NINTH INTERNATIONAL CONGRESS ON SOUND AND VIBRATION, ICSV9 PASSIVE CONTROL OF LAUNCH NOISE IN ROCKET PAYLOAD BAYS

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1 first nae & faily nae: Rick Morgans Page nuber: 1 NINTH INTERNATIONAL CONGRESS ON SOUND AND VIBRATION, ICSV9 PASSIVE CONTROL OF LAUNCH NOISE IN ROCKET PAYLOAD BAYS Rick Morgans, Ben Cazzolato, Anthony Zander, Colin Hansen, Steven Griffin Abstract Departent of Mechanical Engineering University of Adelaide 5005, Australia Boeing-SVS Inc The 5 Way NE Suite 350 Albuquerque, NM 87109, USA e-ail address of lead author: rorgans@echeng.adelaide.edu.au In space launch vehicles, external excitation of the vehicle fairing by acoustic or structural loads can produce large acoustic pressure fluctuations in the internal payload bay. These fluctuations can daage or destroy the payload, and have been blaed for 30% to 60% of first day satellite alfunctions. Passive vibration and acoustic absorbers, called vibro-acoustic devices or VADs, have previously been used experientally to reduce the levels of noise transitted through the fairing. The ai of this project was to produce a odel of the syste (fairing and cavity) coupled to the VADs which allows the optiu VAD placeent and design to be deterined. The odeling procedure used odal coupling to calculate the internal acoustic potential energy, which was used as a cost function to easure the efficiency of the noise reduction strategy. The odal coupling ethod was validated against a purely finite eleent odel and was found to provide results 1000 to 000 ties faster.

2 first nae & faily nae: Rick Morgans Page nuber: A genetic algorith was then used to deterine the optiu VAD placeent and design paraeters. Using 4 separately tuneable VADs with a total ass of approxiately % of the structure, a 3. db reduction was achieved. INTRODUCTION The work described here is directed at optiising passive vibration and acoustic absorbers to iniise the transission of low frequency rocket otor noise into structures that represent launch vehicle fairings. This unwanted noise can daage or destroy the payload, and has been blaed for 30% to 60% of first day satellite alfunctions. In previous work 1, the optial configuration of a passive Vibro-Acoustic Device (VAD) ounted to the interior of a sall cylinder was investigated. The VAD consisted of an acoustic absorber and a vibration absorber (Tuned Mass Daper, TMD) in the one device. This was realised in practice by using a loudspeaker, which had an enclosed rear side and an exposed front side. The loudspeaker diaphrag and backing cavity acted as an acoustic tuned absorber, while attaching the entire device to the structure using spring connectors provided the vibration absorber device. The VAD was ounted to a flexible aluiniu panel used as the cylinder end cap. The study found that the optial VAD design used the TMD essentially as a ass, as the uncoupled resonance frequency of the TMD was just below the upper bound of the frequency band of interest and that the optial loudspeaker diaphrag configuration was highly lossy so that it reduced the odal aplitude of a single acoustic ode. This paper reports on the transferral of the techniques developed in the previous work to the optiisation of structures that ore realistically represent real launch vehicles ; in particular, a large coposite cylinder. LIMITATIONS OF PREVIOUS MODELLING TECHNIQUE It was identified early on that the technique developed previously for analysing the response of the coupled syste, including the VADs to external excitation, would not be feasible for geoetrically larger structures, and consequently the technique required odification. In the previous study, a nuerical fraework was developed for deterining the response of a coupled vibro-acoustic syste, using a cobination of Modal Coupling Analysis and Finite Eleent Analysis, which enabled the response of the structure and internal cavities to be deterined. Boundary Eleent Analysis provided the solutions for the external pressure field and Finite Eleent Analysis provided the structural and cavity natural frequencies and ode shapes. The odels were coupled using the odal coupling technique, which coupled the in-vacuo odal odel of the structure to the rigid-walled odal odel of the cavity. The ethod was developed by Lyon and Maidanik 3, Fahy 4, Pope 5 and Dowell et al. 6 and elegantly suarised by

3 first nae & faily nae: Rick Morgans Page nuber: 3 Fahy 7. The code was ipleented in MATLAB 8, and the uncoupled odes were calculated using ANSYS 9. This approach showed a vast iproveent in coputation speed over the equivalent finite eleent analysis, but still required the coputation of the noral odes of the structure and cavity at the start of each iteration. This involved the use of the ANSYS progra, which was a coputationally tie consuing process, especially with large odels, iplying that any kind of eaningful optiisation would not be possible. This led to the developent of odels of the structural and acoustic coponents of the VAD that did not use the ANSYS progra, but rather allowed the effect of the VAD on the frequency response to be adequately represented. Structural resonator The addition of a structural resonator (TMD) to an existing structure can be represented by the addition of an acoustic cavity with a single ode to the syste at the point of attachent of the structural resonator. This was found to be the ost expedient way to couple the new structural ode to the existing odal odel, as the existing odal coupling code was already set up to calculate the coupling between acoustic and structural odes. The properties of this equivalent acoustic ode can be calculated fro K and M, the spring constant and ass of the single degree of freedo ass spring syste, without perforing a odal analysis in ANSYS. The acoustic ode shape φ of this new ode is defined as φ = 1 over the attachent nodes and φ = 0 elsewhere. The effective area, A, is the su of the individual nodal areas over the attachent area. The odal volue, Λ, can be calculated using the following equation ρ0ca Λ = (1) K where ρ 0 and c are the density of and speed of sound in air. The natural frequency can be calculated fro Equation () K ω = () M Daping ters (the odal loss factor η ζ, where ζ is the daping ratio) can be added if required. A derivation and validation of the structural resonator syste ipleentation appears in Hansen et al..

4 first nae & faily nae: Rick Morgans Page nuber: 4 Acoustic absorber The ipleentation of the acoustic resonator was siilar to the ipleentation of the structural resonator, in that additional structural odes were added to the coupled syste to represent the acoustic odes. Again, this was found to be the ost expedient way to add an acoustic resonator to the existing odal coupling code. In fact, the physical realisation of the acoustic resonator in the physical syste can be a structural coponent, a loudspeaker diaphrag with backing cavity. The properties of the equivalent structural ode can be calculated fro ω a the natural frequency of the single degree of freedo resonator syste and its acoustic ass (Equation 3). M a M = (3) A The structural ode shape ψ a of this new ode is defined as ψ a = 1 over the attachent nodes and ψ a = 0 elsewhere. The effective area, A, is the su of the individual nodal areas over the attachent area. The odal ass of the resonator is equal to the acoustic ass of the diaphrag used. The resonator natural frequency ω a is governed by the stiffness of both the loudspeaker diaphrag and the enclosed volue behind the diaphrag. Daping ters can be added to the ipedance ter if required. In the ipleentation of the acoustic resonator in the MATLAB code, an additional structural shell eleent is created to represent the diaphrag, and the corresponding representative noral outward vectors and areas are calculated. These areas are then scaled so that the size of the acoustic attachent does not vary with nodal eleent density (i.e. the esh size of the eleents). This does not liit the choice to a fixed attachent area, since an equivalent structural ass can be derived using the definition of acoustic ass in Equation (3). A1 M 1 = M (4) A A derivation and validation of the acoustic resonator syste ipleentation appears in Hansen et al.. OPTIMISATION USING GA S A Genetic Algorith (GA) was ipleented to optiise the VAD design and location. In general, GAs are used when an exhaustive search of all possibilities is ipractical and gradient based search ethods are ineffective in searching for a global optiu (these ethods are likely to find local optiu solutions). A GA can be regarded as a guided

5 first nae & faily nae: Rick Morgans Page nuber: 5 rando search, taking soe cues fro evolutionary theory ( survival of the fittest ). It was found that GA techniques can optiise the location and paraeters of ultiple VADs, at least with the sall cylinder used in previous work. One difficulty is that the GA ust have a large population size and run for any generations to be effective. It was also found that for large probles, the odal coupling technique is still too slow for the GA, and easures ust be taken to reduce the tie taken, or long run ties ust be accepted. The GA was run with 4 VADs for 1000 iterations over approxiately 1 onth. The cost function chosen to represent the response of the syste to the external excitation was the acoustic potential energy within the cavity. The acoustic potential energy was calculated by 1 n E( ω) = Λi pi( ω) (5) i= 1 where Λ i is the odal volue for ode i and pi ( ω ) is the odal participation factor for acoustic ode i at frequency ω. The cost function was the su of the potential energies across the frequency range of interest, in this case fro 50 Hz to 300 Hz. ω J = E( ω) (6) ω ω = 1 As shown in Figure, the cost function asyptotes to an approxiately 3. db reduction. For the case considered, the ass of the 4 optial VADs was constrained to approxiately 3% of the ass of the structure. Figure : Acoustic potential energy reduction run over 1000 generations of the GA showing convergence to the final solution.

6 first nae & faily nae: Rick Morgans Page nuber: 6 Figure 3 shows the frequency response for the best solution after 1000 generations for the large coposite cylinder odel with 4 VADs, where it is copared to a baseline solution with no VADs. Figure 4 shows the final position of the VADs on the surface of the cylinder, and Table 1 gives the optial VAD paraeters. The VAD positions are the eleent nubers associated with the underlying finite eleent odel. Figure 3: Acoustic potential energy estiate in the cavity with and without acoustic treatent by VADs placed in the optiu position as predicted by the GA. Figure 4: Representation of the VAD positions on the surface of the large coposite cylinder after 1000 iterations of the GA.

7 first nae & faily nae: Rick Morgans Page nuber: 7 VAD paraeter Optiu value VAD position(eleent nuber) Mass-spring ass 0.5 Kg 0.5 Kg 0.35 Kg 0.35 Kg Mass-spring frequency 9 Hz 73 Hz 315 Hz 50 Hz Mass-spring daping 5% 5% % 5% Acoustic resonator ass Kg Kg Kg Kg Acoustic resonator frequency 66 Hz 64 Hz 47 Hz 17 Hz Acoustic resonator daping 17% 6% 4% 4% Table 1: Optiu VAD paraeters after 1000 generations of the genetic algorith search In this solution the ass-spring systes of the VADs are operating at frequencies within the desired control range, and not operating as siply added ass as in the previous solution. All the optiu VAD locations lie on the flexible coposite cylinder, as expected, rather than on the stiff wooden end-caps. Acoustic resonator 7968 appears to be targeting the first longitudinal acoustic ode at 6 Hz, and is positioned up against one end of the cylinder to be at a pressure anti-node. The other acoustic resonators are closer to the centre of the cylinder. Acoustic resonator 8445 appears to be targeting the second longitudinal acoustic ode, and is located in the centre of the cylinder. The syste is so odally dense that it is difficult to deterine whether the control is structural or acoustic. For exaple, the peak at 50 Hz is targeted by both a structural resonator (8445) and an acoustic resonator (8919). The values of the echanical resonator ass are the axiu possible for two resonators (7968,7978) and 70% of axiu for the other two, with daping for all cases approaching the axiu. All acoustic resonator asses are the iniu possible, ost likely to enhance coupling to the cavity, but the daping varies widely fro near iniu to near axiu. CONCLUSIONS This work has shown that it is possible to optiise the location and paraeters of Vibro Acoustic Devices (VADs) attached to the interior surface of a large coposite cylinder to reduce the sound transitted into the interior cavity. Further work needs to be done on the optiisation of these larger structures once ore efficient ethods of odal coupling are ipleented. There should then be further work related to justifying soe of the assuptions used in developing the VAD odels, such as the negligible influence of the VAD volue on the odal odel, and the developent of alternate VADs (ultiple degrees of freedo).

8 first nae & faily nae: Rick Morgans Page nuber: 8 BIBLIOGRAPHY (1) C.H. Hansen, A.C. Zander, B.C. Cazzolato, and R.C. Morgans. Investigation of passive control devices for potential application to a launch vehicle structure to reduce the interior noise levels during launch. Final report for Stage 1, The University of Adelaide, 000. () C.H. Hansen, A.C. Zander, B.C. Cazzolato, and R.C. Morgans. Investigation of passive control devices for potential application to a launch vehicle structure to reduce the interior noise levels during launch. Final report for stage, The University of Adelaide, 001. (3) R.H. Lyon and G. Maidanik. Power flow between linearly coupled oscillators. Journal of the Acoustical Society of Aerica, 34:, 196. (4) F.J. Fahy. Vibration of containing structures by sound in the contained fluid. Journal of Sound and Vibration, 10(3):-51, (5) L.D. Pope. On the transission of sound through finite closed shells: Statistical energy analysis, odal coupling, and non-resonant transission. Journal of the Acoustical Society of Aerica, 50(3):-1018, (6) E.H. Dowell, G.F. Goran III, and D.A. Sith. Acoustoelasticity : General theory, acoustic natural odes and forced response to sinusoidal excitation, including coparisons with experient. Journal of Sound and Vibration, 5(4):-54, (7) F. Fahy. Sound and Structural Vibration: Radiation, Transission, and Response. Acadeic Press, London, (8) Matlab 5.4. Matlab User Guide. Mathworks, 5.4 edition, (9) ANSYS Theory Manual. Ansys 5.6. Ansys Inc, Canonsburg, PA, 8 edition, 000. (1) B.S. Cazzolato. Sensing systes for active control of sound transission into cavities. Ph.D. Dissertation, The University of Adelaide, March 1999.