Vibration-Based Experimental Identification of the Elastic Moduli Using Plate Specimens of the Olive Tree

Abstract

Mechanical parameters of the olive wood plate have been computed by data inversion of vibrational experimental tests. A numerical-experimental method has allowed the evaluation of the two transverse shear moduli and the four in-plane moduli of a thick orthotropic olive tree plate. Therefore, the natural flexural vibration frequencies of olive trees plates have been evaluated by the impulse technique. For our purposes, we define the objective function as the difference between the numerical computation data and the experimental ones. The Levenberg–Marquardt algorithm was chosen as optimization strategy in order to minimize the matching error: the evaluation of the objective function has required a complete finite element simulation by using the ANSYS code. As input, we have used the uniaxial test data results obtained from the olive plates. The converged elastic moduli with n = 10 natural modes were E1 = 14.8 GPa, E2 = 1.04 GPa, G12 = 4.45 GPa, G23 = 4.02 GPa, G13 = 4.75 GPa, ν12 = 0.42, and ν13 = 0.42. The relative root mean square (RMS) errors between the experimental frequencies and the computed one is 9.40%. Then, it has been possible to obtain a good agreement between the measured and calculated frequencies. Therefore, it has been found that for plates of moderate thickness the reliability of the estimated values of the transverse shear moduli is good.