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The analysis of natural vibration characteristics has become one of the important steps of the manufacture and dynamic design in different industries. The feasibility of using the transfer matrix method of linear multibody systems (MSTMM) to compute the free vibration characteristics of a system composed of continues and discrete elements vibrating in a plane is explored theoretically. A general analytical method based on MSTMM is developed for the frequencies determination of two Euler-Bernoulli beams coupled by a double spring-mass system. 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. Keywords-coupled beams; transfer matrix method; spring-mass; recursive eigenvalue search; free vibration.

Frequency Determination of Beams Coupled by a Double Spring-mass System Using Transfer Matrix Method of Linear Multibody Systems