Free Vibration Problem of Composite Plates of Arbitrary Shape: Where Do We Stand?

The free vibration problem of flat plates is one of the most studied problem in structural mechanics of the last century. However, in recent years the use of composite materials for plated structures has increase enormously. Therefore, researchers focused their efforts in employing several numerical techniques for studying such configurations. The most common engineering theory for isotropic and composite plates is the well-known Reissner-Mindlin theory or First-order Shear Deformation Theory (FSDT). FSDT is assumed to be valid from thin up to moderately thick plates due to its initial hypothesis on the linear kinematic field and negligible through the thickness stress and strain. When composite plates are introduced other hypotheses are needed on the stacking sequence configurations. FSDT demonstrated to work very well for isotropic configurations and for any structural shape. Laminated composite plates of arbitrary shape due to their complex configuration can be difficult to treat analytically and they are generally treated numerically. The most common numerical tool is the Finite Element Method (FEM) which is a weak form domain decomposition approach. Other techniques, for instance based on the strong form, has been recently developed. In the present work, the authors will show convergence accuracy and reliability of both approaches by comparing the natural frequencies of several arbitrarily shaped plates made of isotropic and composite materials.