An accurate higher order plate theory for vibrations of cross-laminated timber panels

In this contribution, bending vibrations of cross-laminated timber (CLT) panels are addressed. The focus is on the low to mid audio frequency range in view of the sound radiation properties of CLT. To this end, a plate theory recently proposed by the authors is adapted by introducing a deformation ansatz for the transverse displacement and neglecting insignificant terms, yielding a theory with six degrees of freedom. From the governing equations of motion, dispersion relations for the propagation of bending wave are derived, which also allow to compute the natural frequencies and mode shapes of bounded plates. The weak formulation of the equations of motion is presented. The accuracy of the proposed theory is validated for a simply supported rectangular CLT panel for which an analytical solution is available. The results are compared with first order shear deformation theory, revealing the limitations of this simplified theory in the present context. Finally, finite element solutions for the rectangular plate with non-classical boundary conditions are presented, as well as incorporating a floating floor construction, underlining the importance of numerical solutions for the practical application of this plate theory.