Dynamic stiffness formulation for composite Mindlin plates for exact modal analysis of structures. Part I: Theory

The dynamic stiffness formulation for both inplane and bending free vibration based on the first order shear deformation theory for composite plates is presented. The explicit terms of the dynamic stiffness matrices are also given. Plates with different boundary conditions are considered. Rotation and offset matrices for the element are developed and an assembly technique given. The Wittrick and Williams algorithm is modified to avoid the troublesome computation of the clamped–clamped natural frequencies when solving the free vibration problem. The validation of the theory and its application to real structures are illustrated in the second part of this paper.

► A powerful and elegant dynamic stiffness method is developed for composite plates.
► Effect of shear deformation and rotatory inertia are included in the formulation.
► Explicit expressions for dynamic stiffness elements are derived.
► The Wittrick–Williams algorithm is modified for ease of computation.
► The method makes exact modal analysis of complex composite structures possible.