An exact transfer matrix method for coupled bending and bending vibrations of a twisted Timoshenko beam

In this study, an exact transfer matrix expression for a twisted uniform beam considering the effect of shear deformation and rotary inertia is developed. The particular transfer matrix is derived by applying the distributed mass and transcendental function while using a local coordinate system. The results obtained from this method are independent for a number of subdivided elements, and this method can determine the required number of exact solutions for the free vibration characteristics of a twisted uniform Timoshenko beam using a single element. In addition, it can be used as a useful numerical method for the computation of high-order natural frequencies. To validate the accuracy of the proposed method, the computed results are compared with those reported in the existing literature, and the comparison results indicate notably good agreement. In addition, the method is used to investigate the effects of shear deformation and rotary inertia for a twisted beam.