Nonlinearities Due to Breathing Cracks in Vibrations of Cross-Laminated Timber Panels

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Abstract

This study examines experimentally and numerically the nonlinear oscillations of cross-laminated timber (CLT) panels caused by the opening and closing of cracks. Due to drying shrinkage of the panels, the narrow face joints between the top and bottom layer timber boards open, resulting in breathing crack behavior even when no global damage is present. In an experimental study of a single CLT panel where shrinkage effects were observed over a period of 20 days, the impact of the nonlinearities is quantified using higher-order frequency response functions obtained from sine-sweep tests. The excitation force contains higher-order harmonics due to shaker-structure interaction as an undesirable by-product, thus deviating from theoretical studies. To reproduce the experimentally observed behavior, a higher-order equivalent single layer plate theory is adapted, using displacement-dependent, linearly varying stiffness coefficients. These scaling coefficients are obtained by manually adjusting the effective thickness of the top layer of the CLT panel for each mode separately, to closely match the experimental results. The derived numerical model considers the contribution of one single vibration mode at a time and includes the interaction with the electrodynamic shaker. In general, the numerical and experimental results show good qualitative agreement. However, the exact magnitudes of the second- and third-order frequency response functions as well as the influence of excitation amplitude are not captured, indicating a more complex type of nonlinearity than the modeled one.

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