Modeling the bending vibration of cross-laminated timber beams

Cross-laminated timber (CLT) is an economical construction material combining good structural properties and environmental advantages. Due to the layered geometry and the associated internal stress boundary conditions, modelling its dynamic behavior is complex. However, accurate vibration level estimations are necessary to estimate the sound insulation performance of CLT constructions. This paper outlines a method to determine the relevant elastic constants and the appropriate equations of motion to predict the vibration of beams cut from a three-ply CLT plate. Modal analysis performed on strips cut along the two principal directions provides insight in the material’s dynamics. The bending mode frequencies are determined experimentally by analyzing the sweep response spectrum using the linear prediction method. In a second step, analytical beam vibration models of increasing complexity are fitted to the measurements using a genetic optimization algorithm. Thin beam theory—the simplest model—does not predict the bending modes with sufficient accuracy. Depending on the strip direction, the bending vibrations can be modeled using Timoshenko’s theory for thick beams, or by a model for three layer sandwich beams respectively. The results show that taking the beam geometry into account is as important as estimating the orthotropic material constants to model the bending modes properly.