THE SPANN VIBROACOUSTIC METHOD Revision A

Transcription

1 THE SPNN VIBROCOUSTIC METHOD Revision By Tom Irvine Deember 15, 01 Figure 1. vionis Installation and Testing Introdution vionis omponents in airraft and launh vehiles may be mounted to surfaes whih are exposed to high intensity aousti exitation. The external aousti pressure field auses the panel and shell surfaes to vibrate. This vibration then beomes a base input to any omponent mounted on the internal side. Components must be designed and tested aordingly. The omponent vibration input levels an be derived via analysis and testing for a given sound pressure level. ousti testing of the struture an be performed in a reverberant hamber or using a diret field method. There is some diffiultly in testing, however, beause the simulated aousti field in the lab faility may be different in terms of spatial orrelation and inidene than that of the flight environment even if the sound pressure level an be otherwise repliated. The vibroaousti analysis tehniques inlude finite element and boundary element methods, as well as statistial energy analysis. These are powerful tools, but they require numerous assumptions regarding external aousti pressure field type, oupling loss fators, modal density, 1

2 impedane, radiation effiieny, ritial and oinident frequenies, distinguishing between aoustially fast and slow modes, et. s an alternative, simple empirial methods exist for deriving the strutural vibration level orresponding to a given sound pressure level. Two examples are the Franken and Spann tehniques. These methods may be most appropriate in the early design stage before hardware beomes available for lab testing and before more sophistiated analysis an be performed. The Franken method is given in Referenes 1 and. The Spann equation will be overed in this paper. The Spann method provides a reasonable estimate of the aoustially exited omponent vibration environments when only the areas exposed to the aousti environment and mass are known, aording to Referene 3. Spann Method This setion desribes the steps required to derive omponent vibration test speifiations for typial aerospae strutures subjeted to high-intensity aousti environments. The appliation of this predition method is based on two onditions: 1. Definition of the aousti environment. n adequate general understanding of struture and omponents to obtain estimates of mass and areas exposed to aousti exitations Step 1 The method begins with an external one-third otave band sound pressure level (db). The sound pressure level SPL(f ) for band enter frequeny f is onverted into a pressure spetral density via the following equation. SPL(f ) W P(f ) pref f Pa /Hz (1) where p is the zero db referene pressure (Pa) ref SPL(f ) is the sound pressure level (db) f is the frequeny bandwidth (Hz)

3 The typial zero db referene is pref p ref 0 Pa () 0 Pa (3) The RMS pressure in p rms (f ) eah band is p rms (f ) p ref 10 SPL(f ) 10 () The pressure PSD is thus rms p (f ) W P(f ) f (5) The one-third otave bandwidth is f 0.316f (6) Preferred enter frequenies are given in ppendix. Step Estimate area (m ) of the omponent and spaeraft support struture supporting the omponent exposed to aousti exitation. Step 3 Calulate total mass M (kg) of the omponent and support struture inluded in the above estimate in step. Step Calulate, at eah one-third-otave band frequeny, the equivalent aeleration response W (f ) (G /Hz) using the following equation and the values of the pressure power spetral density W P(f ) (Pa /Hz), area (m ) and mass M (kg) alulated in steps 1, and 3. 3

4 The aeleration power spetral density in one-third otave format for the omponent base input is P W (f ) Q W (f ) gm (G /Hz) (7) where β is reommended as.5 per experimental data Q is the amplifiation fator reommended as.5 g is the gravitational onstant 9.81 m/se Note that the suggested values for β and Q are taken from Referene 3. The derivation of equation (7) is given in ppendix B. Step 5 Iterate steps, 3 and, using different values of the input parameters to determine maximum W (f ) response urve. Example n example is given in ppendix C Referenes 1. Summary of Random Vibration Predition Proedures, NS CR-130, T. Irvine, Vibration Response of a Cylindrial Skin to ousti Pressure via the Franken Method, Revision H, Vibrationdata, Spaeraft Mehanial Loads nalysis Handbook, ECSS-E-HB-3-6, Noordwijk, The Netherlands, February T. Irvine, Steady-State Vibration Response of a Plate Simply-Supported on all Side Subjeted to a Uniform Pressure, Rev C, Vibrationdata, 01.

5 PPENDIX Preferred One-Third Otave Bands Lower Band Limit (Hz) 1/3 Otave Bands Center Frequeny(Hz) Upper Band Limit (Hz)

6 The previous table is taken from: Note the following relationships. f l f f u Lower band frequeny Band enter frequeny Upper frequeny f fufl (-1) 1/6 fu f (-) 1/6 fl f / (-3) For two onseutive bands, f, i1 f, i (-) The preferred frequenies in the previous table approximately satisfy this set of formulas. 6

7 PPENDIX B Derivation The following is taken from Referene. The baffled simply-supported plate in Figure B-1 is subjeted to a uniform pressure. P (x,y,t) z(x,y,t) ss ss b ss y a x ss Figure B-1. The following equations are taken from Referene. The governing differential equation is z z D x x y z z h y t P(x, y, t) (B-1) The plate stiffness fator D is given by Eh 3 D (B-) 1 1 7

8 where E h P is the modulus of elastiity Poisson s ratio is the thikness is the mass density (mass/volume) is the applied pressure Now assume that the pressure field is uniform suh that W(t) P(x, y,t) (B-) The differential equation beomes w w D x x y w w h y t W(t) (B-3) The mass-normalized mode shapes are m x n y Z mn sin sin (B-) a b h a b The natural frequenies are mn D h m n a b (B-5) The partiipation fators for onstant mass density are b a mn h Zmn(x, y) dxdy 0 (B-6) 0 8

9 a b h mn os n 1os m 1 (B-7) mn The displaement response Z(x, y, ) to the applied fore is 1 mnzmn x, y Z x, y, W (B-8) h m 1n 1 mn jmnmn Z x, y, 1 W h a b h m n m1n 1 m x n y 1 sin sin a b h a b mn jmnmn os n 1os m (B-9) Z h x, y, W m1n 1 1 m n m x n y 1sin sin a b mn jmnmn os n 1os m (B-10) 9

10 The veloity response V(x, y, ) to the applied fore is V x, y, W h m1n 1 j m n mn os n 1os m mn m x n y 1sin sin a b jmnmn The aeleration response (x, y, ) to the applied fore is (B-11) x, y, W h m1n 1 m n mn os n 1os m mn m x n y 1sin sin a b jmnmn (B-1) The aeleration response due to the first mode only at the enter is W (B-13) h 11 j1111 ssume resonant exitation and response for onservatism. 11 (B-1) j Q (B-15) 16 Q W (B-16) h 10

11 gm h (B-17) 16 Q W (B-18) gm For band enter frequeny f. f Wf 16 Q gm (B-19) Let 16 Q (B-0) f Q Wf gm (B-1) (B-) f Q Wf gm f Wf f Q gm f (B-3) Let W = aeleration power spetral density at the enter of the plate W p = uniform pressure power spetral density 11

12 1 f f W (B-) p f W f W (B-5) p f W gm Q f W (B-6)

13 PPENDIX C Example Figure C-1. n avioni box is mounted to a surfae with the following parameters. β.5 Q.5 M 10 lbm 00 in^ The external mounting surfae is subjeted to the sound pressure level in Figure C-1. 13

14 Figure C-. The resulting aeleration PSD is shown in Figure C-. This would be the base input for the avionis omponent. 1