© The Aerospace Corporation 2009 Acoustic Analysis of 1.5- and 1.2-meter Reflectors Mike Yang ATA Engineering, Inc. June 9, 2009

ATA Engineering Background and Objectives Background Satellite manufacturer has a 1.5- and 1.2-meter reflector mounted on a tower Tower placed in reverberant chamber and excited with reverberant sound field Accelerometer measurements taken during -6 dB test Objectives: Use vibro-acoustic analytic model to match test accelerations Predict interface loads between reflector and support structure Presentation Focus 1.5m reflector 1.2m reflector

ATA Engineering Technical Approach Work took place in August 2008 VA-One from ESI used as primary solver Modes solved using NX Nastran 5.0 FEM’s were available in stages Analysis Stages: Stage 1: Analysis of 1.5-meter reflector using breakout model –Initial analysis using FEA –Analysis using BEM –Correlation of model boundary conditions Stage 2: Analysis of 1.2-meter reflector using breakout model –Analysis using BEM –Correlation of model boundary conditions Stage 3: Analysis of both reflectors with tower model (BEM)

ATA Engineering Phase 1: 1.5m Reflector Breakout Model Boundary conditions specified by customer –Clamped in DOF shown below Damping as originally specified by customer In-vacuo modes solved up to 2000 Hz Responses recovered: –At four accelerometer locations (shown below) –Forces at three beams between reflector and support structure (not shown) DOF 123 Restrained DOF Restrained

ATA Engineering Phase 1: FEA response for 1.5m Reflector Methodology: Reverb chamber modeled explicitly as SEA acoustic cavity Connected cavity to FEM with manual area junction –Fluid mass and damping accounted for by FEM/SEA connection Test-measured SPL enforced on cavity Results: Poor correlation to test below 200 Hz –Overprediction of response –FEA assumes baffled edges –230 Hz ~ 1 acoustic wavelength across structure Analytic damping appears too low FEA natural frequencies are too high

ATA Engineering Phase 1: BEM response for 1.5m Reflector Methodology: BEM used –More accurate fluid-structure interaction –Does not assume baffled edges Should reduce low-freq response DAF approximated with ~100 plane waves Same damping and modes as FE analysis Results: Poor correlation to test below 200 Hz Overprediction of response at low-frequencies –Better than FEA Analytic damping appears too low BEM natural frequencies are too high –Non-baffled edges result in higher natural frequencies compared to FEM

ATA Engineering Phase 1: BEM response for 1.5m Reflector Correlated boundary conditions and damping Methodology: BEM used DAF approximated with ~100 plane waves Springs placed at boundaries –Fluid mass estimated from in-vacuo natural frequencies and test peaks –Springs tuned to new in-vacuo natural frequencies using Attune Damping increased at low freqs –(Details not shown due to customer request) Results: Good correlation at most frequencies

ATA Engineering DOF 123 Restrained DOF Restrained Phase 2: 1.2m Reflector Breakout Model Boundary conditions specified by customer –Clamped in DOF shown below Damping as originally specified by customer In-vacuo modes solved up to 2000 Hz Responses recovered: –At four accelerometer locations (shown below) –Forces at three beams between reflector and support structure (not shown)

ATA Engineering Phase 2: BEM response for 1.2m Reflector Methodology: BEM used –1.5m Reflector found this to be best method DAF approximated with ~100 plane waves Modes solved to 2000 Hz Damping as originally specified by customer Results: Poor correlation to test at low frequencies

ATA Engineering Phase 2: BEM response for 1.2m Reflector Correlated boundary conditions and damping Methodology: BEM used –1.5m Reflector found this to be best method DAF approximated with ~100 plane waves Modes solved to 2000 Hz Higher DLF used for 1.5m Reflector Springs placed at boundaries –Fluid mass estimated from in-vacuo natural frequencies and test peaks –Springs tuned to new in-vacuo natural frequencies using Attune Results: Improved match to test data –Low frequency response still doesn’t match

ATA Engineering Phase 2: Analysis and Test Mode Shapes Likely Different First mode is near 36 Hz BEM over-predicts at this frequency Anti-node is near accelerometer –Results in high predicted responses at this location Changing spring stiffness is unlikely to change this mode shape

ATA Engineering Phase 3: Analysis Using Tower Model Customer provided FEM of reflectors with Tower structure –Actual boundary conditions of reflectors now more accurately modeled Tower has several large panels –These can also absorb acoustic power –BEM Fluid also attached to these panels Modes solved up to 2000 Hz Increased DLF from 1.5m Reflector applied 1.5m reflector 1.2m reflector

ATA Engineering Phase 3: BEM response with Tower Structure Best Match with Test Accelerometer Data Tower model provides best match with test data –Reflector boundary conditions accurately modeled –Tower surfaces absorbed acoustic energy and increased reflector response

ATA Engineering Lessons Learned BEM is the best method to solve these problems –Models additional fluid mass and damping –Correctly models unbaffled edges of structure Prevents over-prediction at low frequencies Prevents over-loading of fluid mass at low frequencies Model correlation difficult without modal test data –Correlation of first few natural frequencies is not sufficient –Correlation of mode shapes is critical Correlation attempts with 1.2-meter reflector failed Correlation of damping values is also critical –Damping can be estimated by comparing peak magnitudes and shape if modal test data unavailable Tower assembly model was crucial to successful test correlation –Breakout models did not accurately model boundary conditions –Additional Tower surfaces could absorb and radiate acoustic energy At low frequencies, things within a few acoustic wavelengths become important –Baffled or non-baffled boundary conditions –Nearby reflecting surfaces

© The Aerospace Corporation 2009 Acoustic Analysis of 1.5- and 1.2-meter Reflectors June 9, 2009 (858) Mike Yang ATA Engineering, Inc.

ATA Engineering Appendix: Estimating Fluid Mass Assume modal mass is unity Natural frequency of fluid-loaded system: Solve for fluid mass In-vacuo natural frequency: