A Standardized Framework for Estimating In-Plane Modal Properties of Cable-Stayed Bridges with Algebraic Solutions

Accurate and efficient estimation of natural modal properties provides valuable insights for bridge design and structural health monitoring of cable-stayed bridges (CSBs). This paper proposes a standardized framework for directly estimating the in-plane natural modal properties of CSBs through algebraic calculations. The framework began with a two-step discretization: The entire CSB was discretized into multiple single-pylon substructures; each substructure was then discretized into an integrated system of discrete lumps connected by massless springs. Subsequently, the dynamic governing equations of the system were formulated based on the D’Alembert principle. After algebraically transforming the partial-differential terms using the finite difference method, the fundamental form of the eigenfunction capturing the global natural vibration was derived. Modification submatrices were derived accounting for different pylon-deck connecting types, forming a standardized solution framework. This framework enables the modal properties of CSBs to be estimated by inputting design parameters, applying the modification submatrices, and performing algebraic calculations. Finally, the accuracy and efficiency of the proposed method were validated through laboratory experiments and finite-element modal analysis of a real bridge, demonstrating its practical applicability to complex CSB structures.