Abstract: Influence on the natural vibrating frequencies of the boom is analyzed, which is brought by rigid body and deformation coupling of the boom in a large crane when luffing. Additional influence on natural frequencies of the boom brought by mass of hook and pulley block is also taken into account. Based on theory of flexible multi-body system, equation describing vibration by the nominal motion is created by Lagrange method. And it is uncoupled by state vector approach in complex modal analysis. The results are three pairs of conjugate complex numbers and smaller than those worked out by the structure dynamics method. And the natural vibratioing frequencies are also influenced by rotary speed surrounding the given point and mass of hook and pulley block, but the effects are small.

Key words: Complex frequencies Rigid body and deformation coupling Lagrange’s equation, Flexible mechanics, State vector approach