Abstract
The aim of this study is to investigate free vibration characteristics of arch-frames which consist of two columns and an arch. Firstly, an exact formulation of the problem is presented using the Dynamic Stiffness Method (DSM). The end forces and displacements of column elements are obtained analytically using Timoshenko beam theory (TBT). These are then combined with the end forces and displacements of the semi-circular arch, which is modeled with exact curved beam elements that consider axial and shear deformations and rotational inertia. By employing standard assembly and bisection based root finding procedures, exact free vibration analysis of the whole vibrating system is carried out. Then, in an effort to simplify the formulations, an approach based on approximating the arch as assembly of linear straight beam segments is presented. The calculated natural frequencies using DSM for both exact and approximate results are then tabulated for comparison purposes. The mode shapes are also compared. The results show that the proposed model simplification is effective and produces accurate mode frequency and shape estimations.
Highlights
The dynamic behaviour of arch-frames is of direct relevance for structural bridge engineering applications
In order to simplify the formulations, an approximate model based on segmenting the arch into straight Timoshenko beams is considered
The free vibration analysis of both approximate and exact systems demonstrated that segmenting the arch with linear elastic elements is effective; with only a few straight segments, natural frequency and vibration mode shapes of the curved arch are accurately estimated
Summary
The dynamic behaviour of arch-frames is of direct relevance for structural bridge engineering applications. This is achieved by modeling columns as Timoshenko beams and modeling the arch as a curved beam considering axial and shear deformations and rotational inertia. To simplify this complex formulation, an approximate approach is proposed, where the arch is modelled with equal length straight Timoshenko beam segments. The adequacy of this simplified model is evaluated by comparing mode frequencies and shapes from this model to the exact model in Sections 2 and 3. The main novelty of this study is based on combining the dynamic stiffness approach and segmentation of the arch into straight Timoshenko beam segments for free vibration analysis of arch-frames
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