Elasticity solution for vibration of generally laminated beams by a modified Fourier expansion-based sampling surface method

•An accurate modified Fourier expansion-based sampling surface is developed.•Elasticity solution for vibration of sandwich and laminated beams.•The proposed method is appropriate for arbitrary boundary conditions.•The proposed method is appropriate for general lamination schemes.

A modified Fourier expansion-based sampling surface (MFE-SaS) method for the vibration analysis of generally laminated beams with arbitrary boundary conditions is presented. The method combines the advantages of the sampling surface (SaS) method with those of the modified Fourier expansion (MFE). The formulation is based on the two-dimensional theory of elasticity. In this method, a certain number of non-equally spaced sampling surfaces which parallel to the beam midsurface are primarily collocated in each layer of the beam and, the displacements of these surfaces are introduced as fundamental beam unknowns. This fact gives the opportunity to derive the elasticity solutions for a thick beam with a prescribed accuracy by utilizing a sufficiently large number of sampling surfaces. The desired solutions are obtained by the variational operation. Several examples are given to demonstrate the convergency, accuracy and flexibility of the present method.