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Research Papers

Reliability of Strongly Nonlinear Single Degree of Freedom Dynamic Systems by the Path Integration Method

[+] Author and Article Information
Daniil Iourtchenko

Department of Mathematical Sciences, Saint Petersburg State Polytechnical University, Saint Petersburg, 195251 Russiadaniil@phmf.spbstu.ru

Eirik Mo1

Department of Mathematical Sciences, Norwegian University of Science and Technology, NO-7491 Trondheim, Norwaymo@math.ntnu.no

Arvid Naess

Department of Mathematical Sciences, Centre for Ships and Ocean Structures, Norwegian University of Science and Technology, NO-7491 Trondheim, Norwayarvidn@math.ntnu.no

1

Corresponding author.

J. Appl. Mech 75(6), 061016 (Aug 21, 2008) (8 pages) doi:10.1115/1.2967896 History: Received May 08, 2007; Revised June 23, 2008; Published August 21, 2008

This paper presents a first passage type reliability analysis of strongly nonlinear stochastic single-degree-of-freedom systems. Specifically, the systems considered are a dry friction system, a stiffness controlled system, an inertia controlled system, and a swing. These systems appear as a result of implementation of the quasioptimal bounded in magnitude control law. The path integration method is used to obtain the reliability function and the first passage time.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Probability density of time to failure for the dry friction problem with reliability level 2.5 standard deviations and r=0.15 for the one- and two-sided cases

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Figure 2

One-sided reliability function of the dry friction system for different levels of p

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Figure 3

Probability density of time to failure for the linear system with reliability level 2.5 standard deviations and r=0.1, 0.3, and 0.5

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Figure 4

Probability density of time to failure for the stiffness control problem with reliability level 2.5 standard deviations and r=0.1,0.3,0.3, and 0.5

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Figure 5

Reliability function for the stiffness control problem with one-sided barrier for different levels of p

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Figure 6

Probability density of time to failure for the inertia control problem with reliability level 2.5 standard deviations and r=0.1, 0.3, and 0.5

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Figure 7

Reliability function for the inertia control problem with one-sided barrier for different levels of p

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Figure 8

Probability density of time to failure for the swing problem with reliability level 2.5 standard deviations and r=0.1, 0.3, and 0.5

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Figure 9

Reliability function for the swing problem with one-sided barrier for different levels of p

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