Deflection to natural vibration frequency ratio in a three-layer CLT slab with variable thickness of layers

This study examines the relationship between the maximum deflection and natural frequency of vibration in a three-layer cross-laminated timber (CLT) board at variable thicknesses of the inner and transverse plank layers under different boundary conditions. The finite element method (FEM), implemented in the SCAD++ computer complex by creating a finite element computational model in the form of a composite plate with anisotropic properties of the layers and rigid bonds between the plates, was used for the investigations. As a result, the values of maximum deflections and natural vibration frequencies for plates with different cross-sectional parameters were obtained. The obtained results are compared with the analytical values of the fundamental dependence obtained by Professor V.I. Korobko describing the relationship between the maximum deflection of a composite plate and the frequency of natural vibrations. It was found that the deviation of the numerical values of the K coefficient does not exceed 3% under different boundary conditions of structures and parameters of their cross-section.