1、NASA Contractor Report 3813Propeller AircraftInterior Noise ModelL. D. Pope, E. G. Wilby,and J. F. WilbyCONTRACT NAS1-15782JULY 1984NASAProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NASA Contractor Report 3813Propeller AircraftInterior Noise ModelL
2、. D. Pope, E. G. Wilby,and J. F. WilbyBolt Beranek and Newman Inc.Canoga Park, CaliforniaPrepared forLangley Research Centerunder Contract NAS1-15782NASANational Aeronauticsand Space AdministrationScientific and TechnicalInformation Branch1984Provided by IHSNot for ResaleNo reproduction or networkin
3、g permitted without license from IHS-,-,-Page intentionally left blankPage intentionally left blankProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TABLE OP CONTENTSSection Page1.0 SUMMARY 12.0 INTRODUCTION 22.1 Report Organization. 52.2 Program Manag
4、ement 63.0 ELEMENTS OP THE PROPELLER AIRCRAFT INTERIORNOISE MODEL 73.1 General Solution for the Sound TransmissionProblem 8Power Flow 103.2 Transmission of a Tone 14High Frequencies 163.3 Calculation of the Noise Reduction 21Noise Reduction Calculation 22High Frequencies 233.4 Calculation of the Gen
5、eralized Forces forPropeller Noise Excitation 26ANOPP Computer Program Output 6Geometrical Considerations and ReflectingSurface Effects . 313.5 Interior Coupling Factor f(n,r) 32Calculation of f(n,r) for Cylinderwith Floor 333.6 Joint Acceptances for Cylinder withStructurally Integral Floor 363.7 Re
6、sonance Frequencies. . 40iiiProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TABLE OP CONTENTS(Continued)Section Page3.8 Loss Factors 403.8.1 Acoustic Loss Factors n and n . . . 41n nBare Fuselage (Cabin) 41Calculation of n when sidewalltrim is presen
7、t 413.8.2 Structural Loss Factors 42Influence of trim on structuraldamping 43Influence of internal radiation:closely coupled structural andacoustic modes 43Average radiation loss factors. . 443.9 Validation Studies 4REFERENCES 45APPENDIX A -.SIDEWALL TRIM: TRANSMISSION ANDABSORPTION MODELSTransmissi
8、on A-lTrim Transfer Matrix A-5Sound Absorption 8Vibration Transmission to Trim A-9APPENDIX B - FUNDAMENTALS OF PROPELLER NOISE THEORY. .APPENDIX C - CABIN ACOUSTIC MODESFinite Difference in Two Dimensions C-lIVProvided by IHSNot for ResaleNo reproduction or networking permitted without license from
9、IHS-,-,-TABLE OF CONTENTS(Continued)Section PageBoundary Conditions C-4Solution C-4Normalization 6Sample Results C-7APPENDIX D - FUSELAGE STRUCTURAL MODEL: CYLINDER WITHINTEGRAL FLOORDisplacement Functions D-lConstraint Equations 3Equations of Motion D-4The Mode Shapes (Eigenvectors) D-10Generalized
10、 Mass D-12Sample Output 2APPENDIX E - MODEL VALIDATION STUDIES.Test Hardware E-lPropeller E-5Test Description E-8Measured Interior Sound Levels E-12Propeller Noise Field E-l-4Acoustic Loss Factors E-18Structural Loss Factor E-21Predicted Interior Sound Levels E-24Noise Reduction E-30General Comments
11、 9APPENDIX F - LIST OF SYMBOLSProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LIST OP FIGURESFigure1. Propeller Aircraft Interior Noise Model 32. Propeller and Fuselage Surface Point Geometry . . 4A-l. A Basic Sidewall Trim: Insulation and Lining. .
12、. A-2A-2. Acoustical Properties of Owens-Corning PF-105Fiberglas: Density 9.6 kg/m3 (0.6 Ib/ft3),21 . A-6B-l Lagrangian Coordinate (ri) System B-6C-l Cabin Acoustic Space C-2C-2 Finite Difference Grid Nomenclature . C-3C-3 Acoustic Modes for a Case where 6O = 56.6,q = 0, a = 1 meter C-8D-l Circular
13、Cylindrical Shell with a LongitudinalPartition D-2D-2 Example Shell Mode (Z Dependency Suppressed). . . D-17D-3 A Second Example Mode D-19E-l Model Test Facility (Dimensions in meters). . . . E-2E-2 Fuselage Model E-3E-3 Floor Assembly (Dimensions in meters) E-4E-4 Grid Used for Propeller Noise Pred
14、ictions E-6E-5 Cross-Section of Test Cylinder Showing Trim . . . E-10E-6 Microphone Locations in Test Cylinder E-llE-7 Typical Narrowband Spectra of Interior SoundPressure Levels E-13E-8 Average Sound Pressure Spectra in Cylinder atDifferent Measurement Stations (Propeller NoiseExcitation) E-15VIPro
15、vided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LIST OP FIGURES(Continued)Figure PageE-9 Space-Average and Range of Values for Propeller-Induced Sound Levels Inside Test Cylinder . . . E-l6E-10 Space-Average and 95% Confidence Limits for .Propeller-Indu
16、ced Sound Levels Inside TestCylinder E-17E-ll Measured and Predicted Free-Field Sound Levelsfor Test Propeller. E-19E-12 Measured and Predicted Blocked Sound LevelsInduced by Propeller on Test Cylinder E-20E-13 Measured Acoustic Absorption Coefficients inTest Cylinder E-22E-14 Measured and Predicted
17、 Acoustic Loss Factors forInterior of Test Cylinder (5.1 cm Fiberglassplus Trim) E-23E-15 Measured and Predicted Total Structural LossFactors for Test Cylinder E-25E-16 Comparison of Predicted and Measured SoundLevels in Cylinder Induced by Propeller (Meanand Range of Values) E-26E-17 Comparison of
18、Predicted and Measured SoundLevels in Cylinder Induced by Propeller (Meanand 95% Confidence Limits) E-27E-18 Comparison of Predicted and Measured SoundLevels in Cylinder Induced by Propeller (TrimLoss Factor = 1.0, Total Structural Loss FactorLimited to 0.15 Maximum) E-29E-19 Average Noise Reduction
19、 Measured at Stationat 50% of Cylinder Length E-31E-20 Average Noise Reduction Measured at Stationat 83% of Cylinder Length E-32viiProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LIST OP FIGURES(Continued)FigureE-21 Comparison of Measured and Predict
20、ed Space-Average Noise Reduction for Test Cylinder(Average and Range of Values, Trim LossFactor = 1.0. Total Structural Loss FactorLimited to 0.15 Maximum) E-33E-22 Comparison of Measured and Predicted Space-Average Noise Reduction for Test Cylinder(Average and 95% Confidence Limits, Trim LossFactor
21、 = 1.0, Total Structural Loss FactorLimited to 0.15 Maximum) E-34E-23 Measured Noise Reductions for Cylinder withDifferent Thicknesses of Fiberglass Batts onEnd Plates E-36E-24 Predicted Noise Reduction for Cylinder withDifferent Thicknesses of Fiberglass Batts onEnd Plates E-37E-25 Predicted Acoust
22、ic Loss Factors for Cylinder withDifferent Thicknesses of Fiberglass Batts onEnd Plates E-38viiiProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LIST OF TABLESAppendix - Table No. PageC-l. Example Program Output. Phase III Test Article,Angle subtended
23、 by Floor Edge with Vertical00 = 56.6 degrees C-15D-l. Example Program Output. Phase III Test Article:1.803m (71 in.) long cylinder, stiffened 0.0008m(0.032 in.) skin, 0.508m (20 in.) radius withfloor at 56.6 D-13ixProvided by IHSNot for ResaleNo reproduction or networking permitted without license
24、from IHS-,-,-1.0 SUMMARYAn analytical model for aircraft interior noise prediction isconsidered in this report. The model can be used to predict thesound levels inside an airplane cabin caused by the rotation ofa propeller (of any design) alongside. The fuselage model isthat of a cylinder with a str
25、ucturally integral floor. Thecabin sidewall and the floor are stiffened by ring frames andstringers or floor beams of arbitrary configurations. The cabininterior is covered with a trim (i.e., layers of insulation andsepta with a lining) to increase the sidewall sound isolationand provide absorption
26、in the cabin.The results are the culmination of a three phase programsponsored by NASA Langley Research Center. In Phase I the basicanalytical modeling of the transmission problem (interaction ofthe structure with the exterior and interior acoustic fields)was undertaken and preliminary validation st
27、udies were completedusing an unpressurized, unstiffened cylinder as a test article.Results of that work are presented in Reference 3. In PhaseII, the general aircraft interior noise model was developed andpreliminary work on the laying out of the basic master computerprogram began. Validation studie
28、s were conducted using moreadvanced test articles (one being a stiffened cylinder with afloor partition and interior trim). Results of that work arefound in References 4 and 7. In Phase III, the analyticalmodels and the software were completed (including the propellerexcitation work). Validation stu
29、dies using a scale model fuse-lage excited by a propeller were undertaken and the documenta-tion of the finalized model and software package was completed.The present model is believed to be the only one in existencethat can be used to calculate the interior sound levels using asinput data, the prec
30、ise propeller noise signature over thefuselage.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2.0 INTRODUCTIONThis report presents the details of a basic airplane interiornoise model. The elements of this model include a fuselage anda propeller (Fig
31、ures 1 and 2). The fuselage consists of a cy-linder stiffened by ring frames and stringers, and a floor thatis structurally an integral part of the fuselage. The cabinspace is the volume above the floor. The interior surface ofthe cabin (sidewall) is finished out with a trim consisting ofinsulation
32、covered with a lining. The propeller rotates about anaxis parallel to the centerline of the fuselage. The model canbe used to predict the sound levels in the cabin space for eachof the various harmonics of the propeller.The excitation of the exterior of the fuselage is obtained usinga propeller nois
33、e prediction model developed by NASA Langley.The present model works with the pressure time histories (signa-tures) as defined over the fuselage at a number of closelyspaced points on a grid that lies in the fuselage skin. Thepressure signatures are Fourier analyzed to define the ampli-tudes and pha
34、ses of each of the harmonics of the propeller tones(at each location on the grid). The cross power spectral den-sity function for each harmonic, for all grid point pairs (adelta function in the frequency domain) is used to compute thevalues of the generalized forces for each structural mode of thefu
35、selage.The fuselage structural modes are developed for the case of astiffened cylinder with a floor partition. The structural modesare described by their eigenvalues (resonance frequencies),eigenvectors (mode shapes), and loss factors. The mode shapesinclude not only the cylinder wall normal displac
36、ement (w com-ponent) but also the normal displacement of the floor, and thein-plane axial and circumferential displacements (u and vcomponents) of cylinder and floor as well. The loss factors ofProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-FIGURE 1
37、. PROPELLER AIRCRAFT INTERIOR NOISE MODEL Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Propeller Plane FUSELAGEy - Incidence Anglenx = (a, 9, z) = Location of Freem Field PredictionPoint(r ,: 2 ) = Propeller PositionP PFIGURE 2. PROPELLER AND FUSE
38、LAGE SURFACE POINT GEOMETRYProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-the bare fuselage are input and must come from measurements.When trim is installed on the sidewall, the structural lossesincrease due to the trims presence against the sidewal
39、l andthis is computed for the particular trim installation.The displacement of the trim lining induced by the fuselage skinvibration is determined using a transfer matrix which relatesthe pressures on the inside of the skin and the inside of thelining to the displacement of the skin and of the linin
40、g. Thetransfer matrix contains all of the physical properties of theinsulation and lining required for the calculation. The waveimpedance of the insulation and complex acoustic wavenumber areinput as physical parameters to describe the insulation.The coupling of the lining to the interior acoustic f
41、ield iscalculated for each acoustic and structural mode. The acousticmodes are defined by their resonance frequencies, mode shapes,and loss factors. The acoustic loss factors must be input for abare fuselage but are calculated when a cabin trim is installed,from elements of the trim transfer matrix.
42、The model allows for the calculation of the space average meansquare pressure in the cabin for each propeller harmonic, (up toa maximum of ten (10) harmonics).2.1 Report OrganizationThis report considers the analytical derivations, experimentaltests, and validation studies. The analytical derivation
43、s arepresented in Section 3 and Appendices A through D. Appendix Eis devoted to test comparisons and to the determination of thequality of the predictions. Appendix F is a list of symbolsused.Early in Section 3, general solutions are given for the basicsound transmission problems of concern. Problem
44、s of toneProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-transmission (propeller) and noise transmission (reverberantexterior field) are considered. Solutions that are to be usedin the low and high frequency regimes are presented (the lowfrequency fo
45、rmulations apply until the acoustic modal density ofthe cabin space is equivalent to 10 to 15 modes in every one-third octave band). Beginning with Section 3.4, the variousterms appearing in the general solutions are evaluated, literal-ly specialized to create the desired interior noise model.These
46、terms include the generalized forces for propeller noiseexcitation, interior coupling factors, joint acceptances,resonance frequencies and loss factors. Information needed tocomplete these calculations are derived in the first fourappendices.The model validation undertaken in Phase III is considered
47、 inAppendix E. The experiment and the data acquired are discussedand a statistical comparison of predictions and measurements ispresented.2.2 Program ManagementThe work was accomplished in joint effort by BBN/Los Angeles andNASA Langley Research Center. The experimental work was done atNASA Langley
48、by C. M. Willis and W. H. Mayes. Mr. Mayes actedas LaRC technical representative of the contracting officer(TRCO). L. D. Pope served as BBN program manager.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-3.0 ELEMENTS OP THE PROPELLER AIRCRAFT INTERIORNOISE MODELA detailed description of the propeller aircraft interiornoise prediction model is given in the following
