Material Damping Prediction in Timber Beams Based on Timoshenko Free-Free Beam Model

Abstract

Damping in vibrating structures is much less understood than their stiffness and inertial properties and in timber structures it is even less understood how damping is generated in motion characteristic of bending and shear separately. We analyse these contributions through application of the so-called method of complex moduli, arising in constant-hysteretic models of damping. We separate the influences on overall damping due to these independent material properties by considering a partial differential equation of undamped motion and substituting Young's and shear moduli with their complex counterparts. We keep the rotary inertia present in the model to assess its own damping contribution and design an experimental setup in which vibration of a free-free beam is simulated so that no reaction (i.e., no contact damping) should be present, which allows us to assess the contribution due to bending, shear and rotary inertia to material damping only. We show that, in the present model, the overall loss factor is indeed smaller than in the literature, while the damping due to shear effects grows in higher vibration modes and beams with smaller length-to-height ratio. Finally, we propose a damping prediction model built on simple linear regression in which the vibration modes are processed separately.