Free vibration analysis of angle-ply symmetric laminated plates with free boundary conditions by the discrete singular convolution

Abstract

The discrete singular convolution (DSC) is used for free vibration analysis of three-layer angle-ply symmetric laminated plates with free boundaries, including laminated plates with two adjacent free edges. During formulating the weighting coefficients of derivatives having different orders, two Taylor series expansions with different orders are used to eliminate the degrees of freedom at fictitious points outside the physical domain. Thus, the difficulty in handling free boundary conditions by using the DSC is overcome. Results are presented and compared with either exact solutions or the ones obtained by the differential quadrature method (DQM). It is shown that the DSC with the novel way to apply the boundary conditions yields very accurate lower mode frequencies as well as relatively accurate higher mode frequencies. The excellent performance of the DSC on high mode frequencies of beams and isotropic plates is retained and also independent of boundary conditions.