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Moment Lyapunov
exponents and stochastic stability of coupled viscoelastic
systems driven by white noise
Jian Deng, Wei-Chau Xie and Mahesh D. Pandey |
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Vol. 9 (2014), No. 1, 27–50
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Abstract |
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The moment and almost-sure stochastic stability of two-degree-of-freedom coupled viscoelastic systems, under parametric excitation of white noise, are investigated through moment Lyapunov exponents and Lyapunov exponents, respectively. The system of stochastic differential equations of motion is first decoupled by using the method of stochastic averaging for dynamic systems with small damping and weak excitations. Then a new scheme for determining the moment Lyapunov exponents is proposed for a coupled viscoelastic system. The largest Lyapunov exponent is calculated through its relation with moment Lyapunov exponent. The moment and almost-sure stability boundaries and critical excitation are obtained analytically. These analytical results are confirmed by numerical simulation. As an application example, the stochastic stability of flexural-torsional viscoelastic beam is studied. It is found that, under white noise excitation, the parameters of damping and the viscoelastic intensity have stabilizing effects on the moment and almost-sure stability. However, viscosity parameter plays a destabilizing role. The stability index decreases from positive to negative values with the increase of the amplitude of noise power spectrum, which suggests that the noise destabilize the system. These results are useful in engineering applications. |
Keywords
stochastic stability, moment Lyapunov exponents, white
noise, viscoelasticity, coupled system
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Milestones
Received: 14 April 2013
Revised: 26 December 2013
Accepted: 11 February 2014
Published: 23 March 2014
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Authors |
| Jian Deng | |
| Department of Civil
Engineering Lakehead University Thunder Bay, ON P7B 5E1 Canada |
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| Wei-Chau Xie | |
| Department of Civil and
Environmental Engineering University of Waterloo Waterloo, ON N2L 3G1 Canada |
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| Mahesh D. Pandey | |
| Department of Civil and
Environmental Engineering University of Waterloo Waterloo, ON N2L 3G1 Canada |
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