Propeller Synchrophase Angle Optimisation Study

Transcription

1 Propeller Synchrophase Angle Optimisation Study David M. Blunt and Brian Rebbechi 2 Department of Defence Defence Science and Technology Organisation, Melbourne, Australia [Abstract] Interior noise and vibration can be a serious problem in military propeller aircraft. Noise levels often exceed db, and typical vibration levels can be hazardous to sensitive cargo. This noise and vibration is dominated by the propeller blade-pass frequency and its low-order harmonics. It is generally accepted that propeller synchrophasing is a way of minimising this noise and vibration, however synchrophasing has only achieved limited success in practice. It is thought that the reasons for this are twofold: firstly, the synchrophase angles may be poorly optimised, and secondly, the optimal synchrophase angles may be influenced by flight conditions such as airspeed and altitude. This paper outlines an investigation into these effects for the Royal Australian Air Force AP-3C Orion and C-30J-30 Hercules aircraft. Comprehensive flight trials to examine and quantify these effects were conducted in November The C-30J-30 trial also included different cargo configurations. Twenty one microphones and seven accelerometers were used in the AP-3C trial, and thirty three microphones, eighteen floor accelerometers and fifteen cargo accelerometers were used in the C-30J-30 trial. Preliminary results are presented for the AP-3C trial. These show that the optimum synchrophase angles do change with altitude and airspeed, and compromises must be made to accommodate these effects. α p  k A B β φ p k K p P Q Ŝ p,k S Nomenclature = shaft angle (synchrophase angle) of propeller p = amplitude of the noise (or vibration) at location k = matrix of noise (or vibration) amplitudes = number of blades on each propeller = matrix of unit phase angle vectors = phase angle of signature of propeller p = location index = number of measurement locations = propeller index = number of propellers = number of synchrophase angle sets = signature of propeller p at location k = matrix of propeller signatures I. Introduction he interior noise and vibration in military propeller aircraft is dominated by the propeller Blade-Pass Frequency T (BPF) and its low-order harmonics. 2-5 Typical blade-pass frequencies range from 60 Hz to 20 Hz, and the passive control of these frequencies can be difficult, due to the weight penalties involved. 6 However, most aircraft with two or more propellers have synchrophasers, and previous analytical and experimental studies have indicated that synchrophasing can globally reduce interior noise and vibration,, 7-6 not just redistribute it. It is believed that this global reduction arises from the rearrangement of the relative amplitudes of the fuselage vibration modes in such a way that they couple less efficiently with the interior cabin acoustic, or floor vibration, modes. However, Senior Engineer, DSTO Air Vehicles Division, 506 Lorimer Street, Fishermans Bend VIC 3207, david.blunt@dsto.defence.gov.au; also Ph.D. candidate at the School of Mechanical Engineering, The University of Adelaide, SA 5005, Australia; non-member. 2 Principal Engineer, DSTO Air Vehicles Division, 506 Lorimer Street, Fishermans Bend VIC 3207, non-member.

2 synchrophasing has only achieved limited success as a method of noise and vibration control in practice, and the possible reasons for this are twofold: a) Firstly, the synchrophase angles in some aircraft may not be properly optimised. b) Secondly, and perhaps more importantly, the fixed synchrophase angles found in most synchrophasers, may be inadequate to cope with the changes in the noise and vibration environment brought about by different flight conditions. For example, it is known that the noise generated by propellers is influenced by thrust and inflow distortion, 7 and that cabin noise levels in propeller aircraft can be influenced by altitude and airspeed. 3, 4 Military aircraft also have a much broader range of flight conditions as part of normal operations than civilian passenger aircraft, which may exacerbate the problem. The Royal Australian Air Force (RAAF) operates two four-engine turboprop aircraft: the AP-3C Orion, and the C-30J-30 Hercules (Fig. ). Flight trials were conducted in November 2006 in order to discover the optimum synchrophase angles for these aircraft, and the possible effects of different altitudes and airspeeds on these angles. This paper outlines the measurements that were taken in those trials, the analysis that has been done to date, and some preliminary results from the AP-3C trial. Propeller signature theory is being used to simplify the task due to the large number of potential synchrophase angles combinations; e.g., there are 5,832 possible combinations of three four-bladed slave propellers with respect to a master propeller using shaft angle steps of 5. Figure. RAAF AP-3C Orion (left) and C-30J-30 Hercules (right). II. Propeller Signature Theory Propeller signature theory was first described in a paper by Johnston, Donham and Guinn. Embodiments of the theory have since appeared in a number of other papers and patents. 6, 8, 9 In this theory, the total propeller-related noise or vibration at a particular cabin location is calculated by taking the vector sum of the contributions from each propeller. This assumes local linearity, which appears to be valid based on the reported results, and the results shown here. With the propeller speeds synchronised, the noise or vibration for any combination of shaft angles is predicted by changing the phase of each signature in proportion to the change in shaft angle, and calculating the sum of the resulting contributions. An example illustrating this is shown in Fig. 2, where the BPF signature components (S p φ p ) at a point inside the cabin are shown in the top half of the figure, and the predicted noise at this same point for a different set of synchrophase angles is shown in the bottom half of the figure. Note that Propeller 2 is the master propeller in this case, and that the changes in the slave propeller shaft angles (α p ) are multiplied by the number of blades to arrive at the appropriate phase changes at the BPF. Propeller signature theory uses an influence-coefficient approach to identifying the contributions from individual propellers. This is similar to measuring the influence coefficients in a balancing problem. Instead of a trial weight, a trial synchrophase angle is applied, and the change in acoustic or vibration response is measured. Mathematically, the predicted effect of synchrophasing on the BPF noise at each location can be expressed as P p Aˆ = Sˆ e, () k p= p, k ibα 2

3 α 4 = 0 α 3 = 0 Ref α 2 = 0 α = 0 S 4 (φ 4 ) S 3 (φ 3 ) Resultant S 2 (φ 2 ) S (φ ) Synchrophase Angle Set {0º, 0º, 0º, 0º} Vector Sum of Signatures at BPF α 4 α 3 Ref α 2 = 0 α S 2 (φ 2 ) S 3 (φ 3 + 4α 3 ) S (φ + 4α ) Resultant S 4 (φ 4 + 4α 4 ) Synchrophase Angle Set {α, α 2, α 3, α 4 } Vector Sum for {α, α 2, α 3, α 4 } Figure 2. Propeller signature example. where  k is the noise at location k, Ŝ p,k is the signature of propeller p at location k, α p is the shaft angle (synchrophase angle) of propeller p in radians, B is the number of blades on each propeller, and P is the number of propellers. A multiple of B is used for the BPF harmonics. In matrix notion Eq. () becomes A S β =, (2) where A is a column of complex numbers representing the noise at K locations, S is an K P matrix of complex numbers representing the propeller signatures, and β is a column of P unit vectors with phases angles equal to Bα p. To solve Eq. (2) for S requires measurements for at least P independent sets of synchrophase angles. When there are measurements for more than P sets of angles, the system is over-determined, and the least-squares solution for the propeller signatures can be obtained from T T [ β β ] S = A β, (3) where A is an K Q matrix of measurements, β is a P Q matrix of phase angle vectors, and Q is the number of synchrophase angle sets. III. Flight Trials The flight trials were conducted over the periods of 6-0 November 2006 for the AP-3C, and November 2006 for the C-30J-30. All signals were digitally recorded with a bandwidth of 20 khz and a sample rate of 44 khz using a Heim D20f data recorder fitted with five 8-channel ANR20 analogue input modules, and a 44 GB hard disk. A. AP-3C Orion The AP-3C was instrumented with 2 Brüel and Kjær Type 4935 microphones, and 7 PCB Piezotronics J353B33 accelerometers. The microphones were mounted on the crew seat headrests (total of 2), and at intervals of 20 inches along the overhead grab rail (total of 8) using 8-inch goose necks clamps, so that they were positioned at head 3

4 Table 2. AP-3C Flight Conditions. Four-Engine Operation Altitude Airspeeds (KIAS) * 500 ft ASL ft ASL ft ASL FL FL FL FL FL Three-Engine Operation (No. Shut Down) Altitude Airspeeds (KIAS) 0 ft ASL ft ASL * Knots Indicated Air Speed Above Sea Level Flight Level Table. AP-3C Synchrophase Angle Sets. Default Angles 2 Default + (25,0,0,0 ) 3 Default (25,0,0,0 ) 4 Default + (0,25,0,0 ) 5 Default (0,25,0,0 ) 6 Default + (0,0,0,25 ) 7 Default (0,0,0,25 ) height in both seating and standing positions. One microphone was also mounted above the galley table, below the bunk. The accelerometers were mounted on the rear seat rails of 7 of the crew seats to measure the vertical vibration passing into the seats. The sensor locations can be seen in Fig.. The Figure 3. Synchrophase Angle once-per-rev pulse signals from the four propellers were also recorded in order Display & Adjustment Unit. to accurately measure the actual synchrophase angles. These signals were conveniently available at a connector normally used for propeller balancing that is adjacent to the synchrophaser. Twenty eight different flight conditions were flown in order to get a representative spread of airspeeds and altitudes (Table 2). For each condition, measurements were taken for the default synchrophase angle set plus six other sets, where 25 was respectively added or subtracted from the shaft angles of each slave propeller in turn (Table ). This angle increment was chosen to allow the signatures for the BPF and its first three harmonics to be computed with reasonable accuracy. It gave phase angle steps of, 200, 300, and 400 respectively at these frequencies. The synchrophase angles were changed in flight using a custom-built display and adjustment unit (Fig. 3) connected to a modified synchrophaser. The unit displayed the synchrophase angles (derived from the synchrophaser circuitry via a test point at the rear of the synchrophaser) in real time, and bypassed the trim potentiometers in the synchrophaser. Approximately 2 minutes of data were collected for each measurement, and the total flying time was about 2 hours over two flights. B. C-30J-30 Hercules The C-30J-30 was flown in both cargo and troop configurations. In the cargo configurations, all but the most forward cabin seats were removed, and three cargo pallets of differing sizes (single, double, and triple) and differing weights (260 lbs, 3200 lbs, and 9500 lbs) were secured in two different arrangements in the cabin area. In these configurations, 8 PCB J353B33 accelerometers were mounted in a 3 6 grid on the cargo floor beneath the pallets, one Endevco 2258A- tri-axial accelerometer was mounted near the centre of each pallet, and two PCB J353B33 or Dytran 304A2 accelerometers were mounted on the cargo on each pallet. Six Brüel and Kjær Type 4935 microphones were also used to check for possible acoustic differences between the cargo and troop configurations: four in the cargo cabin and two on the flight deck. In the troop configuration, the cargo pallets were removed, and the seats frames installed. Thirty two Type 4935 microphones and one Type 488A02 microphone were used. Thirty of these were arranged in a 3 0 grid in the cargo cabin at seated head height, and two were mounted on the headrests of the flight deck seats. Six PCB J353B33 floor mounted accelerometers were used to check for vibration differences between the cargo and troop configurations. Seven different altitudes and up to three airspeeds at each altitude were flown, as shown in Table 3. Measurements were taken for the default synchrophase angle set plus six other sets, where the shaft angle of each slave propeller was respectively incremented and decremented 4 Table 3. C-30J-30 Flight Conditions. Altitude Airspeeds (KIAS) 6000 ft ASL ft ASL 250 FL FL FL FL FL

5 by a set amount, although the angle increment used was 7, as the C-30J-30 has six-bladed propellers. This increment gave phase angle steps of 02, 204, 306, and 408 respectively for the BPF and its first three harmonics. The synchrophase angles were changed by the pilot via a multifunction display on the flight deck, and a bus analyser was connected to the aircraft data bus to monitor the measured synchrophase angles reported on the bus. IV. Results Selected data from the AP-3C trial are presented in this section illustrating the performance of the synchrophaser, the acoustic environment inside the cabin, the differences between the actual and predicted signals, and some angle optimisations. The synchrophase angles were calculated by measuring the relative positions of the master and slave once-per-rev pulses, using the same method as the actual synchrophaser; i.e., a synchrophase angle of 0 was defined as the point when the slave and master pulses were exactly apart, with a positive synchrophase angle occurring when the slave pulse arrived before the midpoint between two master pulses. All the data were analysed using Matlab. A. Synchrophaser Performance. Angle Tolerance The ability of the synchrophaser to hold the set angles was estimated by calculating the standard deviations of the synchrophase angles during steadystate conditions. Tolerances of about ± 6 in smooth air (Fig. 4), and about ± 0 in moderate turbulence (Fig. 5) were found by assuming a range of three times the standard deviation. It should be noted that the AP-3C synchrophaser acts through a speedbias servo-motor in the hub of each propeller. This motor adjusts the tension on a spring in the propeller speed governor, thereby advancing or retarding the propeller via fine adjustments to the blade pitch. The performance of the synchrophaser is therefore limited by the performance of the hydro-mechanical governor. Smaller tolerances can be expected for electronic governors such as those found in the C-30J Settling Time It can be seen from Figs. 4 and 5 that there was a considerable overshoot after each angle adjustment, and it took at least 500 propeller revolutions (about 30 s at 020 rpm), for the synchrophaser to settle on the new angle. Sync Angle, degrees Prop Prop 2 Prop 4 Serial 9 Master Propeller Revolutions Figure 4. Synchrophase Angles for Serial 9 (220 KIAS at FL) Smooth Air. Sync Angle, degrees Prop Prop 2 Prop 4 Serial Master Propeller Revolutions Figure 5. Synchrophase Angles for Serial (200 KIAS at 500 ft) Moderate Turbulence % Speed % Speed 5

6 3. Master Propeller Perturbations A spike in the master propeller speed can clearly be seen near the 6,000 revolution mark in Fig. 4. Because the synchrophaser measures the synchrophase angles with respect to the master propeller, it interprets any perturbations of the master as perturbations of the slaves, and unnecessarily tries to compensate for these. This effect could be eliminated, or at least reduced, if the synchrophase angles were calculated in a different way. One way would be to generate an artificial master signal and to make all the propellers slaves. Another might be to filter out the perturbations in the master propeller signal. B. AP-3C Cabin Acoustic Environment The spectral content, up to 500 Hz, of all sensor signals was examined for Serial (200 KIAS at 500 ft) in order to determine the typical importance of the low-order BPF harmonics throughout the cabin and any other frequencies in this range. Spectrograms for some of the signals illustrating the changes from front-to-rear, and the time-dependent nature of some of the components, are shown in Figs It was found that the fundamental and first three harmonics of the BPF were the dominant tones in the front half of the cabin, particularly near the propeller plane, and that the 6 th harmonic (7x BPF = 476 Hz) was significant just aft of the propeller plane. The harmonics of the BPF waned towards the rear of the cabin, where only the fundamental remained dominant, although there was more broadband noise present there. The propeller rotational frequency (7 Hz) was observed in many signals, but at significantly lower amplitudes than the BPF. A high-amplitude, low-frequency component near 6 Hz was also present in most signals. It is suspected that this was an axial acoustic resonance of the cabin, possibly excited by the cabin pressurization system. C. Propeller Signature Calculation Variations in the synchrophase angles are undesirable when it comes to computing the propeller signatures, as any change in the shaft angle must be multiplied by the number of blades to arrive at the effective phase angle change at the BPF. For example, if a limit of 3 is placed on the deviation of the synchrophase angle, this equates to 2 at the Figure 6. Spectrogram of Pilot Seat Microphone, Serial (200 KIAS at 500 ft). Figure 7. Spectrogram of Grab Rail Microphone at Flight Station 420, Serial (200 KIAS at 500 ft). Figure 8. Spectrogram of Grab Rail Microphone at Flight Station 7, Serial (200 KIAS at 500 ft). 6

7 BPF, 24 at 2 BPF, 36 at 3 BPF and 48 at 4 BPF. Steps must be taken to limit these deviations, as large phase angle variations will otherwise render the calculated signatures meaningless. The approach taken here was to limit the data used from each measurement to only 4 propeller revolutions so that the synchrophase angles would not vary by more than about 2 in the worst case; i.e., when there was moderate turbulence. The data were also synchronously averaged with respect to the master propeller once-per-rev signal to partially attenuate the non-synchronous components (i.e., noise unrelated to the propellers), but mostly to ensure that the BPF and its harmonics would fall in the middle of the frequency bins formed when the data were transformed using the Discrete Fourier Transform (DFT). Eq. (3) was solved separately for each of the following frequency components: shaft rotational frequency, BPF, 2 BPF, 3 BPF, and 4 BPF. For each component, the DFT was used to extract the amplitude and phase at that frequency from the synchronous averages of every sensor signal and populate the A matrix. The β matrix was populated with the actual synchrophase angles experienced during those measurements (i.e., not the set angles). D. Predicted vs. Measured Noise Levels At least four sets of synchrophase angles are required to solve Eq. (3) for an aircraft with four propellers. As seven sets of angles were used, the signatures computed from some of the 7 Sound Pressure, Pa Serial, Sync Angle Set Pilot Microphone Signal Comparison Measured Predicted Actual SPL = 95.7 db -4 Predicted SPL = 95.4 db Propeller Shaft Angle, degrees Figure 9. Predicted vs. Measured Pilot Seat Microphone Signals, Serial (200KIAS at 500 ft), Default Synchrophase Angle Set. Sound Pressure, Pa Serial 9, Sync Angle Set Pilot Microphone Signal Comparison Measured Predicted Actual SPL = 94.3 db -4 Predicted SPL = 93.8 db Propeller Shaft Angle, degrees Figure 0. Predicted vs. Measured Pilot Seat Microphone Signals, Serial 9 (220KIAS at FL), Default Synchrophase Angle Set. measurements can be used to predict the other measurements, thus providing a partial validation of the signature theory. However, in practice, using more than four sets of angles allows a least-squares approach to be adopted in order to get the best fit to the actual data. Figs. 9 and 0 show two comparisons between the synchronous average of a signal measured using the default set of synchrophase angles, with the corresponding signal predicted using the signatures computed from the other six synchrophase angle sets. The predictions incorporated the st, 4 th, 8 th, 2 th, and 6 th shaft-order frequencies. It can be seen that there was good agreement in both cases. These results were typical of most of the other measurements, although the agreement was not as good where there were frequency components in the measured signals that were not modelled by the signatures; e.g., where the 6 th harmonic of the BPF was present, or where the broadband noise levels were higher. However, if those frequencies were ignored, the comparisons were still generally good. E. Synchrophase Angle Optimisation Many different strategies can be used to optimise the synchrophase angles; e.g., uniform or varying sensor and/or frequency weighting can be applied to signatures. For simplicity, uniform weighting of all microphones signatures, and zero weighting of all accelerometers signatures, were used in the results shown below. An example of the predicted sound and vibration levels combining the BPF, 2 BPF, 3 BPF, and 4 BPF signatures for one flight condition ( KIAS at FL2) is shown in Fig.. The sound pressure levels are shown in decibels re Pa, and the vibration levels in decibels re 0-5 g. The top half of the figure shows the minimum and maximum levels for each sensor over all synchrophase angle combinations. The bottom half shows the predicted levels for the default and optimum synchrophase angles. It can be seen that the local effect of synchrophasing on the sound pressure levels is around 20 db for most locations, but that the global effect is smaller. In this case, there is a difference of 4 db in the average Sound Pressure Level (SPL) between the two sets of angles (averaged over all microphones), and the angle sets differ by (39,26,0,6 ).

8 Serial 22, Sensor Minima Predicted Levels, db 0 Serial 22, Sensor Maxima Predicted Levels, db Seat Mic Grab Rail Mic Accel Seat Mic Grab Rail Mic Accel Serial 22, Default Angles Predicted Levels, db 0 Serial 22, Optimised for All Microphones Predicted Levels, db Seat Mic Grab Rail Mic Accel Seat Mic Grab Rail Mic Accel Figure. Predicted Sensor Levels, Serial 22 ( KIAS at FL2). Separate optimisations were done for each four-engine flight condition, and the optimum angles were found to change significantly between each condition. The predicted average SPLs for the best, default, and worst angle sets for all four-engine flight conditions are shown in Fig. 2. The default and worst case levels are shown as increments over the best case (e.g., the average SPL for the worst case is obtained by adding the red and green bars to the blue bar). It can be seen that noise levels generally increase with airspeed and altitude, and that the effect of synchrophasing on the average SPL varies from about 5 db up to about 0 db (i.e., the difference between the best and worst cases). This is comparable to earlier reported results., 6 The results for the default angle set are also reasonably close to those of the optimum angle sets in most cases (except at FL2), indicating that the default angle set is a relatively good compromise, 220 KIAS, FL2 200 KIAS, FL2 KIAS, FL2 240 KIAS, FL KIAS, FL KIAS, FL KIAS, FL KIAS, FL KIAS, FL200 2 KIAS, FL 260 KIAS, FL 240 KIAS, FL 220 KIAS, FL 260 KIAS, FL 240 KIAS, FL 220 KIAS, FL 260 KIAS, 3000 ft 240 KIAS, 3000 ft 220 KIAS, 3000 ft 240 KIAS, 0 ft 220 KIAS, 0 ft 200 KIAS, 0 ft 220 KIAS, 500 ft 200 KIAS, 500 ft Average SPL for Best, Default, & Worst Synchrophase Angles Sets Sound Pressure Level, db Figure 2. Predicted Spatially-Averaged Sound Pressure Levels. 8 Best Def ault Worst

9 although other optimisations strategies may produce better results for the aircrew at high-workload stations. Interestingly, the results for the default and best cases are practically the same for 220 KIAS at 3000 ft, and this is also reflected in the angle sets, which are no more than 2 apart. V. Conclusions and Future Work It has been shown that propeller signature theory can be used to predict cabin noise levels, and that good agreement between the predicted and measured results can be achieved in most situations. However, care needs to be exercised to limit propeller shaft angle perturbations during measurements, and a least-squares approach is recommended to get the best fit with the data. In the AP-3C, the local effect of synchrophasing on the SPL at individual locations was predicted to be around 20 db, but the global effect averaged over all microphone locations was only 5 db to 0 db, depending on the flight condition. The optimum synchrophase angles were found to vary with both airspeed and altitude, and the default angles seem to be a good compromise except at high altitude. However, only one optimisation strategy was used, and others need to be investigated, such as biasing the optimisation to produce lower noise levels at the highworkload stations and/or the locations where the noise levels are very high. The performance of the AP-3C synchrophaser, and the acoustic environment of the AP-3C cabin were also characterised. Future work will include further investigation of alternative optimisation strategies and the analysis of the C-30J-30 data. Acknowledgments This study would not have been possible without the flight trials in the AP-3C and C-30J-30 aircraft. The authors wish to thank all those involved in the trials; in particular, the personnel from the RAAF Maritime Patrol Systems Program Office and the Air Lift Systems Program Office who literally got the trials off the ground; and Scott Dutton, Paul Marsden, Tony Galati, and Ken Vaughan from DSTO who all participated in the trials. References Johnston, J. F., Donham, R. E., and Guinn, W. A., "Propeller signatures and their use," AIAA Journal of Aircraft, Vol. 8, No., Mixson, J. S. and Wilby, J. F., "Interior Noise," in Aeroacoustics of Flight Vehicles: Theory and Practice, edited by H.H. Hubbard, NASA Reference Publication 258, WRDC Technical Report , NASA, 99, pp Farrell, P. A., Mouser, C. R., Conser, D. P., and Rider, C. D., "C-30J-30 Cargo Vibration Flight Test," DSTO-TR-30, Defence Science and Technology Organisation, Department of Defence, Australia, Smith, D. H., "Wavelet Multi-Resolution Analysis of C-30J Vibration Data - Steps Towards Environment Characterisation," DSTO-TR-626, Defence Science and Technology Organisation, Department of Defence, Australia, Smith, D. H., "Propeller blade signatures in the wavelet domain," Australian and New Zealand Industrial and Applied Mathematics Journal, Vol. 46, No. E, 2005, pp. C75-C88. 6 Hansen, C. H. and Snyder, S. D., Active Control of Noise and Vibration, E & FN Spon (an imprint of Chapman & Hall), London, Fuller, C. R., "Noise Control Characteristics of Synchrophasing - an Analytical Investigation," AIAA/NASA 9th Aeroacoustics Conference, AIAA , AIAA, Jones, J. D. and Fuller, C. R., "Noise Control Characteristics of Synchrophasing - an Experimental Investigation," AIAA/NASA 9th Aeroacoustics Conference, AIAA , Fuller, C. R., "Analytical Investigation of Synchrophasing as a Means of Reducing Aircraft Interior Noise," NASA Contractor Report 3823, NASA, Mahan, J. R. and Fuller, C. R., "An Improved Source Model for Aircraft Interior Noise Studies," Collection of Technical Papers - AIAA/ASME/ASCE/AHS Structures, Structural Dynamics & Materials Conference 26th, AIAA , 985, pp Fuller, C. R., "Noise Control Characteristics of Synchrophasing, Part : Analytical Investigation," AIAA Journal, Vol. 24, No. 7, 986, pp Fuller, C. R., "Analytical model for investigation of interior noise characteristics in aircraft with multiple propellers including synchrophasing," Journal of Sound and Vibration, Vol. 09, No., 986, pp Jones, J. D. and Fuller, C. R., "Noise Control Characteristics of Synchrophasing, Part 2: Experimental Investigation," AIAA Journal, Vol. 24, No. 8, 986, pp Jones, J. D. and Fuller, C. R., "An Experimental Investigation of the Interior Noise Control Effects of Propeller Synchrophasing," NASA CR-7885, NASA, Johnston, J. F. and Donham, R. E., "Attenuation of propeller-related vibration and noise," AIAA Journal of Aircraft, Vol. 9, No. 0,

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