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Technical Brief

The Stochastic Response of a Class of Impact Systems Calculated by a New Strategy Based on Generalized Cell Mapping Method

[+] Author and Article Information
Liang Wang, Wei Xu

Department of Applied Mathematics,
Northwestern Polytechnical University,
Xi'an 710129, China

Shichao Ma

Department of Applied Mathematics,
Northwestern Polytechnical University,
Xi'an 710129, China
e-mail: shihchaoma@mail.nwpu.edu.cn

Chunyan Sun

Department of Mathematics and Statistics,
Shandong University at Weihai,
Weihai 264209, China

Wantao Jia

Department of Applied Mathematics,
Northwestern Polytechnical University,
Xi'an 710129, China
e-mail: jiawantao@nwpu.edu.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received August 18, 2017; final manuscript received February 22, 2018; published online March 19, 2018. Assoc. Editor: Walter Lacarbonara.

J. Appl. Mech 85(5), 054502 (Mar 19, 2018) (4 pages) Paper No: JAM-17-1447; doi: 10.1115/1.4039436 History: Received August 18, 2017; Revised February 22, 2018

In this paper, a new strategy based on generalized cell mapping (GCM) method will be introduced to investigate the stochastic response of a class of impact systems. Significant difference of the proposed procedure lies in the choice of a novel impact-to-impact mapping, which is built to calculate the one-step transition probability matrix, and then, the probability density functions (PDFs) of the stochastic response can be obtained. The present strategy retains the characteristics of the impact systems, and is applicable to almost all types of impact systems indiscriminately. Further discussion proves that our strategy is reliable for different white noise excitations. Numerical simulations verify the efficiency and accuracy of the suggested strategy.

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Figures

Grahic Jump Location
Fig. 2

The PDFs of Duffing-Van del Pol system with initial position (0.0.5)

Grahic Jump Location
Fig. 3

The PDFs of Duffing-Van del Pol system with initial position (0,0.1)

Grahic Jump Location
Fig. 4

The PDFs of Reyleigh system with initial position (0,0.2)

Grahic Jump Location
Fig. 5

The PDFs of Reyleigh system with initial position (0,2)

Grahic Jump Location
Fig. 1

Schematic of the impact system with unilateral zero offset barrier

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