise used herein is a sinusoid with an argument composed of a random (Wiener) process deviation about a mean frequency. By this approach, a noise parameter may be used to investigate the behavior through the spectrum from simple harmonic forcing, to a bounded random process with very little harmonic content. The stability of both the trivial and non-trivial stationary solutions of an axially-loaded column (which is modeled as a second order nonlinear equation) under parametric bounded noise excitation is investigated by use of Lyapunov exponents. Specifically the effect of noise magnitude, amplitude of the forcing, and damping on stability of a column is investigated. First order averaging is employed to obtain analytical approximations of the Lyapunov exponents of the trivial solution. For the non-trivial stationary solution however, the Lyapunov exponents are obtained via Monte Carlo simulation as the stability equations become analytically intractable.