DYNAMIC BEHAVIOR OF TIMBER BEAMS WITH UNCERTAIN PROPERTIES

D.A. GARCIA; M.B. ROSALES; R. SAMPAIO

Buenos Aires

Congreso; 1st. Pan-American Congress on Computational Mechanics PANACM 2015; 2015

The dynamic behaviour of sawn timber beams of Argentinean Eucalyptus grandis using a stochastic model is herein presented. In first place, the free vibrations case which, after solved, yields the natural frequencies and modes is studied. Finally, the damped forced vibration of the structural element is addressed. For the first problem, the governing differential equations are stated starting from the Euler-Bernoulli (E-B) beam theory. The lengthwise variability of the Modulus of Elasticity (MOE) and of the second moment of the cross sectional area are simulated to account for the presence of knots. The variability of the mass density among structural elements also is considered. For the second problem the governing differential equations are stated starting from the Timoshenko beam theory. Through the elastic and shear complex modulus the damping is introduced . This material damping model provides us of an adequate description of the energy dissipation under the action of harmonic loads. Uncertainties in this problem are introduced in the elastic and shear modulus and its corresponding bending and shear loss factor, respectively. The governing equations are discretized and numerically approximated through the Finite Element Method (FEM). The statistics of the solutions are obtained. The Probability Density Functions (PDFs) of the natural frequencies and the FRF are numerically obtained through the Stochastic Finite Element Method (SFEM) and Monte Carlo Simulations (MCS). Numerical results of the first natural frequency are validated with experimental values. Also, the mode shapes statistics are analyzed. The problems herein studied contribute to attain a more realistic description of the dynamic behavior of structures made out of sawn timber.