Free vibration analyses of Timoshenko beams with free edges by using the discrete singular convolution

In this paper, the free vibration analysis of Timoshenko beams with various combinations of boundary conditions are performed by using the discrete singular convolution (DSC). Since Timoshenko beams with clamped–free, pinned–free, slide–free, and free–free boundaries have not been successfully solved by using the DSC thus far, the main objective of the present paper is focused on the way to apply the free boundary conditions in using the DSC for the free vibration analysis of Timoshenko beams. A simple method to apply the free boundary conditions is proposed and verified. Results for various ratios of thickness-to-length (h/L) are presented and compared with either existing solutions in the literature or the results obtained by the differential quadrature method (DQM). It is shown that accurate results can be obtained by using the DSC together with the proposed method for applying the free boundary conditions. The research extends the application range of the DSC method.