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	1. Reliability of MDOF nonlinear oscillators with fractional derivative damping driven by real noise excitation
	CHEN Lincong
	Mechanics 08 October 2013
	Show/Hide Abstract \| Cite this paper︱Full-text: PDF (0 B)

	Abstract:In this paper, the reliability of multi-degree-of-freedom (MDOF) nonlinear oscillators with fractional derivative damping under real noise excitation is considered. First, the original system is reduced to a set of averaged It? equations by using the stochastic averaging method. Then, the conditional reliability function and the conditional mean of the first passage time are obtained by formulating and solving the backward Kolmogorov equation. Finally, an example is worked out for illustration. .
	TO cite this article:CHEN Lincong. Reliability of MDOF nonlinear oscillators with fractional derivative damping driven by real noise excitation[OL].[ 8 October 2013] http://en.paper.edu.cn/en_releasepaper/content/4562833


	2. A bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping
	CHEN Licong,ZHU Weiqiu
	Mechanics 18 July 2012
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	Abstract:In this paper, a bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping is proposed. First, the partially averaged Itô equations for the energy processes are derived by using the stochastic averaging method. Then, the dynamical programming equations for the control problems of maximizing the reliability function and maximizing the mean first passage time are established from the partially averaged Itô equations by using the dynamical programming principle and solved to obtain the optimal control law. The conditional reliability function and mean first passage time of the optimal control system are obtained by solving the backward Kolmogorov equation and Pontryagin equation associated with the fully averaged Itô equations, respectively. The application of the proposed procedure and effectiveness of the control strategy are illustrated by using two examples. In addition, the effect of fractional derivative order on the reliability of optimally controlled system is examined.
	TO cite this article:CHEN Licong,ZHU Weiqiu. A bounded optimal control for maximizing the reliability of randomly excited nonlinear oscillators with fractional derivative damping[OL].[18 July 2012] http://en.paper.edu.cn/en_releasepaper/content/4485187


	3. First-passage problem of 5DOF strongly nonlinear oscillators under wide-band stochastic excitation
	Wu Yongjun,Gao Yangyan,Zhang Lei
	Mechanics 04 November 2011
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	Abstract:First-passage problem of 5DOF strongly nonlinear oscillators under wide-band stochastic excitations is studied theoretically in this paper. By using stochastic averaging method, the equations of motion of the original system are reduced to a set of averaged Itô stochastic differential equations about the amplitudes. The 6-dimensional backward Kolmogorov equation and the 5-dimensional Pontryagin equation are established. These two high-dimensional partial differential equations are solved by using finite difference method to yield the conditional reliability function and mean first-passage time, respectively. The accuracy of the theoretical method is verified by Monte Carlo digital simulation.
	TO cite this article:Wu Yongjun,Gao Yangyan,Zhang Lei. First-passage problem of 5DOF strongly nonlinear oscillators under wide-band stochastic excitation[OL].[ 4 November 2011] http://en.paper.edu.cn/en_releasepaper/content/4448523


	4. An extended stochastic response surface method for random field problems
	Shuping Huang
	Mechanics 26 April 2006
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	Abstract:An efficient and accurate uncertainty propagation methodology for mechanics problems with random fields is developed in this paper. This methodology is based on the stochastic response surface method (SRSM) which has been previously proposed for problems dealing only with random variables. This paper extends SRSM to problems involving random fields or random processes fields. The favourable property of SRSM lies in that the deterministic computational model can be treated as a black box, as in the case of commercial finite element codes. Numerical examples are used to highlight the features of this technique and to demonstrate the accuracy and efficiency of the proposed method. A comparison with Monte Carlo simulation shows that the proposed method can achieve numerical results close to those from Monte Carlo simulation while dramatically reducing the number of deterministic finite element runs.
	TO cite this article:Shuping Huang. An extended stochastic response surface method for random field problems[OL].[26 April 2006] http://en.paper.edu.cn/en_releasepaper/content/6410

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