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In this paper an analytical method is proposed to investigate the vibration and power flows of periodically stiffened plate with general boundary conditions.Both the plate and stiffening beams are modelled as 3D structural components, and the couplings at the interfaces are specified in terms of 3D elastic joints.The displacement function for each stiffening beam is expressed as a modified Fourier cosine series, and the transverse and in-plane displacements for the plate are similarly expressed as the 2-D versions of the modified Fourier cosine series expansions.