Modelling bridges and pipelines as periodic Timoshenko–Ehrenfest beams

In this paper, we investigate the dynamic behavior of bridges and pipelines, which, due to their repetitive spatial configuration, can be modelled as periodic structures composed of elastic beams and equally spaced elastic/inertial supports. To account for both shear deformation and rotational inertia effects, the Timoshenko-Ehrenfest beam theory is employed. The dynamic characteristics of these periodic systems are determined through their dispersion relations, calculated using a method based on the transfer matrix. Independent finite element simulations of full three-dimensional engineering models, specifically a bridge and a suspended pipeline, are performed to study their eigenvalue properties. Comparison between analytical and numerical dispersion curves reveals very good agreement when using the Timoshenko-Ehrenfest theory, whereas significant discrepancies arise with the classical Euler–Bernoulli beam theory. The results quantify the frequency range and dispersion branches beyond which the Euler–Bernoulli theory becomes inadequate, highlighting that the Timoshenko–Ehrenfest theory provides an accurate and computationally efficient analytical tool for medium- and high-frequency design and analysis of three-dimensional periodic structures. • Periodic systems of Timoshenko-Ehrenfest beams and regular supports are studied. • The analytical formulation is based on the Transfer Matrix Method. • Two examples of periodic structures are investigated: bridges and pipelines. • Finite element simulations are performed on full 3D structural models. • Analytical and numerical dispersion curves show excellent agreement.