Inverse Vibration and Optimization Approach for Estimating Young’s Modulus of Structural Steel

Abstract

Accurate estimation of Young's modulus is essential for reliable structural analysis and design. This study presents an integrated vibration-based inverse optimization methodology for estimating the Young's modulus of structural steel cantilever beams through the combined use of experimental modal analysis, analytical modelling, finite element analysis, and static deflection testing. Free vibration experiments were performed on nineteen steel cantilever beam specimens using an impact hammer and the FFT analyzer to determine the first and second bending natural frequencies. In addition, a static deflection experiment was conducted on a representative beam specimen to experimentally determine the Young's modulus based on Euler–Bernoulli beam theory. An analytical model was developed to predict the natural frequencies, while a finite element model was established to validate both the static deflection and modal responses. The experimentally measured natural frequencies were subsequently used in an inverse optimization framework to estimate the Young's modulus by minimizing the squared error between the measured and predicted frequencies. The analytical and finite element predictions showed good agreement with the experimental results for both vibration modes over the investigated range of beam lengths. The Young's modulus estimated using the proposed optimization approach was 177 GPa, compared with 181.7 GPa obtained from the static deflection experiment, corresponding to a percentage error of only 2.59%. The close agreement between the independent approaches demonstrates the accuracy and reliability of the proposed methodology. The developed framework provides a practical, computationally efficient, and non-destructive approach for material characterization and has potential applications in structural health monitoring and condition assessment of beam-like engineering structures.