Band, Jonathon L.

Davis, Robert Ben

Fulcher, Clay W.

Hunt, Ronald A.

Jones, Douglas C.

LaVerde, Bruce T.

Smith, Andrew M.

NASA Technical Reports Server

Determining System Response using Uncoupled 
Transfer Functions - And Advantages Using      
Response Matching Methods 
Andrew M. Smith Dr. Robert Ben Davis
Vibroacoustics Specialist
Vehicle Loads and Strength Branch (EV31)
NASA Marshall Space Flight Center
Acoustics and Structural Dynamics Specialist
Propulsion Structural & Dynamics Analysis Branch (ER41)
NASA Marshall Space Flight Center
Bruce T. LaVerde,  ERC Inc Ronald  A. Hunt, Triumph Aerospace
Vibroacoustics Lead Engineer
ESTS Contract Support to 
Vehicle Loads and Strength Branch (EV31)
NASA Marshall Space Flight Center
Clay W Fulcher (ER41) Douglas C Jones (EV31) & Jonathon L Band (EV31)
Structural Dynamics Specialist 
ESTS Support to Vehicle Loads and Strength Branch (ES20)
NASA Marshall Space Flight Center
 .  ,  .       .   
Structural Dynamics Specialist 
Jacobs Engineering, 
ESTS Contract Support to Vehicle Loads and Strength Branch 
NASA Marshall Space Flight Center
NASA/Marshall Space Flight Center/
Vehicle Loads and Strength Branch (EV31)
19–21 June 2012
© The Aerospace Corporation 2010
https://ntrs.nasa.gov/search.jsp?R=20120015315 2019-08-30T22:18:16+00:00Z
Introduction/Agenda
• Introduction  Goal
• Development of a Tool that provides best-in class-accuracy for vibration response 
assessments of Mass loaded panels.
• The tool should also place capability in the hands of the end user with less 
complexity for each assessment.
• Development of methodology for calculating system vibrations response using 
uncoupled models (uncoupled transfer function sets) is provided.
• Background - Addressing What need:
• Validation and refinement of the approaches used to estimate the vibration 
environments associated with Equipment mass loaded exterior panels of launch 
vehicles is of major importance to new vehicle programs
• This Validation has been identified by the NASA Engineering and Safety Center 
(NESC) as an area of uncertainty that is worthy of on-going study (References 1 and 
2).
• System damping values can increase with greater levels of integration.
• Important to test validate damping under flight like conditions. 
• Validation Test Program Test Conditions
• Methodology:
• Response comparisons
• Conclusions/Future Work
2
Background
• Background - Addressing What need:
• In response to the NESC's critical technological need (References 1 and 2), the authors have presented a 
pair of validated methodologies for calculating both vibration response and dynamic loads for equipment 
mounted to vehicle exterior panels.
• RPTF applies a correlated pressure field across the surface of a vehicle panel This is A direct method.             .       
calculating response from input excitations. A diffuse acoustic field (DAF) pressure assumption was assumed.  
Pressure spectra provided as RMS sound pressure levels are first converted to pressure autospectral density.  
Then cross-spectra associated with the pressure field excitation are calculated according to the best fit for a 
DAF (References 4 and 5).
• The second method, the Response Matching Method (RMM), provides the basis for much of the theoretical 
development presented here.  It is a indirect method. Response is calculated based on a ratio of Transfer 
functions and the known response of one of the two systems. 
• The third method, RPTF – Uncoupled, represents the methodology under development for this 
technical paper. RPTF – Uncoupled is also a direct approach.        
3
Database Tool
Uncoupled Approach
• Development of a Tool that provides best-in class-accuracy for vibration response assessments of Mass loaded panels.               
• The tool should also place a flexible capability in the hands of the end user with less complexity for each assessment.  
An Uncoupled Approach.
4
Database Tool
Uncoupled Approach
• Database Library will provide Selectable Primary Structure Panels (Yellow and Green Brackets at left).
• Database Library will provide Selectable Secondary Structure Equipment/Component Examples (Table On           
Right).
• An Uncoupled Approach. Database Library is expandable.
5
Database Tool
Features
• Tool will be delivered to the 
customer as a standalone 
executable.
• Cross-platform compatibility 
(Windows, OSX, Unix).  
• Designed for speed and ease 
of use. 
• Tool consists of two main 
modules: Database Browser 
and Analysis/Results.
1
Database Browser Features:
1: Several filters allow for quick 
access to different file types and 
interface footprints stored on the 
database (models pressure 2 ,  
FFs, etc.). 
2: Database list allows the user 
to view all available files stored 
on the database.
4
3: File attributes provides quick 
access to relevant information.
4: Display provides FEM 
3
geometry with patch definitions 
or forcing function plots.
6
Database Tool
Features
Analysis/Results Features:
1: Footprint filter identifies 
compatible Primary and 
Secondary structures via stored 
interface location definitions. 
2: Frequency range boxes allow 
the user to specify the desired 
evaluation frequencies (with 
error checking to ensure range is 
within model and FF limits)
1
2
    .
3: Lists allow the user to select a 
Primary and Secondary structure 
for coupling. 3
4: Response location sets the 
desired DOF or DOFs for 
response output.
5: Comprehensive error checking 4
ensures all inputs are provided 
and valid (all panels turn green) 
before allowing response 
computation.
6: Results panel stores all 5
6
     
responses calculated and allows 
for overlay plots.
7
Validation Test Program Test Conditions
(a.) Acoustic or Fluctuating 
Pressures affect the exterior 
surface of Vehicle panels.
(b.) Ground test setup.
(a.)
(c.) Flight like excitation of 
exterior surface in Baffled panel 
test setup. (Reverberant)
(c.) View of Flight like test article 
from Anechoic receiver room. (b.)
• Note that the Vehicle Panel Test 
Article can be configured as a       
bare panel As in (d.) 
• or further integrated with 
equipment/cables.
(c.) (d.)
8
Validation Test Program Test Conditions
(b.)
• In figure (a.) at the below the test article is configured with an equipment assembly near the 
center:
(a.)
Medium  footprint
8 fasteners
9
Validation Test Program Test Conditions
• The plots labeled a and b below present response at locations 1 and 2 for configurations 
with and without cables.
• Both provide evidence of attenuation in the range from 100 to 400 Hz.  Note these two 
responses have nearly identical spectral shapes below 600 Hz.  In this frequency range the 
structural bending wavelengths remain large relative to the orthogrid cell size.  Global panel 
behavior is exhibited.
• Above 600 Hz, the responses shown in diverge from each other:
• the bending wavelengths are small enough for the response at the center of an 
orthogrid cell to be different from the response on the perimeter. 
(a.) (b.)
10
Validation Test Program Test Conditions
• The plots labeled a and b below present response at locations 4 and 16 for 
configurations with and without 
11
Methodology Development
Vehicle Panel Responding to Fluctuating Acoustic Pressure Excitation
Response of Structural Panel with an Attached Component
The Multi Degree of Freedom Frequency Response Equation:
Consider a Partition where the coupling/boundary DOF are grouped at the top:
12
Methodology Development
Vehicle Panel Responding to Fluctuating Acoustic Pressure Excitation
Response of Structural Panel with an Attached Component
The Forces at the coupling/boundary dof can be written:
Imposing the Constraint Equation
Combining Eqs. (2) and (3) and solving for ab ,the acceleration at the interface 
in terms of the interface transfer f nctions and the e ternal force is      u    x    :
13
Methodology Development
Vehicle Panel Responding to Fluctuating Acoustic Pressure Excitation
Response of Structural Panel with an Attached Component
The Forces at the coupling/boundary dof can be written:
Equal and opposite Forces
Combining Eqs. (2) and (3) and solving for ab ,the acceleration at the interface 
in terms of the interface transfer f nctions and the e ternal force is      u    x    :
14
Methodology Development
Vehicle Panel Responding to Fluctuating Acoustic Pressure Excitation
Response of Structural Panel with an Attached Component
Now consider points p that are located on the panel, but not at interface points. 
The acceleration response of such points is given by:
Using Eqs (3) and (5) as well as acceleration continuity(imposing a constraint .           
condtion), the response at points p is :
Since Eqs. (4) and (6) will be used later to find the response of the component 
loaded panel subject to random pressure excitation, we begin to express these 
quantities in the modal form of the equations.  Imposing the  same Constraint Equation
15
Methodology Development
Vehicle Panel Responding to Fluctuating Acoustic Pressure Excitation
Response of Structural Panel with an Attached Component
The response at a single point p due to a single force excitation e. For linear 
structural systems, the complex scalar elements of the force/acceleration TF 
t i h i E (4) d (6) b d ti f t lma r ces s own n qs.  an   can e expresse  as a summa on o  na ura  
frequencies and modes:
where the TF elements given by Eq. (7) take the same form for responses at 
interface and non-interface points. This form also applies regardless of whether 
one is assembling matrices of bare structure TFs or component TFs (provided, 
of course, that the appropriate structure or component natural frequencies and
modes are used).  An Uncoupled use of the Models.
M is the number of modes.  Avoid truncation errors by including many 
modes from the uncoupled models.
16
Transition to Patch Method
Vehicle Panel Responding to Fluctuating Acoustic Pressure Excitation
7x3 =21 patches
At the top are the first three system mode 
shapes of the test article (57.0, 59.5 and 
61.5 Hz respectively) Hundreds of modes 
are used across the frequency range for
  
       
Vibroacoustics.
On the left the System model is shown 
including some facility structures that     
represent the boundary conditions at the 
perimeter of the test article.
17
Methodology Development
Vehicle Panel Responding to Fluctuating Acoustic Pressure Excitation
Pressure Excitation of Panel (The Patch Method) 
Cross correlation may be calculated between the pressures any pair of patches 
(exhibiting a non-zero cross-spectral density between them). The random 
fi ld i t d H iti t i f t l d iti fpressure e  s represen e  as a erm an ma r x o  spec ra  ens es o  
dimension Np, the total number of pressure patches. The pressure autospectra 
occur on the diagonal of the matrix. The cross-spectra appear off diagonal:
where                  . If spatial functions               are defined to relate the 
autospectra to the cross-spectra, Eq. (8) may be written as :
18
Methodology Development
Vehicle Panel Responding to Fluctuating Acoustic Pressure Excitation
Pressure Excitation of Panel (The Patch Method) 
15x15 =225 patches
When j = k the spatial functions 
coincide with the patch 
autospectra and the gamma 
approaches unity by L'Hopital's 
Rule. 19
Methodology Development
Vehicle Panel Responding to Fluctuating Acoustic Pressure Excitation
P E i i f P l (Th P h M h d)ressure xc tat on o  ane  e atc  et o  
Finally, the components of the pressure matrix may be expressed as products 
of frequency-dependent scaling functions, Wjk and an arbitrary reference 
t t Pau ospec rum pressure, ref :
and:
or more compactly: 
and for a DAF: 
20
Methodology Development
Vehicle Panel Responding to Fluctuating Acoustic Pressure Excitation
System Response from Uncoupled TF sets
In terms of patches 
21
Methodology Development
Vehicle Panel Responding to Fluctuating Acoustic Pressure Excitation
22
Validation of Methodology and Critique
If the acceleration PSD response of the bare structure to the same excitation is known, it 
is possible to combine Eqs. (20) and (21) to obtain a relation that is independent of 
pressure:
Note from the figure above that the result from the direct RPTF Coupled and RMM 
Coupled response compare as an exact match.
23
Validation of Methodology and Critique
The response of a mass-loaded panel at an interface point calculated using the coupled 
TF and uncoupled TF formulations of the RPTF method. Not yet an exact match.  
Note the interface locations were not a measurement location during the ground test.
24
Validation of Methodology and Critique
Acceleration response spectra from uncoupled RPTF formulation and the coupled RPTF formulation 
compared with test data at one measurement location.
Improvements based upon Component Modes synthesis as described by Craig-Bampton and others are 
contemplated.  Modal truncation has already been explored as a reason for slight mismatch. 
Next improvement trial will be including static interface displacement shapes          
so that more strain energy is represented at the interfaces.
25
Conclusions and Future Work
• The uncoupled Transfer Function formulations were presnted and validated 
for the uncoupled RPTF and system RMM methods.  
• A simple, but powerful, database analysis tool for the MSFC vibroacoustics 
t i d d l t t ti t ib ti t i team s un er eve opmen  o es ma e v ra on responses a  equ pmen  
mounting locations.  
• This useful estimating tool will supplement he heritage processes that 
typically required:
• the development of detailed system analysis models> 
• and/or the collection and processing of substantial ground and flight 
test data.  
• This puts powerful capability into the hands of the propulsion and vehicle            
system departments to provide input vibration environment requirements 
for a new launch vehicle program.
Status:
• “RPTF Coupled” and “RMM Coupled” have been fully vetted for use within 
the Database Tool.
• “RPTF Uncoupled” methodology was described and demonstrated.
• A few improvements to The “RPTF Uncoupled” are planned before the tool            
is complete.  
26
Conclusions and Future Work
Future Work:
Approach methodology for producing system transfer functions 
appropriate for vibroacoustics proof of concept trials from 
uncoupled models will be improved using several standard         
approaches was also verified in part.  
• For instance truncation of modes does result some 
inaccuracy, the team demonstrating that keeping 
significantly greater number of modes from the uncoupled 
models improved the results (already demonstrated).
• It is well known that the free-free modes of subsystems may 
not demonstrate as much strain in the elastic elements near          
coupling degrees of freedom as they may after coupling.  
Therefore it is expected that further improvement is 
possible by including some static fixed interface 
shapes.
Future work may also involve expanding the methods to accept other 
types of source environments as input.  For instance, the aero-fluctuating 
pressure environment associated with vehicle ascent is often modeled 
with what is known as a Corcos model.  This would provide even greater 
capability for predicting environments across all flight regimes.
27
References
28
12Smith, A., Davis, R.B., LaVerde, B., Hunt, R., Fulcher, C., Jones, D., Band, J., “Calculation of Coupled Vibroacoustics Response
Estimates from a Library of Available Uncoupled Transfer Function Sets,” AIAA SDM April 2012.
Determining System Response using Uncoupled 
Transfer Functions - And Advantages Using      
Response Matching Methods 
Andrew M. Smith Dr. Robert Ben Davis
Vibroacoustics Specialist
Vehicle Loads and Strength Branch (EV31)
NASA Marshall Space Flight Center
Acoustics and Structural Dynamics Specialist
Propulsion Structural & Dynamics Analysis Branch (ER41)
NASA Marshall Space Flight Center
Bruce T. LaVerde,  ERC Inc Ronald  A. Hunt, Triumph Aerospace
Vibroacoustics Lead Engineer
ESTS Contract Support to 
Vehicle Loads and Strength Branch (EV31)
NASA Marshall Space Flight Center
Clay W Fulcher (ER41) Douglas C Jones (EV31) & Jonathon L Band (EV31)
Structural Dynamics Specialist 
ESTS Support to Vehicle Loads and Strength Branch (ES20)
NASA Marshall Space Flight Center
 .  ,  .       .   
Structural Dynamics Specialist 
Jacobs Engineering, 
ESTS Contract Support to Vehicle Loads and Strength Branch 
NASA Marshall Space Flight Center
NASA/Marshall Space Flight Center/
Vehicle Loads and Strength Branch (EV31)
19–21 June 2012
© The Aerospace Corporation 2010
© The Aerospace Corporation 2012


Determining System Response using Uncoupled Transfer Functions - And Advantages Using Response Matching Methods

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server