A semi-analytical and semi-numerical method for vibration analysis of parabolic arch and its experiment study

This study establishes a semi-analytical and semi-numerical method for free vibration analysis of parabolic arch, and further modifies the boundary condition of a parabolic arch experimental model by considering rotational elastic boundary constraints. The parabolic arch is divided into segments approximated as circular arcs for analytical processing. These segments are then coordinated and assembled to form the complete system, enabling the calculation of natural frequencies. Calculation convergence is examined by increasing the segment number, determining the threshold for frequency calculation stability. The key physical parameters of the parabolic arch are varied, and calculation results are compared with finite element simulations, confirming the semi-analytical and semi-numerical method's accuracy. The proposed method demonstrates strong agreement with finite element method results, with the first-order frequency error around 10 % and other order errors within 5 % compared to finite element analysis. The experimental model is constructed, and both impact and random excitation tests are conducted to gather acceleration data and extract natural frequencies. By adjusting rotational elastic stiffness, the calculated frequencies utilizing semi-analytical and semi-numerical method are compared with experimental results using fast Fourier transform analysis, enabling modification of experimental model boundary conditions. After determining an appropriate rotational stiffness, all frequency errors relative to experiments are kept under 10 %, validating the method's effectiveness and precision. Additionally, it is noteworthy that the method proposed in this paper is also applicable to arches of curves other than parabolic types. Data availability: Data will be made available on request.