An alternative solution for the determination of elastic parameters in free–free flexural vibration of a Timoshenko beam

Abstract

An alternative inversion solution is presented to compute the elastic parameters based on the Timoshenko equation of motion in free flexural vibration. The interest of this solution was its relatively simple formulation and its validity domain, which was not restricted to the initial frequencies and a certain range of length-to-height ratio. The uniqueness of the solution was verified numerically, and the best optimization strategy was deduced. It was underlined that the shear modulus determination depended on the length-to-height ratio coupled with the number of resonance frequencies involved in the computation. The accuracy of the computed elastic modulus values was in the same scale as that for the measurement errors of frequency. However, the sensitivity of the shear modulus was found to be very high and depended on the number of frequencies taken into account. The theoretical model was found to be more accurate and to better estimate the frequency values than a classic solution of the Timoshenko equation. Furthermore, the inversion procedure gave equivalent elastic property values to those obtained with a classic solution (in the validity range of the classic solution) and was more robust when the number of frequencies taken into account was low.