Spectral dynamic stiffness formulation for inplane modal analysis of composite plate assemblies and prismatic solids with arbitrary classical/nonclassical boundary conditions

This paper presents an analytical spectral dynamic stiffness (SDS) formulation for exact inplane modal analysis of composite plate assemblies and prismatic solids subjected to any arbitrary boundary conditions, arbitrary non-uniform elastic supports, mass attachments and coupling constraints. First, the elemental SDS matrix is derived symbolically from the exact general solution of the governing differential equation, which is assembled directly to model complex geometries. Then, any arbitrary classical and/or non-classical boundary conditions are applied directly in a strong form, which makes the method versatile for a wide range of engineering problems. As the solution technique, the Wittrick-Williams algorithm is applied by resolving the mode count problem of a fully clamped element. It is demonstrated that the method gives exact solutions with prominent computational efficiency. The proposed method provides an efficient and accurate analytical tool for the parametric and optimization analysis on the inplane vibration of various composite structures.