Numerical aspects for free vibration of thick plates part I: Formulation and verification Original Research Article

This paper investigates the numerical aspects for free vibration analysis of a class of thick (relative thickness ratio tb > 0.2), shear deformable, rectangular plates with all possible combinations of edge conditions. These thick plate vibration frequencies most probably cannot be accurately determined using the classical thin plate theory or the Mindlin plate theory. The effect of transverse shear strain has been considered by using a higher-order plate theory without the need for a shear correction factor. Unlike some domain discretization methods, this analysis assumes a single global element for the entire plate. The strain and kinetic energy integrals of the global plate element are formulated and the energy functional is minimized to yield the natural frequencies. A set of boundary-compliant admissible shape functions is developed to obtain solutions which are unattainable using the classical trigonometric admissible functions. The numerical efficiency of symmetry classification is investigated and, on certain computational platforms, more than 80% of the execution time can be saved while maintaining the same level of accuracy.