Research Papers

Stochastic Analysis of a Nonlinear Forced Panel in Subsonic Flow With Random Pressure Fluctuations

[+] Author and Article Information
Peng Li

e-mail: meiyongyuandeze@163.com,

Guo Chen

School of Mechanics and Engineering,
Southwest Jiaotong University,
Chengdu 610031,China

Manuscript received September 26, 2011; final manuscript received July 23, 2012; accepted manuscript posted October 10, 2012; published online May 16, 2013. Assoc. Editor: Nesreen Ghaddar.

J. Appl. Mech 80(4), 041005 (May 16, 2013) (10 pages) Paper No: JAM-11-1346; doi: 10.1115/1.4007819 History: Received September 26, 2011; Revised July 23, 2012; Accepted October 10, 2012

The stochastic behavior of a two-dimensional nonlinear panel subjected to subsonic flow with random pressure fluctuations and an external forcing is studied in this paper. The total aerodynamic pressure is considered as the sum of two parts, one given by the random pressure fluctuations on the panel in the absence of any panel motion, and the other due to the panel motion itself. The random pressure fluctuations are idealized as a zero mean Brownian motion. Galerkin method is used to transform the governing partial differential equation to a series of ordinary differential equations. The closed moment equations are obtained by the Itô differential rule and Gauss truncation. The stability and complex responses of the moment equations are presented in theoretical and numerical analysis. Results show that a bifurcation of fixed points occurs and the bifurcation point is determined as functions of noise spectral density, dynamic pressure, and panel structure parameters; the chaotic response regions and periodic response regions appear alternately in parameter spaces, the periodic responses trajectories change rhythmically, and the route from periodic responses to chaos is via doubling-period bifurcation. The treatment suggested in this paper can also be extended for the other fluid-structure dynamic systems.

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Fig. 1

Schematic diagram of a thin panel in subsonic flow with an external forcing

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Fig. 2

Schematic diagram of the number of fixed points and their stabilities of Eq. (22) in parameter space Δλ-D1r

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Fig. 3

When Δλ=1.3,Ω=1.0,f=0.025, the responses Eu of Eq. (22) before and after bifurcation: (a) before bifurcation D1r=0.0015; (b) after bifurcation D1r=0.0010

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Fig. 4

When Ω=1.0,f=0.025,D1r=0.0015, the response Eu of Eq. (22) before and after bifurcation: (a) before bifurcation Δλ=-1.5; (b) after bifurcation Δλ=1.5

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Fig. 5

Two-parameter spaces, sketches of boundaries for different types of response: (a) (f - D1r) space for Δλ=2.0, Ω=1.0; (b) (f - Δλ) space for D1r=0.0005, Ω=1.0. The different periodic responses are P+ or P- in ⋄-regions, P(1,1) in ○-regions, P(1,2) or P(2,1) in ▵-regions, P(2,2) in □-regions, respectively. The responses in ×-regions are chaos.

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Fig. 7

(Eu,Ev)-phase plots of periodic responses to chaos by period-doubling process for D1r=0.0025, Δλ=2.0 with initial condition (Eu)0=0.1: (a) period-1 response; (b) period-2 response; (c) period-4 response, (d) chaos

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Fig. 8

Poincaré maps of different f with initial condition (Eu)0=0.1: (a) corresponding to Fig. 7(b); (b) corresponding to Fig. 7(d)

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Fig. 9

Maximum Lyapunov exponents of different f with initial condition (Eu)0=0.1: (a) corresponding to Fig. 7(b); (b) corresponding to Fig. 7(d)




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