Free vibration analysis of thin rectangular laminated plate assemblies using the h-p version of the finite element method

A vibration study of thin, laminated plate assemblies is conducted by using the h-p version of the finite element method (FEM). Polynomially-enriched stiffness and mass matrices are derived from classical plate theory using Symbolic Computing, and then stored in algebraic form for a single, generic element. A number of such elements may then be combined to form the global stiffness and mass matrices for a more general planar assembly. Any of the classical edge conditions, or point corner supports, may be accommodated in the analysis, and the natural frequencies are sought from a standard matrix-eigenvalue problem. Excellent agreement has been found with the work of other investigators. The h-p method is shown, by example, to offer considerable savings in computational effort when compared with the standard h-version of the FEM. One further development of the method is presented which illustrates how it might form the basis of a condition monitoring measuring technique based on natural frequency shifts arising from non-propagating, through-the-thickness, crack damage.