Inverse dynamic analysis for uncertain boundary condition parameters of a stepped beam subjected to an axial force

Generally, in engineering applications, the boundary condition parameters of axially loaded beam-like components with non-uniform cross-sections are unknown. This study investigates these uncertain parameters using inverse dynamic analysis of a stepped beam with elastic sup-ports subjected to an axial force. A dynamic coefficient method is introduced in the dynamic analysis model to fundamentally overcome the numerical instability often encountered in tradi-tional exact methods. Subsequently, a novel approach is proposed to evaluate the measurement error of the axial forces in an actual axially loaded beam-like component through inverse analysis of uncertain boundary condition parameters using two or only one observed natural frequency. The unknown rank orders of the measured natural frequencies can also be determined using the proposed method. Numerical examples are provided to verify the exactness and numerical robustness of the proposed method. Finally, during the construction of a real tied-arch bridge, the proposed approach was successfully applied to precisely control the tension forces of the bridge hangers.