Development of free vibration analysis algorithm for beam structures by combining Sylvester's inertia theorem and transfer stiffness coefficient method

A new free vibration analysis method, which is called the Sylvester-transfer stiffness coefficient method (S-TSCM), is developed by combining Sylvester's inertia theorem and the transfer stiffness coefficient method. In this paper, the free vibration analysis algorithm of a straight-line beam structure is formulated by S-TSCM. From the computation results of the free vibration analysis for the three types of beam structures, we confirm that S-TSCM is a very effective method. In particular, S-TSCM is superior to both the transfer stiffness coefficient method and the transfer matrix method in terms of computational accuracy and time. In the free vibration analysis for the beam structure with a large number of degrees-of-freedom, S-TSCM is superior to the finite element method in terms of computational time and storage.