Development of a transfer matrix method to obtain exact solutions for the dynamic characteristics of a twisted uniform beam

• We developed a TMM that can determine exact solutions for twisted uniform beams.
• The computed results are independent of the number of subdivisions.
• A transcendental function and local coordinates are employed in deriving the TM.
• The effect of pre-twisting on the eigenpairs is examined via a parametric study.
• Exact eigenpairs of a twisted two-stepped beam are computed using two sub-elements.

In this study, a novel transfer matrix method is developed to determine the exact natural frequencies and mode shapes of free vibrations in a twisted uniform beam. It is possible by applying the distributed mass and transcendental function while using a local coordinate system in the derivation of the transfer matrix method. In addition, the computed results in the proposed method for a twisted uniform beam are independent of the number of subdivisions, but the accuracy of the conventional transfer matrix method for a twisted uniform beam depends on the number of subdivided elements. To validate the accuracy of the proposed method, the computed results are compared with those reported in the existing literature, and relevant conclusions are drawn.