Reliability of the tensile force identification in ancient tie-rods using one flexural mode shape

This paper presents an investigation into the reliability of an experimental procedure for the axial load identification of tie-rods with unknown boundary conditions, that uses one vibration frequency and five amplitudes of the corresponding mode shape. The method adopted does not require the knowledge of the effective length of the tie-rod under examination, but only the flexural rigidity and the mass per unit length. In particular, the influence of measurement errors as well as of inaccurate estimates of geometric and elastic properties on the accuracy of the axial force identification is investigated. The effect of the added mass of the sensors is also analyzed. The proposed algorithm is verified by means of many numerical tests on ancient tie-rods having large scatter values of geometric and elastic properties. Good estimates of the axial forces are obtained. Moreover, it is shown that the reliability of the tensile force identification, using one flexural mode shape, relies on the magnitude of the measurement errors rather than on accurate guess of Young modulus