The modal behaviour of the wooden bridge over the Rhine described by Julius Cæsar in the De Bello Gallico is analysed by a simple analytical model, i.e., a Kirchhoff–Love (KL) plate. The overall structure is indeed modelled as a thin plate, representing the walking surface, resting on elastic supports that approximate the compliance of the underlying structure. Firstly, these elastic constraints are represented by linear springs; in a refined step, beam elements with equivalent stiffness and mass are adopted. The system complexity arises from the consequent non-trivial boundary conditions and is tackled by selecting suitable auxiliary functions to operate with discretised equations of motion, in a Galërkin-like approach. MATLAB helped to develop in-house scripts capable of reconstructing the flexural behaviour as the governing parameters vary, without repeated experimental tests. The analytical results are compared with theoretical predictions and between the two assumed elastic supports, allowing verification of model consistency and explanation of differences in the bridge behaviour. The ease of implementation of these codes also enables the evaluation of the structural potential of historical constructions, the investigation of modular characteristics and connections between subcomponents, and the assessment of the effects of external loads. The study of historical structure dynamics is thus relevant not only for reconstruction, but also for modern mechanical design, with potential applications in civil, mechanical, materials, and naval engineering.
Giontella et al. (Sat,) studied this question.