Strength Analysis - Finite Element Analysis for Satellite Structures - page 119

extend from 20 up to 2,000 Hz. These values were gathered from the historical
experience in carrying out dynamic tests of similar small satellites. Therefore,
the entire model of the satellite is solved for modal analysis to calculate the
satellite natural frequencies up to 2,000 Hz.
4. Review the results: Results from modal analysis of the entire finite-element
model of the satellite structure are written to the structural results files. They
contain the following data:
• Natural frequencies.
• Expanded mode shapes.
• Participation factor and effective mass calculations for the expanded mode
shapes in each excitation direction (U X , U Y , U Z , ROT X , ROT Y , and ROT Z ).
4.10.3 Modal Analysis Results
Natural frequencies of Small Sat structure are determined as a result of the modal
analysis performed by ANSYS. The total numbers of natural frequencies of Small
Sat up to 2,000 Hz are found to be 121 modes. The user's guide of Dnepr Launch
Vehicle cautions that the payload of LV (Small Sat satellite) should be designed
with a structural stiffness which ensures that the values of fundamental frequencies
of the satellite, hard mounted (rigidly constrained) at the launch vehicle interface,
are not less than:
• 20 Hz in the longitudinal axis; and
• 10 Hz in the lateral axis.
This constraint must be satisfied to ensure that the satellite's dynamic charac-
teristics do not adversely affect the LV's control system. For Small Sat structure,
the first natural frequency is found to be 33 Hz and the 121th is 1963.5 Hz. Thus,
the Small Sat first natural frequency (33 Hz) satisfies the minimum fundamental
frequency constraint of Dnepr LV.
The modal analysis is intermediate calculations to define the natural frequencies
of the satellite structure. The results of modal analysis are used to perform har-
monic response analysis and stress fatigue analysis for Small Sat structure, which
will be a very complicated process if the first 121 modes (up to 2,000 Hz) are used.
For simplicity, a reduction method should be applied to reduce the size of modal
frequencies used during subsequent analyses. The problem to be solved in this
section is: Determine the smallest number of natural frequencies which accurately
construct the frequency response characteristics through a given frequency range
(up to 2,000 Hz). The first step is to define the eigenvector elements for all modes
for only the input and output DOF which have a contribution on the satellite
response. The second step is to analyze the model contributions of all modes, and
sort them to define which ones have the greatest contribution.
One method for reducing the size of a modal model is to simply truncate the
higher frequency modes. If this truncation is performed without understanding the