Free vibration analysis of thin coplanar rectangular plate assemblies .1. Theory, and initial results for specially orthotropic plates

This paper communicates a new h-p finite element methodology for studying the free vibration of generally orthotropic coplanar plate assemblies. In Part I, hierarchically enriched stiffness and mass matrices of a generally orthotropic rectangular plate element are derived using symbolic computing. These may then be combined, via a special connectivity matrix, to form the global stiffness and mass matrices of a more general coplanar plate structure. A variety of different boundary conditions may be accommodated in the model by specifying whether an element edge is simply supported, clamped, free, or whether an element corner is point supported. The natural frequencies, and the associated normal modes, are then sought from the resulting matrix-eigenvalue problem. Detailed comparisons with the work of other investigators confirm the validity of the methodology for specially orthotropic plates; the validation for generally orthotropic plates, and plate assemblies, is addressed in Part II.