NATURAL FREQUENCIES AND MODE SHAPES OF A FREE–FREE BEAM WITH LARGE END MASSES

An analytical solution is presented for the natural frequencies, mode shapes and orthogonality condition, of a free–free beam with large off-set masses connected to the beam by torsion springs. Results are given for a range of masses with various fixed orientations and the validity of the method is confirmed against established results for natural frequencies of beams with five different boundary conditions. The study lays the foundation for investigations into the dynamics and vibration control of multi-link articulated systems such as the Space Shuttle Remote Manipulator.