Vibration of a large space beam under gravity effect

The structural characteristics of a large simply supported beam subjected to gravity are described. The nonlinear governing equations for both the static and the dynamic response are derived and solved analytically. The results show the feasibility of verifying the on-orbit dynamic characteristics of a large space beam by utilizing ground test data of such a structure. It is noted that the gravity effect interacts mostly with the first vibration mode. It was also found that the system of a large space beam subjected to its own weight is a hardening system. The differential equation for the asymmetric mode is a Duffing type equation. However, the governing equation for the symmetric mode has an additional quadratic term. It is this term that causes the maximum vibration amplitudes at different phases to be non-identical.