Correlation of the Vibroacoustic Response of Structural ... of the Vibroacoustic ... Isight for use...

ATA Engineering, Inc.

Date:Prepared by:Prepared for:

May 15, 2012

11995 El Camino Real, Suite 200

San Diego, CA 92130

T 858.480.2000

F 858.792.8932

www.ata-e.com

Correlation of the VibroacousticResponse of Structural Panels with Isight for use in Statistical Energy Analysis in Aerospace Applications

Cory Rupp

Lina Maricic

2012 SIMULIA

Community

Conference

11995 El Camino Real, Suite 200 | San Diego, CA 92130 | T 858.480.2000 | F 858.792.8932 | www.ata-e.com

SCC 2012

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Outline

• Objectives and background

• Overview of the correlation process

• Example correlation problem of a sandwich panel

• Example correlation problem of a ribbed panel

• Potential use cases for Isight in vibroacoustic

analysis

• Conclusions


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Objectives and Background

• Vibroacoustic analysis at high frequency is often performed by statistical

energy analysis (SEA) using analysis packages such as VA-One.

• A difficulty in performing SEA on complex aerospace structures is

ensuring that the SEA subsystem (e.g. a structural panel) properly

represents the actual structure.

• The model is often checked by comparing the response of a subsystem

to that of a refined finite element (FE) mesh of the subsystem.

• However, modifying the SEA properties to improve the correlation

between the SEA and FE responses is often cumbersome and time-

consuming, primarily involving guess-and-check work.

• To alleviate the difficulties in this process, we have developed a

methodology and an interface between SIMULIA’s Isight simulation

management software and VA-One that automates the correlation

process.

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1. Use Isight to drive an optimization algorithm and make changes to design

variables.

2. Use VA-One to solve vibroacoustic problems for a set of design variables and

return the vibroacoustic response. Control via Matlab-based API.

3. Use Matlab as an interface between Isight and VA-One and to calculate the

objective function.

Sim-flow

Data-flow

Methodology Setup:

Isight + Matlab + VA-One


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• Several objective function formulations were tested when developing the methodology for the correlation process.

• The formulation found to perform the best resembles a weighted least-squares approach:

• More weight on high frequencies to emphasize more accurate solution when SEA has more modes-in-band.

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Simulation

(SEA)

response

Target

(FE)

response

Weight

function

( More weight on higher frequencies)

Objective Function Resembles a

Weighted Least-Squares Approach


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Example 1:

Conical Sandwich Panel

• Conical sandwich panel

properties:

- 0.75” honeycomb Aluminum core

- 0.04” carbon fiber composite

facesheets

- 50” maximum radius, 30” in height

at 30°

• 109 modes calculated up to

4,600 Hz in NX Nastran

- Free-free boundary condition

- First bending mode is 126 Hz

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SCC 2012

FEA and SEA Models in VA-One

• FE subsystem of the sandwich panel created in VA-One

- Modes imported into VA-One

- Vibroacoustic solution to 4000 Hz in 1/42 octave bands

- Panel-averaged vibroacoustic acceleration response

recovered and converted to 1/3 octave bands

• SEA subsystem of the same sandwich panel created in

VA-One as “singly curved shell”

- Default properties used as the “initial guess”


• Diffuse acoustic field (DAF) applied on both subsystems

• Four “dummy” SEA panels were connected to the

boundaries of both FE and SEA subsystems

- Response of FEM highly dependent on boundary conditions,

but not the case for SEA

- “Dummy” SEA panels ensure appropriate comparison

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FE

SEA

“Dummy”

SEA

panels


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• Panel-averaged acceleration response is under-predicted at high frequencies

• The low frequency SEA response can only capture the general trend because of the modal nature of the response

“Initial Guess” Model Under-

Predicts Response Above 800 Hz.

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• SEA subsystem design variables:

- Material densities of core and facesheets

- Thicknesses of core and facesheets

- Panel radius

• Optimization algorithms used:

- Modified method of feasible directions (MMFD)

- Gradient based algorithm

- Default parameters used

- Downhill simplex (DS)

- Simplex based exploratory algorithm

- Default parameters used

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Isight Optimization Tools Used to

Improve Correlation


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Both Algorithms Performed Equally

Well at Improving Correlation

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Low frequency response ( < 600Hz)

unchanged, because of low modes-in-

band for SEA to conform to variation

in FE response.

• Both optimization algorithms improve correlation.

• Objective function value improved from 11.1 to:• MMFD – 3.95

at 89 function evaluations

• DS – 4.18 at 64 function evaluations


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Comparison of Initial and Optimized

SEA Panel Properties

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Sandwich panel property Initial guessOpt -

MMFD

Opt -

DS

Core thickness (in) 0.75 0.54 0.47

Core density (lbm/in³) 0.0018 0.0016 0.0017

Facesheet thickness (in) 0.04 0.042 0.050

Facesheet density (lbm/in³) 0.0654 0.0623 0.0706

Radius of curvature (in) 46.75 39.37 40.39

• Final designs reveal relative sensitivities of design variables

near the correlated design point.

• The panel is most sensitive to core thickness.


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Example 2:

Cylindrical Ribbed Panel

• Cylindrical ribbed panel properties:

- Varying thickness facesheet

- Varying thickness ribs spaced 4.5” apart

- 36” in height, 50” radius of curvature, 60°span

- Titanium used for both facesheet and ribs

• 368 modes calculated up to 3700 Hz in

NX Nastran

- Free-free boundary condition

- First bending mode is 35 Hz

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Ribbed Panel FEA and SEA Models

in VA-One

• FE subsystem of the ribbed panel created in VA-

One

- Modes imported into VA-One

- Vibroacoustic solution to 3150 Hz in 1/42 octave

bands

- Panel-averaged vibroacoustic acceleration response

recovered and converted to 1/3 octave bands

• SEA subsystem of the same ribbed panel created

in VA-One

- Default properties used as the “initial guess”


• DAF applied on both FE and SEA subsystems

• Four “dummy” SEA panels were connected to the

boundaries of the FE and SEA subsystems

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FE

SEA

“Dummy”

SEA

panels


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• Clearly poor correlation at most frequencies

• Reasonable modes-in-band (MIB) only above ~500 Hz

• Very difficult to correlate by hand because of MIB “dropouts”

• Nonlinear relationship with design variables

Poor Correlation Between “Initial

Guess” and FE Models


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• SEA subsystem design variables:- Material density

- Facesheet thickness

- Offset of the ribs from the facesheet

- Spacing between ribs

• Optimization algorithms used:- Multi-island genetic algorithm (MIGA)

- Number of islands: 5

- Pointer algorithm- Combination of several different types of

algorithms

- Allowable job time set to 1 hour

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Isight Optimization Tools Used to

Improve Correlation


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Both Algorithms Significantly

Improved Overall Correlation

• Correlation is significantly improved, especially at high frequency

• Objective function value improved from 85.6 to:• MIGA – 6.83 at

501 function evaluations

• Pointer – 3.22 at 692 function evaluations

Low frequency response difficult to

correlate because of few modes-in-

band.


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Comparison of Initial and Optimized

SEA Ribbed Panel Properties

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Ribbed panel property Initial guessOpt -

Pointer

Opt -

MIGA

Panel skin density (lbm/in³) 0.16 0.17 0.14

Panel skin thickness (in) 0.17 0.14 0.16

Rib 1 spacing (in) 4.5 7.05 3.32

Rib 1 offset (in) 0.75 1.83 2.76

Rib 2 spacing (in) 4.5 11.98 38.77

Rib 2 offset (in) 0.75 0.17 0.09

• Final designs show very different design points even though

the responses are somewhat similar.

• Would be difficult to explore the design space without Isight.


SCC 2012

Other Potential Use Cases for Isight

in Vibroacoustic Analysis

• Multidisciplinary design optimization where vibroacoustic

analysis is an integral part of the solution

- For example: have design parameters in Isight update an FE

model used for static, random vibration and other analysis

- Then correlate the SEA model to a new FE model definition

using methodology presented here

• Sensitivity analysis of SEA responses due to a variety of

input factors

- Monte Carlo analysis due to uncertainty in the acoustic

environment.

- Find the sensitivity of cabin noise level or panel responses to

structural inputs such as panel stiffness or mass factors.

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Conclusions

• Isight can be effectively used to improve the correlation

between SEA and FE vibroacoustic models.

• Since FE results are very sensitive to boundary

conditions, realistic boundary conditions should be used

to correlate SEA panels.

• The effort necessary to complete any panel correlation

can be cut from up to a day of manual work to about 1.5

hours

• Significant reduction in the amount of engineering effort

and time results in reduced costs and more accurate SEA

models.

Correlation of the Vibroacoustic Response of Structural ... of the Vibroacoustic ... Isight for use...

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