Explicit Vibration Formulas Applicable to Timber Plates with Free and Simply Supported Edges

Advances in research and development have led to the application of high-strength timber plates to flooring-slab construction. It is envisaged that floors built from timber plates will have different vibration behavior from conventional jointed floors. In this paper, explicit formulas are developed based on a matrix formulation that links both the symmetric and antisymmetric vibration modes of orthotropic plates. The developed solution can be used for the dynamic analyses of orthotropic timber floor slabs. The solution presented in this paper overcomes limitations associated with previous solutions by eliminating the need for approximate series expansions for solving the characteristic equations. Its application is demonstrated by considering responses of plates with all or two simply supported edges. The new solutions agree closely with classical and Finite-Element Method (FEM) solutions, as well as with the experimental results for Cross-Laminated Timber (CLT) plates. The advantage of the new approach versus alternatives is a combination of accuracy and computational efficiency.