Free vibration analysis of circular thin plates with stepped thickness by the DSC element method

Novel formulation is presented by using the discrete singular convolution (DSC) for free vibration analysis of circular thin plates with uniform and stepped thicicness. Different from the commonly used ones in literature, regularity conditions are not needed at the circular plate center point to avoid singularity. DSC circular and annular thin plate elements are established. For the DSC circular plate element with radius of R-1, the stiffness equation is first formulated in region [-R-1,R-1] with even number of nodes and then reduced to region [0, R-1] by using either symmetric or anti-symmetric conditions. The proposed DSC circular and annular plate elements are used for obtaining frequencies of uniform/stepped circular thin plates or annular thin plates with different boundary conditions. Comparison of the present DSC results to existing analytic and numerical solutions verifies the proposed formulations. The present research extends the DSC method to free vibration of circular thin plates with stepped thicknesses. (C) 2014 Elsevier Ltd. All rights reserved.