Transfer Matrix Method of Linear Multibody Systems for Free Vibration Analysis of Beam Carrying Elastically Mounted Point Masses

The analysis of natural vibration characteristics has become one of the important steps of the manufacture and dynamic design in different industries. An efficient approach called transfer matrix method of linear multibody systems (MSTMM) is proposed to determine the free vibration of a cantilever beam carrying any number of elastically mounted point masses vibrating in a plane. The components of the transfer matrix are all functions of the system’s natural frequency. The overall transfer equation only involves boundary state vectors, whereas the state vectors at all other connection points do not appear. The state vectors at the boundary are composed of displacements, rotation angles, bending moments and shear forces, which are partly known and partly unknown. Recursive eigenvalue search algorithm is used to determine the system frequencies. A numerical example is presented to demonstrate the validity of the proposal method. The proposed method is easy to formulate, systematic to apply, and simple to code.