Vibrational problems of timber beams with knots considering uncertainties

Abstract

A stochastic model of the dynamic behavior of sawn timber beams of Argentinean Eucalyptus grandis is herein presented. The aim of this work is to study the influence of the timber knots in the dynamical response of timber beams. The presence of knots is known to be the main source of the lengthwise variability and reduction of bending strength and stiffness in timber beams. The following parameters of the timber knots are considered stochastic: position along the beam span and within the beam cross section, shape and dimensions. Experimental data, obtained from bending and density tests, are employed to find the timber modulus of elasticity (MOE) and density. On the other hand, the characteristic of the timber knots used in the stochastic model was obtained from a visual survey performed with 25 beams of the same species. The problem of the natural vibration frequencies of the timber beam is approximated with the finite element method. Numerical results are obtained using Monte Carlo Simulations (MCS). The uncertainties of the timber knots parameters and their influence are quantified with the probability density function (PDF) of the frequencies. Statistical results obtained by means of MCS are compared with experimental measurements in order to assess the accuracy of the stochastic model. The present approach that gives a more realistic description of timber structures, correlatesbetter with experiments.