Acoustic excitation and mechanical analysis of a satellite antenna Claes Fredö Ingemansson Technology AB Magnus Baunge Saab Ericsson Space AB

Why acoustic excitation? Example spectrum at the payload 180-190 dB © Ingemansson Technology AB 2

What does a satellite antenna look like? These antennas are not the analysis example © Ingemansson Technology AB 3

Past projects Vibration excitation has been the dominating load. Acoustic excitation could be replaced by vibration test Analysis technology was not developed to accurately handle the case of acoustic diffuse field excitation © Ingemansson Technology AB 4

Today A higher lifting boost of launchers has increased the acoustic load Analysis technology can now handle acoustic diffuse field excitation & fully coupled fluid/structure interaction However, in-depth mechanical analysis tasks are not yet supported by vibro-acoustic analysis software Stress elements must have a single Gauss point (i.e. Tet4, TRIA3, .. elements), i.e. use elements of poor quality. Displacement, Acceleration and Stress must be analysed in the global co-ordinate system. © Ingemansson Technology AB 5

Local/Global coordinates A local coordinate system The global coordinate system © Ingemansson Technology AB 6

In-depth post-processing Local analysis co-ordinate systems are needed to correctly analyse interface loads. The analysis of acceleration, displacement and force benefits from the use of local co-ordinate systems as it better follows transducer alignment. Analysis at centre- and at ply- layers is needed for correct evaluation of composites. Stress/strain analysis benefit from less conservative estimates on major/minor principal and Von Mises data. © Ingemansson Technology AB 7

How can such postprocessing be accomplished? Use global coordinates for the vibro-acoustic analysis (required). Use local coordinates for the mechanical analysis task. Extract the structure’s modal response Power Spectral Densities generated by the acoustic load as this provides a complete description of the mechanical response. Use modal PSD information in a separate analysis run in a mechanical CAE postprocessor that allow more in-depth mechanical analysis. © Ingemansson Technology AB 8

Three models are at work BE - acoustic domain Project data from this mesh onto the simplified mesh Fluid/Structure interaction FE structure analysis model (w. local coordinate systems) FE - structure domain (global coordinate system only) © Ingemansson Technology AB 9

Some mathematics Analysis output: Each analysis frequency generates a correlated N by N PSD matrix for the N structure modes Sum the PSD matrix rows into N modal PSD responses This yields the modal participation factors for each analysis frequency Example analysis frequency Modal PSD for three modes © Ingemansson Technology AB 10

Contribution from high frequency modes Fit the RMS value of a SDOF response to the fluid/structure calculated modal responses for the analysed frequency range Use the excitation sensitivity from the above step to estimate the mode response at higher frequency Calculate the modal RMS displacement value for this contribution and add this to the response summation. Modal RMS response © Ingemansson Technology AB 11

Import to mechanical CAE software Analysis work flow Acoustic load Projection onto simplified mesh Projection to global coordinates Fluid/Structure interaction Structure Modes Import to mechanical CAE software Modal summation (SModalParticipFact) Modal PSD RMS calculation Results evaluation © Ingemansson Technology AB 12

End results Response PSD and RMS value at any node or element of the FE model and in any coordinate system Estimation of high frequency mode contribution (not shown) Acceleration/Displacement Force @ elements/MPCs/SPCs Stress/Strain @ ply/centre layer RMS PSD © Ingemansson Technology AB 13

Results so far Analyses have been made for various antennas with different boundary conditions RMS values for acceleration are of expected and acceptable magnitudes. Analysis shows that the fluid/structure interaction influences response magnitudes Analysis covers the frequency range that governs the highest loads Testing of end product is planned for next year. © Ingemansson Technology AB 14

Conclusions Fully coupled fluid/structure analysis with acoustic diffuse field loading can be used to predict mechanical response (displacement, acceleration & stress) In-depth mechanical analysis can be facilitated by specialised post-processing and allows results to be procured in wider variety of analysis options. Experimental verification is planned, but results obtained so far are of expected and acceptable magnitudes. © Ingemansson Technology AB 15