This study is appointed to discover the dynamic behavior related to one of the most applicable systems used in engineering, namely coupled beam bridge system. For this reason, the system, which is constructed by two circular arch beams and an elastic layer between them, is vibrationally investigated here. In addition, the geometrical strategy is hired to modify the essential position associated with the situation of the two beams lying on each other. Moreover, the first-order shear deformation theory (FSDT) and the cylindrical panel scheme are employed to discover the fundamental features of the relationships linked to the system. Moreover, by engaging Hamilton’s principle and part-by-part integration (or Green–Gauss theory), the governing equations related to the motion of the system are achieved. Furthermore, the robust semi-analytical technique, renowned by the generalized differential quadrature operator is executed to split up the motion equations linked to the system. Additionally, to confirm the offered configuration, some benchmarks are chosen and solved. Finally, the influence of the diverse boundary conditions, geometrical characteristics, and different values related to the elastic mid-layer stiffness on the natural frequencies of the coupled circular arch–arch beam bridge system are determined.

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