Vibration Analysis for Monitoring of Ancient Tie-Rods

Abstract

This paper presents an application of vibration analysis to the monitoring of tie-rods. An algorithm for the axial load estimation based on experimentally measured natural frequencies is introduced and its application to a case study is reported. The proposed model of a tie-rod incorporates elastic bed-type boundary conditions that represent the contact between stonework and the tie-rod. The weighed differences between experimentally and numerically determined frequencies are minimized with respect to the parameters of the model, the main being the axial load and the stiffness at the tie-rod/wall interface. Thus, the multidimensional optimization problem is solved. Results are analysed in comparison to a model with simple fixed-end boundary conditions. In addition, the analytical formulation of the problem is delivered.