Determination of the Fundamental Lateral Bending Mode Frequency of a Spacecraft from its Static Deflection

The primary structure of a spacecraft that involves the central cylinder is designed to meet a specific value of fundamental lateral mode frequency. Though this frequency can be theoretically estimated by using a finite element model, its experimental verification is only possible when the entire spacecraft is made ready. However, static load tests are done on the primary structure of the spacecraft as soon as the structure is realized. In this work, a methodology to determine the fundamental bending mode frequency of a spacecraft from the deflections measured when the structure alone is subjected to static load tests is developed. An expression relating the fundamental lateral bending mode frequency of a spacecraft, having several masses attached at different locations, and the deflection at its tip is derived. Two spacecraft, one of 3000kg class and the other of 6000kg class are taken as examples. The fundamental lateral frequencies are determined using this methodology. These frequencies are also obtained through resonance search tests. It is shown that the derived expression will be very useful in estimating the fundamental lateral mode frequency of a spacecraft with the help of the measured deflection.