Moment Lyapunov exponents of a two-dimensional system under both harmonic and white noise parametric excitations |
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| Institution: | 1. AMEC Nuclear Safety Solutions (NSS) Limited, Toronto M5G1X6, Canada;2. Department of Civil Engineering, Southwest Jiaotong University, Emei 614202, China;3. School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China;4. Department of Civil and Environmental Engineering, University of Waterloo, Waterloo N2L3G1, Canada;1. University of Niš, Department of Mechanical Engineering, A. Medvedeva 14, 18000 Niš, Serbia;2. Mathematical Institute of the SANU, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11001 Belgrade, Serbia;1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;2. School of Mechanical Engineering, Shanghai Institute of Technology, Shanghai 201418, China;3. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China;4. Department of Mechanics, Shanghai University, Shanghai 200444, China |
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| Abstract: | The moment Lyapunov exponents and the Lyapunov exponents of a 2D system under both harmonic and white noise excitations are studied. The moment Lyapunov exponents and the Lyapunov exponents are important characteristics determining the moment and almost-sure stability of a stochastic dynamical system. The eigenvalue problem governing the moment Lyapunov exponent is established. A singular perturbation method is applied to solve the eigenvalue problem to obtain second-order, weak noise expansions of the moment Lyapunov exponents. The influence of the white noise excitation on the parametric resonance due to the harmonic excitation is investigated. |
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