Strength Analysis - Finite Element Analysis for Satellite Structures - page 126

4.11.1 Definition of Harmonic Response Analysis
Any sustained cyclic load will produce a sustained cyclic response (a harmonic
response) in a structural system. Harmonic response analysis gives the ability to
predict the sustained dynamic behavior of any structure, thus enabling to verify
whether or not structural designs will successfully overcome resonance, fatigue,
and other harmful effects of forced vibrations. Harmonic response analysis is a
technique used to determine the steady-state response of a linear structure to loads
that vary sinusoidally (harmonically) with time. This analysis technique calculates
only steady-state forced vibrations of a structure. Transient vibrations, which occur
at the beginning of the excitation, are not accounted for in a harmonic response
analysis.
The general idea of harmonic response analysis is to calculate the structure's
response at several frequencies, and obtain a graph of some response quantity
(usually displacements) versus frequency. ''Peak'' responses are then identified on
the graph and stresses are reviewed at those peak frequencies. Peak harmonic
response occurs at forcing frequencies that match the natural frequencies of the
structure (resonance frequencies). Therefore, before performing harmonic analysis,
the natural frequencies of the structure should be first determined through a modal
solution. Amplitudes of cyclic load stresses at each resonance frequency are calcu-
lated for the structure. These peak stresses are needed to calculate fatigue damage due
to mechanical vibrations during transportation and launch vehicle flight.
4.11.2 Small Sat Dynamic Vibration Loads
By reviewing the satellite mechanical loads represented in Appendix A, there are
two types of dynamic vibrations acting on the satellite structure during transpor-
tation and LV flight. The first type is harmonic oscillations which are characterized
by the amplitude of vibroaccelerations and frequency. These sinusoidal vibrations
influence the satellite interface in three mutually perpendicular directions during
air transportation. They have a frequency band from 5 to 310 Hz along a duration
of 750 min. During launch vehicle flight, the satellite/LV interface is affected by
sinusoidal vibrations in the lateral and axial directions. The frequency band in the
lateral direction ranges from 2 to 15 Hz over 300 s, while in the axial direction it
ranges from 5 to 20 Hz over 100 s.
Random vibrations are the second type of mechanical dynamic vibrations
acting on the satellite interface. They are characterized by acceleration power
spectral density and the duration of influence. The values of amplitude and spectral
densities are given in the extreme octave points. The random vibrations' param-
eters are defined for rail and road transportation in three perpendicular directions.
In rail transportation, the frequency band is from 0 to 100 Hz. The duration is
specified corresponding to rail transportation distance, which is approximately