Estimation of Stress State in an Axially Loaded Beam Using Modal Data

Abstract

Abstract Residual stresses are found to play a vital role in the dynamic behavior of the beam. These stresses are sometimes induced unintentionally due to manufacturing processes where temperate plays a role, while at other times, beams are subjected to stresses to alter their dynamic behavior for a particular application. Owing to the ubiquitous presence of the stressed beam, the estimation of its stress state becomes imperative to prevent structural failures. This study employs an approach to estimate the stress state of a beam from the natural frequencies and mode shapes. Using the modal data, the wave-numbers are calculated, and hence a dispersion relation is established. Modal analysis for a beam subjected to axial load is performed in a standard finite element software package, and the natural frequencies and the mode shapes are extracted. The analysis is performed for different values of loads, both compressive and tensile. The dispersion relation for the load cases is calculated, and the relationship between the wave-number, natural frequency, and load value is established using a curve-fitting approach. It was found that the discussed approach estimated the load value accurately. The discussed approach can be utilized to estimate the buckling of structures and stress states in a beam directly from the experimental data of the axially loaded beam.