Research Papers

Extreme-Value-Based Statistical Bounding of Low, Mid, and High Frequency Responses of a Forced Plate With Random Boundary Conditions

[+] Author and Article Information
A. Seçgin

J. F. Dunne1

L. Zoghaib

School of Engineering and Design,  The University of Sussex, Falmer, Brighton BN1 9QT, UK


Corresponding author.

J. Vib. Acoust 134(2), 021003 (Jan 13, 2012) (12 pages) doi:10.1115/1.4005019 History: Received May 26, 2010; Revised July 02, 2011; Published January 13, 2012; Online January 13, 2012

The problem of statistically bounding the response of an engineering structure with random boundary conditions is addressed across the entire frequency range: from the low, through the mid, to the high frequency region. Extreme-value-based bounding of both the FRF and the energy density response is examined for a rectangular linear plate with harmonic point forcing. The proposed extreme-value (EV) approach, previously tested only in the low frequency region for uncoupled and acoustically-coupled uncertain structures, is examined here in the mid and high frequency regions in addition to testing at low frequencies. EV-based bounding uses an asymptotic threshold exceedance model of Type-I, to extrapolate the m-observational return period to an arbitrarily-large batch of structures. It does this by repeatedly calibrating the threshold model at discrete frequencies using a small sample of response data generated by Monte Carlo simulation or measurement. Here the discrete singular convolution (DSC) method – a transfrequency computation approach for deterministic vibration - is used to generate Monte Carlo samples. The accuracy of the DSC method is first verified (i) in terms of the spatial distribution of total energy density and (ii) across the frequency range, by comparison with a mode superposition method and Statistical Energy Analysis (SEA). EV-based bound extrapolations of the receptance FRF and total energy density are then compared with: (i) directly-estimated bounds using a full set of Monte Carlo simulations and (ii) with total mean energy levels obtained with SEA. This paper shows that for a rectangular plate structure with random boundary conditions, EV-based statistical bounding of both the FRF and total energy density response is generally applicable across the entire frequency range.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 4

Hasofer-Wang hypothesis tests at (a) 130 Hz, (b) 132.5 Hz, (c) 367.5 Hz, (d) 370 Hz, and FRF Receptance Bounds: (e) 10–250 Hz, (f) 250–500, with confidence intervals: (g) 100–150 Hz and (h) 350–400 Hz

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Figure 5

Hasofer-Wang hypothesis tests at (a) 720 Hz, (b) 725 Hz, (c) 1547.5 Hz, (d) 1550 Hz, and FRF Receptance Bounds: (e) 500–1000 Hz, (f) 1000–2000, with confidence intervals: (g) 700–800 Hz and (h) 1400–1600 Hz

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Figure 6

Hasofer-Wang hypothesis tests at: (a) 2545 Hz, (b) 2550 Hz, (c) 4160 Hz, (d) 4165 Hz, and FRF Receptance Bounds: (e) 2000–3000 Hz, (f) 3000–5000, with confidence intervals: (g) 2400–2600 Hz and (h) 4100–4400 Hz

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Figure 1

DSC discretization for a plate (Structure points: ir=0,1,2,…,Nr-1, r:x,y)

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Figure 2

Spatial response of a simply-supported plate subjected to the point force: (a) at 100 Hz (η=0.01), (b) at 100 Hz (η=0.1), (c) at 500 Hz (η=0.01), (d) at 500 Hz (η=0.1), (e) at 1000 Hz (η=0.01), (f) at 1000 Hz (η=0.1), (g) at 2500 Hz (η=0.01), (h) at 2500 Hz (η=0.1), (i) at 5000 Hz (η=0.01), (j) at 5000 Hz (η=0.1), (___: Analytical solution, ×: DSC) (spatial response at y = 0.5 m)

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Figure 3

Frequency response functions and modal properties for a simply-supported plate with η=0.01: (a) Receptance FRF, (b) Total energy density (___: Analytical solution, ×: DSC; - - -: SEA), (c) Modal overlap factor and modal density

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Figure 7

Total Energy Density Bounds: (a) 10–250 Hz, (b) 250–500 Hz, (c) 500–1000 Hz, (d) 1000–2000 Hz, (e) 2000–3000 Hz, and (f) 3000–5000 Hz



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