Correlation of the Vibroacoustic Response of Structural ... of the Vibroacoustic ... Isight for use...
Transcript of 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
11995 El Camino Real, Suite 200 | San Diego, CA 92130 | T 858.480.2000 | F 858.792.8932 | www.ata-e.com
SCC 2012
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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SCC 2012
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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
11995 El Camino Real, Suite 200 | San Diego, CA 92130 | T 858.480.2000 | F 858.792.8932 | www.ata-e.com
SCC 2012
• 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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SCC 2012
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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11995 El Camino Real, Suite 200 | San Diego, CA 92130 | T 858.480.2000 | F 858.792.8932 | www.ata-e.com
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”
- Vibroacoustic solution to 4000 Hz in 1/3 octave bands
• 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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SCC 2012
• 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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SCC 2012
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
11995 El Camino Real, Suite 200 | San Diego, CA 92130 | T 858.480.2000 | F 858.792.8932 | www.ata-e.com
SCC 2012
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.
11995 El Camino Real, Suite 200 | San Diego, CA 92130 | T 858.480.2000 | F 858.792.8932 | www.ata-e.com
SCC 2012
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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SCC 2012
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”
- Vibroacoustic solution to 3150 Hz in 1/3 octave bands
• 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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SCC 2012
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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
11995 El Camino Real, Suite 200 | San Diego, CA 92130 | T 858.480.2000 | F 858.792.8932 | www.ata-e.com
SCC 2012
• 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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SCC 2012
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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.
11995 El Camino Real, Suite 200 | San Diego, CA 92130 | T 858.480.2000 | F 858.792.8932 | www.ata-e.com
SCC 2012
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.
11995 El Camino Real, Suite 200 | San Diego, CA 92130 | T 858.480.2000 | F 858.792.8932 | www.ata-e.com
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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SCC 2012
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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.