Continuous Model for Vibrations of Thin-Walled Box Beams Filled with Polymer Concrete

This study presents a continuous analytical model for the dynamic analysis of thin-walled steel box beams filled with polymer concrete. The model incorporates transverse, longitudinal, and torsional vibrations, includes damping effects, and enables the calculation of frequency response functions. Its formulation is based on a coupled system of partial differential equations derived from Timoshenko beam theory and de Saint Venant’s torsion model, providing a closed-form solution for modal parameters and vibrational response. Experimental validation performed on a steel-polymer concrete beam showed close agreement between predicted and measured natural frequencies, mode shapes, and frequency response functions. Additional comparisons with one-dimensional, three-dimensional finite element models as well as rigid finite element models from the literature confirmed that the proposed approach can serve as an attractive alternative to other computational methods. The model offers a favorable balance between accuracy and simplicity, making it well suited for preliminary design and vibration analysis of steel-polymer composite structures.