Free vibration analysis of beams and rectangular plates with free edges by the discrete singular convolution

In this paper, free vibration of beams, annular plates, and rectangular plates with free boundaries are analyzed by using the discrete singular convolution (DSC). A novel method to apply the free boundary conditions is proposed. Detailed derivations are given. To validate the proposed method, eight examples, including the free vibrations of beams, annular plates and rectangular plates with free boundaries are analyzed. Two kernels, the regularized Shannon's kernel and the non-regularized Lagrange's delta sequence kernel, are tested. DSC results are compared with either analytical solutions or/and differential quadrature (DQ) data. It is demonstrated that the proposed method to incorporate the free boundary conditions is simple to use and can yield accurate frequency data for beams with a free end and plates with free edges. Thus, the proposed method for applying the boundary conditions extends the application range of the DSC.