Axial load determination using modal analysis

Abstract: The report investigates the use of measured transversal vibrations to estimate the axial load on beams/columns. A literary review of the basic theory is performed, which clearly shows the theoretical relation between natural frequency and axial loading of linear structural elements (strings & beams). Current journal articles show that research has been done on mathematical models as well as some experimental studies. Basic theory and current research show that the impact of support conditions is of great importance to the relation between frequency and load. Thus an approach which models the support conditions as unknowns (springs) is suggested and used in the remainder of the study. The method requires the measurement of both the natural frequency and the corresponding mode shape for calculation purposes.The calculations are performed using both an analytical and a discrete approach. Numerical testing shows that the method is highly sensitive for the measured shape of the vibration mode. Testing of the discrete algorithm has shown stability/convergence issues if the discretization level is too detailed. However the ability to use an excess of measurement points than necessary (overdetermined system) to describe the mode shape seems to overcome some stability issues. The experimental studies to date have mainly focused on tensile tests performed on slender structures. Laboratory testing on four compressive samples with varying slenderness is performed in order to investigate the applicability on real-life structures. Testing results show that the presented approach yields loading estimates highly sensitive to the mode shape. Estimation quality is significantly improved by the use of excess shape measurements. Also the load estimations seem to overestimate the magnitude of loading. The use of both Bernoulli-Euler and Timoshenko beams show that the former tends to yield even higher estimates of loading. The study shows that the suggested method is promising for axial load identification, yet further investigations are required. Specifically improvements to the measurement/calculation of the mode shape are necessary.