Free vibration of structures composed of rigid bodies and elastic beam segments

Free vibration of structures composed of rigid bodies and elastic beam segments is considered, assuming that the mass centers of rigid bodies are not located on the neutral axes of undeformed elastic beam segments. It is assumed that the rigid bodies of the system perform planar motion in the same plane and that their mass centers are located in that plane. The elastic beam segments are treated as the Euler-Bernoulli beams. In order to determine natural frequencies of the system, modification of the conventional continuous-mass transfer matrix method has been done. The order of the overall transfer matrix has been reduced by this modification. Theoretical considerations are accompanied by two numerical examples.