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Research Papers

Influence of Nonzero Mean Impulse Amplitudes on the Response Statistics of Dynamical Systems

[+] Author and Article Information
Siu-Siu Guo

Associate Professor
School of Civil Engineering,
Xi'an University of Architecture and Technology,
Xi'an 710055, China
e-mail: siusiuguo@xauat.edu.cn

Qing-Xuan Shi

Professor
School of Civil Engineering,
Xi'an University of Architecture and Technology,
Xi'an 710055, China
e-mail: shiqx@xauat.edu.cn

Hai-Tao Zhu

Associate Professor
State Key Laboratory of Hydraulic Engineering
Simulation and Safety,
Tianjin University,
Tianjin 300072, China
e-mail: htzhu@tju.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 26, 2016; final manuscript received September 29, 2016; published online January 19, 2017. Assoc. Editor: Bogdan I. Epureanu.

J. Comput. Nonlinear Dynam 12(4), 041002 (Jan 19, 2017) (9 pages) Paper No: CND-16-1102; doi: 10.1115/1.4034996 History: Received February 26, 2016; Revised September 29, 2016

This paper investigates the influences of nonzero mean Poisson impulse amplitudes on the response statistics of dynamical systems. New correction terms of the extended Itô calculus, as a generalization of the Wong–Zakai correction terms in the case of normal excitations, are adopted to consider the non-normal property in the case of Poisson process. Due to these new correction terms, the corresponding drift and diffusion coefficients of Fokker–Planck–Kolmogorov (FPK) equation have to be modified and they become more complicated. Herein, the exponential–polynomial closure (EPC) method is employed to solve such a complex FPK equation. Since there are no exact solutions, the efficiency of the EPC method is numerically evaluated by the simulation results. Three examples of different excitation patterns are considered. Numerical results indicate that the influence of nonzero mean impulse amplitudes on system responses depends on the excitation patterns. It is negligible in the case of parametric excitation on displacement. On the contrary, the influence becomes significant in the cases of external excitation and parametric excitation on velocity.

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Figures

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Fig. 1

PDF and logarithmic PDF of displacement in example 1: (a) PDF of displacement and (b) Log (PDF) of displacement

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Fig. 2

PDF and logarithmic PDF of velocity in example 1: (a) PDF of velocity and (b) log (PDF) of velocity

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Fig. 3

Statistics of displacement varying with mean of impulse amplitude in example 1: (a) mean and skewness of displacement and (b) variance and kurtosis of displacement

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Fig. 4

Statistics of velocity varying with mean of impulse amplitude in example 1: (a) mean and skewness of velocity and (b) variance and kurtosis of velocity

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Fig. 5

PDF and logarithmic PDF of displacement in example 2: (a) PDF of displacement and (b) log (PDF) of displacement

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Fig. 6

PDF and logarithmic PDF of velocity in example 2: (a) PDF of velocity and (b) log (PDF) of velocity

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Fig. 7

Statistics of system responses varying with mean of impulse amplitude in example 2: (a) variance and kurtosis of displacement and (b) variance and kurtosis of velocity

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Fig. 8

PDF and logarithmic PDF of displacement in example 3: (a) PDF of displacement and (b) log (PDF) of displacement

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Fig. 9

PDF and logarithmic PDF of velocity in example 3: (a) PDF of velocity and (b) log (PDF) of velocity

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Fig. 10

Statistics of system responses varying with mean of impulse amplitude in example 3: (a) variance and kurtosis of displacement and (b) variance and kurtosis of velocity

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