Statistical Energy Analysis Software & Training Materials, Part II Tom Irvine Dynamic Concepts, Inc. NASA Engineering & Safety Center (NESC) 20-22 June 2017 The Aerospace Corporation 2010 The Aerospace Corporation 2012 Vibrationdata
Whimsical but Accurate Quote The process of deriving environments by whatever means is the process of building a justification story for one s own engineering judgment of what those levels should be, heavily weighted with past experience with empirical data. - Tom Irvine
NASA-HDBK-7005 Example 1 Launch Vehicle Fairing Electronic Component Ring Frame Equipment Shelf in Fairing Acoustic Cavity a,d Equipment Shelf Subject Fairing to External Liftoff SPL Direct Mechanical Path Actual field is oblique incidence but model as a diffuse field Lump Ring frame in with Fairing f,d s,d Rename Fairing as Cylindrical Shell
NASA-HDBK-7005 Example 2 A simplified SEA energy flow model is commonly used within the aerospace industry to predict interior acoustic levels
SEA Approach A Vibroacoustic system can be divided into a series of connected subsystems Statistical Energy Analysis (SEA) solves for the subsystem energy as function of the external applied acoustic or mechanical power, over mid and high frequency bands The acoustic power can be calculated from the sound pressure level Velocity, acceleration, stress and other response metrics can be calculated from each subsystem s energy SEA depends heavily on a series of mostly empirical and semi-empirical parameters for each subsystem, including Mass Driving Point Impedance & Mobility Modal Density Wave Speed for both Dispersive & Non-Dispersive Waveforms Radiation Efficiency & Resistance Dissipation Loss Factor Coupling Loss Factor between Subsystems Critical Frequency & Cylinder Ring Frequency
Some SEA Assumptions The subsystems in SEA are finite, linear, elastic structures or fluid cavities For a system with two subsystems, the energy flow is proportional to the acoustic or vibrational energies of the two subsystems Subsystem modes in each band must be uncoupled from one another or have equal energies Subsystems have small modal damping, equal for all modes in a given frequency band The primary response is resonant Acoustical fields are diffuse Acoustic volumes have much higher modal density than the structures in models A cylindrical shell behaves as a flat plate above its ring frequency Traditional SEA has assumed steady-state incoherent broadband random excitation Transient SEA methods have also been developed Boundary conditions become less relevant at higher frequencies A circular plate has the same modal density as a rectangular plate of the same surface area.
Progress Ongoing... The Vibrationdata Matlab GUI package is freely available via Tom s blog and email distribution list https://vibrationdata.wordpress.com/2013/05/29/vibrationdata-matlab-signal-analysis-package/ An SEA section has been added to the blog as part of an ongoing improvement effort Mailing list also created, new members welcome The following slides are screenshots of the Matlab GUI with examples and equation references
Table 1. Fairing, Honeycomb Sandwich Gas Mass Density 0.076487 lbm/ft^3 Gas Speed of Sound 1125 ft/sec Length 360 in Diameter 90 in Uniform Dissipation Loss Factor 0.03 Face Sheet Material Graphite/Epoxy Face Sheet Mass Density 0.058 lbm/in^3 Face Sheet Poisson Ratio 0.3 Individual Face Sheet Thickness 0.032 in Core Shear Modulus 50000 psi Core Mass Density 0.003 lbm/in^3 Core Thickness 1in Payload Fairing Acoustic Transmission Example from NASA-HDBK-7005 The internal and external gasses are assumed to have the same properties The gas is air Table 3. Blanket Mass Density Thickness 0.7 lbm/ft^3 2 in Percent Coverage 90% Table 2. Acoustic Cavity Enclosed Volume 1.9467e+06 in^3 Fairing Interior Surface Area 91609 in^2 Percent of Fairing Volume Occupied by Payload 70% Clearance between Fairing Interior Wall & Payload Exterior 6 in Fairing Bare Wall Absorption Coefficient 0.05 Uniform Loss Factor for Gas Molecular & Viscous Effects 0
Vibrationdata Main GUI, Import Data
Read Typical Liftoff SPL
Liftoff SPL
SEA Functions
SEA Function Dialog
SEA Model Dialog Box, Simple Fairing
Fairing Analysis Dialog
Some Formulas The average transmission coefficient ave is 8f V plf,int plf,ext ave int,ext 1B B blanket cs plf,d The Noise Reduction NR is NR(dB) 10log 1 f V c S blanket References Frequency (Hz) Volume Speed of sound, interior Fairing surface area Blanket transmission coefficient from insertion loss 1. NASA-HDBK-7005 Dynamic Environmental Criteria, 2001. Equations (4.36) & (4.41) 2. K. Weissman, M. McNelis, W. Pordan, Implementation of Acoustic Blankets in Energy Analysis Methods with Application to the Atlas Payload Fairing, Journal of the IES, July, 1994. int,ext plf,int plf, ext plf,d B Coupling loss factor, interior to exterior (mass law) Coupling loss factor, fairing to interior Coupling loss factor, fairing to exterior Dissipation loss factor, fairing Average absorption coefficient, as calculated from the area-weighted section absorption coefficients for the case of added blankets Ratio of surface area covered by blankets
Non-Resonant, Mass Law R N R random f Transmission Loss Normalincidence Transmission Loss Randomincidence Frequency (rad/sec) Frequency (Hz) Normal-incidence s R N 10log 1 2oc o 2 Random Incidence R R 10 log 0.23R random N N f cr s Critical frequency (Hz) Panel mass per area Valid for f << f cr Assume random incidence for launch vehicle o c o Characteristic impedance of the gas, assume the same on both sides Reference: Beranek and Ver, Noise and Vibration Control Engineering Principles and Applications, Wiley, New York, 1992. Equations (9.80c) & (9.99)
Coupling Loss Factors int,ext plf,int plf, ext Coupling loss factor, interior to exterior S Surface area Coupling loss factor, fairing to interior V Internal air volume Coupling loss factor, fairing to exterior c Speed of sound R Mass Law Transmission loss (db) f Frequency (Hz) Transmission coefficient S Surface area Frequency (rad/sec) m Mass per area of fairing c Characteristic impedance of the air rad Radiation efficiency References 1. NASA-HDBK-7005 Dynamic Environmental Criteria, 2001. Equations (4.41) & (4.43) 2. Hyun-Sil Kim, Jae-Seung Kim, Seong-Hyun Lee and Yun-Ho Seo, A Simple Formula for Insertion Loss Prediction of Large Acoustical Enclosures using Statistical Energy Analysis Method, Int. J. Nav. Archit. Ocean Eng. (2014). Equation (9) int, ext cs 10 ^ R /10 8f V c plf,int m rad 3. Beranek and Ver, Noise and Vibration Control Engineering Principles and Applications, Wiley, New York, 1992. Equations (9.80c) & (9.99) Assume plf, ext plf,int
Payload Fill Factor The fill factor FF is f V r H c Frequency (Hz) Ratio of acoustic volume inside fairing or with and without the payload present Clearance between fairing inner wall and the payload exterior Speed of sound in the acoustical volume c 1 2f H FF(dB) 10 log 10 c 1 1V r 2f H Reference: NASA-HDBK-7005 Dynamic Environmental Criteria, 2001. Eq (4.46)
Vent Noise All payload fairings and bays are vented to relieve the atmospheric pressure inside the fairing or bay as the launch vehicle gains altitude during launch. In many cases, the vents are covered during liftoff to suppress leakage through the vent openings of the intense liftoff acoustical environment into the fairing or bay. Open vents can create a Helmholtz resonator effect with a tonal acoustic response inside the fairing. The response is typically composed of a fundamental frequency with integer harmonics. This effect is not included in this software. Reference: NASA-HDBK-7005 Dynamic Environmental Criteria, 2001. Section (4.6.7)
Fairing Sandwich Construction
Honeycomb Sandwich Cylindrical Shell Radiation Efficiency The natural frequencies and wave numbers are calculated per the method in Bing-ru. The corresponding radiation efficiencies are calculated via Szechenyi. See also Lyon. Cylinder modes must be categorized as either acoustically fast (AF) or acoustically slow (AS) in order to determine their ability to interact with sound waves. The distinction between these two classes is that an AF mode has a structural wavenumber smaller than the acoustic trace, according to Szechenyi. k / c 2 / m / L air air k m k n n d n d k k m k n air L d c air Acoustic wave number Axial wave number, index m Circumferential wave number, index n Radiation efficiency Length Diameter Frequency (rad/sec) Speed of sound in air k 2 k 2 m k 2 n for acoustically fast (AF) modes 2 2 m n rad 1 2 (k k ) rad 1 k for 2 2 2 k k m k n
References for Previous Slides 1. Bing-ru, et al, Study on Applicability of Modal Analysis of Thin Finite Length Cylindrical Shells using Wave Propagation Approach, Journal of Zhejiang University SCIENCE, 2005. 2. E. Szechenyi, Modal Densities and Radiation Efficiencies of Unstiffened Cylinders using Statistical Methods, Journal of Sound and Vibration, 1971. (Section 5.1, page 73) 3. G. Maidanik, Response of Ribbed Panels to Reverberant Fields, Journal of the Acoustical Society of America, Volume 34, Number 6, June 1962. (Equation 2.16).
Acoustic Cavity
Acoustic Blankets
Acoustic Blankets, References Acoustic Absorption Coefficients The absorption coefficients should be obtained from test measurements of the blanket. An empirical method is given in Reference 1 for preliminary analysis. The peak absorption coefficient peak for a blanket with thickness t (inches) is with an upper limit of peak =1 Compute the peak frequency f peak and round to the nearest one-third octave band center frequency, Construct the curve for frequencies f f < f peak using = peak ( f / f peak ) f > f peak using = peak (f peak / f) Reference K. Weissman, M. McNelis, W. Pordan, Implementation of Acoustic Blankets in Energy Analysis Methods with Application to the Atlas Payload Fairing, Journal of the IES, July, 1994.
Acoustic Blankets, Insertion Loss
Absorption Coefficient Foam by itself has an absorption coefficient approach unity at mid and higher frequencies But curve includes reflective effect of polymer blanket covering per reference data
Final Calculation
Radiation Efficiency, Bare Fairing The radiation efficiency approaches unity near the critical frequency which is 288 Hz The critical frequency is the frequency at which the speed of the free bending wave in a structure becomes equal to the speed of the airborne acoustic wave The acoustic and structural wavelengths are likewise equal at this frequency
Payload Fill Factor, 70% Case The fill factor is the SPL increase due to the payload s presence relative to an empty fairing.
Transmission Loss for Non-resonant Mass Law The transmission loss from the mass law is not realized across the middle and higher frequencies due to the resonant-mode transmission In addition, the fill factor reduced the transmission loss, especially at low frequencies
Coupling Loss Factors A coupling loss factor is similar to an energy transmission coefficient The transmission of energy from a source to a receiver is also the energy lost by the source via the transmission path The blue curve is the transmission ratio for sound due to the non-resonant mass law. The red curve represents the resonant energy transmission ratio from the fairing to the interior cavity
Total Transmission The mass law drives the transmission coefficient below about 50 Hz The structural resonant transmission dominates at mid and high frequencies
Fairing and Internal Cavity Parameters, alpha & tau alpha is the average absorption coefficient tau is the average transmission coefficient The ratio of alpha over tau is needed for the noise reduction calculation A higher ratio yields a higher noise reduction
Fairing Net Noise Reduction The net noise reduction includes the transmission loss, internal absorption and fill factor Again, the transmission loss includes both resonant and non-resonant effects
SPL Results, External & Internal Now assume that this analysis is being performed for a proposal A good practice would be to vary the parameters in order to obtain a statistical distribution of internal levels The key frequencies are: Ring Frequency = 711.3 Hz Critical Frequency = 288.2 Hz Shear region = 4410 to 2.4634e+05 Hz
Conclusions Tom will continue to work on this project intermittently His other ongoing projects include Rainflow Fatigue & Spectral Methods Multi-axis Fatigue Enveloping Nonstationary Vibration Environments Shock Response Spectra Time History Synthesis, Seismic & Pyrotechnic Shock NASA Shock Working Group NASA-HDBK-7005 Revision SLS Day of Launch Vehicle Load Indicator Software Certification Receptance Decoupling Structural Dynamics, Finite Element Analysis, and Coupled Loads Webinar series Matlab GUI & Supporting Documents available at: https://vibrationdata.wordpress.com/2015/12/09/vibroacousticsstatistical-energy-analysis/ Feedback and contributions are welcome!