A novel structural dynamic load reconstruction method based on discrete variational symplectic integrators for Birkhoffian systems

Accurately obtaining the dynamic load of a structure is crucial for structural design, optimization, and maintenance. However, dynamic methods based on classical mechanics systems often introduce artificial dissipation and other flaws. This paper presents a novel time-domain centralized load identification method to address structural dynamic load problems, leveraging Birkhoffian system dynamics and its symplectic integrators. State variables are first introduced, and Birkhoffian functions are constructed to reformulate the structural dynamic problem into dynamic equations under the Birkhoffian system. Based on the discretized Birkhoffian equations, a symplectic difference scheme is then established for a time-domain load-solving algorithm within the Birkhoffian framework. To tackle large-scale engineering problems and noise pollution encountered in practice, preprocessing methods based on modal decomposition and post-processing methods based on the Savitzky-Golay filter are also proposed. Compared to traditional numerical algorithms, the symplectic algorithms based on the Birkhoffian dynamics framework do not introduce algorithmic dissipation, offering better stability and accuracy. Finally, three numerical examples and one experimental case demonstrate the effectiveness and precision of the proposed method. The results show that, in terms of overall error and peak error metrics, the proposed method offers high accuracy and improved stability under noisy input conditions.