Strength Analysis - Finite Element Analysis for Satellite Structures - page 176

solution, and acceleration solution. Each one of these can be calculated relative
to the base or in absolute value. Finally, the model is solved to calculate the
spectrum results.
4. Combine the Modes: The modes can be combined in a separate solution phase.
Only the PSD mode combination method is valid in a random vibration anal-
ysis. This method triggers calculation of the one-sigma displacements, stresses,
etc., in the structure.
5. Review the Results: Results from a random vibration analysis are written to the
structural results file. They consist of the following quantities:
• Expanded mode shapes from the modal analysis
• Static solution for base excitation
The following output, if mode combinations are requested:
• 1 r displacement solution (displacements, stresses, strains, and forces)
• 1 r velocity solution (velocities, stress velocities, strain velocities, and force
velocities)
• 1 r acceleration solution (accelerations, stress accelerations, strain accelera-
tions, and force accelerations)
Nodal stress averaging may not be appropriate in a random vibration analysis
because ''stresses'' here are not actual stresses, but stress statistics.
4.13.4 PSD Spectrum Analysis Results
As mentioned before, the PSD spectrum analysis is performed to calculate stresses
and deformations in structural modules due to random vibration loading acting on
the satellite during rail and road transportation and flight of launch vehicle. By
reviewing the random vibration loads listed in Appendix A, the most severe power
spectral density affecting the satellite structure is the base excitation during the
first loading phase of launch. Figures 4.62 , 4.63 , 4.64 , 4.65 , 4.66 , 4.67 , 4.68 , 4.69 ,
4.70 , 4.71 , 4.72 and 4.73 depict Von Mises stress and displacement distributions in
the structural modules of Small Sat due to random vibrations in the first phase of
launch. The obtained values of the maximum stresses and displacements are rms
values representing the first standard deviation (1 r) of the instantaneous response
described by a normal distribution with zero mean. For random vibrations, the load
at any given time has a 99.87 % probability of being less than this value (1 r), but
the structure must withstand the maximum load experienced during the total time
of exposure to the random environment.
The maximum expected load during a random environment is a function of the
number of positive relative maxima (number of cycles applied of a load corre-
sponding to the random vibrations). With a single response frequency, this number
equals the frequency multiplied by the exposure time. For wide band vibration,
which includes a spectrum of response frequencies, the number of loading cycles