Based on the displacement-induced linearity error curve and the theory of wavelet packet analysis, a bridge structural damage identification method is proposed, integrating two damage indicators: Quasi-Static Displacement-Induced Linearity Error Curve (QSDIL) and Relative Energy Rate of Wavelet Packet Energy Spectrum (RES). This method first constructs the QSDIL damage indicator based on a quasi-static displacement-induced linearity error, which is used for the preliminary localization of the bridge structural damage. Subsequently, relying on the principles of wavelet packet analysis, the method constructs the RES damage indicator for accurate positioning of the damage location in the bridge structure. The proposed method is experimentally validated, and the impact of factors such as single-point damage, multi-point damage, signal noise, lane position, and vehicle weight on the experimental results is investigated. The results indicate that the proposed method exhibits excellent identification performance for the location of structural damage in both single-point and multi-point damage scenarios, with good agreement between experimental and theoretical values. As the signal-to-noise ratio decreases, the accuracy and precision of the RES curve in locating the bridge structural damage position exhibit a nonlinear decreasing trend, with relatively small identification errors observed at noise levels of 90 dB to 100 dB. Different lane positions have a minimal impact on the damage identification effectiveness. With increasing vehicle weight, both QSDIL and RES curves show an increasing trend in peak values, facilitating the localization of bridge structural damage positions.

A finite element analysis (FEA) model was developed for Euler and Timoshenko curved beam elements by incorporating trigonometric displacement distribution patterns. Local polar coordinate stiffness matrices were derived based on force-displacement relations and static equilibrium conditions. By employing the kinetic energy theorem and triangular displacement functions, an expression for the consistent mass matrix of a curved beam element was obtained. A coordinate transformation matrix for the curved beam element was established by relating the local polar coordinate system to the global polar coordinate system. Calculation programs were implemented in the Fortran language to evaluate the static–dynamic performance and natural frequency characteristics of curved beam bridges. The obtained results were then compared with those obtained using ANSYS solid models and “replace curve with straight” beam element models. The comparison demonstrated a strong agreement between the results of the Euler and Timoshenko curved beam element models and those of the ANSYS solid models. However, discrepancies were observed when comparing with the results of the “replace curve with straight” beam element model, particularly in terms of lateral static displacement. This discrepancy suggests that the characteristic matrix derived in this study accurately represents the stiffness and mass distribution of the curved beam, making it suitable for mechanical performance analysis of curved beam bridges. It should be noted that the “replace curve with straight” method overlooks the initial curvature and the bending–torsion coupling effects of a curved beam, resulting in calculation deviations. On the other hand, the use of curved beam elements in numerical analysis provides a simple and practical approach, which facilitates further research in areas such as vehicle–bridge coupling vibrations and seismic analysis of curved beam bridges.