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TECHNICAL PAPERS

# Panel Flutter Model Identification Using the Minimum Model Error Method on the Forced Response Measurements

[+] Author and Article Information
Oleg V. Shiryayev1

Department of Mechanical and Materials Engineering, Wright State University, 3640 Colonel Glenn Hwy., Dayton, OH 45435shiryayev.2@wright.edu

Joseph C. Slater

Department of Mechanical and Materials Engineering, Wright State University, 3640 Colonel Glenn Hwy., Dayton, OH 45435

1

Address all correspondence to this author.

J. Vib. Acoust 128(5), 635-645 (Feb 08, 2006) (11 pages) doi:10.1115/1.2202160 History: Received January 07, 2005; Revised February 08, 2006

## Abstract

This work illustrates application of the minimum model error system identification method to obtain the nonlinear state space models of a fluttering panel. Identification using position and velocity data from forced response of the panel is presented here. The response was numerically simulated using two different discretization approaches: through finite differences and using the Galerkin’s method. Data from two different parts of response time history were considered. First, data where transients due to initial conditions and the forcing were present were used for identification. Then, data when only transients due to forcing were present were used for identification. The models obtained using the forced response of the panel were able to capture the behavior of the true system relatively accurately. Identification of models of different sizes is also discussed. Reduced size models can be successfully created from the forced response data using the minimum model error method. It is demonstrated that the number of degrees of freedom in the model attempted to be identified should be consistent with the number modes observed in the measurements. The response surface method was successfully applied to generate models for various flow regimes.

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## Figures

Figure 1

Panel geometry

Figure 2

POD analysis: energy in the modes

Figure 3

Results from identification using the data from Galerkin’s approach, case 1. True (solid), identified after step 1 (dashed), identified after step 2 (dotted), ξ=0.75. (a) Position data from Galerkin’s approach, case 1. (b) ASD from Galerkin’s appraoch data, case 1.

Figure 4

Results from identification using the data from finite differences approach, case 1. True (solid), identified after step 1 (dashed), identified after step 2 (dotted), ξ=0.75. (a) Position data from finite differences approach, case 1. (b) ASD from finite differences approach data, case 1.

Figure 5

Results from identification using the data from Galerkin’s approach, case 2. True (solid), identified after step 1 (dashed), identified after step 2 (dotted), ξ=0.75. (a) Position data from Galerkin’s approach, case 2. (b) ASD from Galerkin’s approach data, case 2.

Figure 6

Results from identification using the data from finite differences approach, case 2. True (solid), identified after step 1 (dashed), identified after step 2 (dotted), ξ=0.75. (a) Position data from finite differences approach, case 2. (b) ASD from finite differences approach data, case 2.

Figure 7

Noisy displacement measurements. (a) Noisy displacement measurement for DOF 1, Galerkin’s approach. (b) Noisy displacement measurement for DOF 1, finite differences approach.

Figure 8

LCO prediction by models identified from noisy measurements. (a) Model from Galerkin’s approach: true (solid), step 1 (dashed). (b) Model from finite differences approach: true (solid), step 1 (dashed).

Figure 9

Predictions by models of larger sizes. (a) Position prediction by four DOF models. (b) Position prediction by five DOF models. (c) Position prediction by six DOF models.

Figure 10

Prediction by six DOF model identified from measurements with wide bandwidth excitation. (a) Position prediction by six DOF model. (b) ASD for six DOF model data.

Figure 11

Response surface fitted for the coefficient of the x1x22 term

Figure 12

Response surface fitted for the coefficient of the ẋ1 term

Figure 13

LCO amplitude versus Mach number: True (solid), identified three DOF models after step 1 (dashed), experimental points (+)

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