Determination of free vibration properties of masonry arch bridges using the dynamic stiffness method

Masonry arch bridges constitute over half of the European bridge stock. The dynamic response of these bridges to traffic loads is influenced by their free vibration properties, i.e. their natural vibration frequencies and mode shapes. However, these properties have not been systematically examined to date. This paper utilises the dynamic stiffness method (DSM) to obtain an improved fundamental understanding of the free vibration properties of idealised single and multi-span arch bridges. In this approach, the piers and arches are modelled as an assembly of linear Timoshenko beam segments, the backing and infill are represented with axial struts and the underlying soil with concentrated spring elements. These idealisations enable rapid but accurate calculations of in-plane free vibration properties. To demonstrate this, the proposed procedure is applied to a simply-supported arch structure, a small-scale single-span arch bridge model and a multi-span arch bridge, where published experimental data is available. Then, free vibration analyses of representative single and multi-span arch bridges are performed. The results obtained from DSM analyses agree with detailed 3D finite element models and reveal the critical influence of backing elements and the interactions between adjacent spans on free vibration properties. Lastly, a range of arch bridge geometries are examined to reveal the shortcomings of existing provisions for modal frequency estimation in codes of guidance.