Investigation on the propagation of uncertainties of a timber floor under human excitation

Abstract

Due to the characteristics of high stiffness-weight ratio, timber floors are prone to annoying vibrations under human excitation. Given the natural origin of timber, its mechanical properties exhibit significant variability. The randomness inherent in human excitation cannot be overlooked during structural dynamic analysis. Consequently, the adoption of a stochastic approach is imperative for attaining reliable serviceability evaluation results. However, current research on human-induced vibrations in the timber floor, accounting for this randomness, remains inadequate. In this paper, an experimental investigation is conducted on the dynamic properties and human-induced responses of a timber floor composed of glued laminated timber and oriented strand board. A finite element model is developed and subsequently validated for accuracy in terms of modal properties and dynamic responses. The probability density evolution method is introduced for stochastic analysis, which demonstrates that both the natural frequency and dynamic responses of the floor exhibit considerable variability when uncertainty factors are considered. The Kullback–Leibler divergence indices are used to assess the impact of each uncertain variable quantitatively. The results indicate that the longitudinal elastic modulus has the greatest influence on the natural frequency, while the first dynamic load factor, α_z1, exerts the most significant impact on dynamic responses. Notably, both material mechanical properties and load model parameters contribute to the uncertainty of dynamic responses, with the influence of the load model parameters being significantly greater than that of material mechanical properties.