ST-PINN-based dynamics analysis and parameter identification for variable cross-section cantilevers

This study presents a novel ST-PINN framework for the dynamic analysis and parameter identification of variable cross-section cantilevers. The PINN often encounter convergence failures as applied to the dynamic analysis of variable cross-section cantilevers. This failure primarily stems from the imbalance between the temporal and spatial terms in the governing equations, which leads to numerical stiffness. The parameter variations induced by the variable cross-section further exacerbate this issue. To address this issue, the proposed ST-PINN decomposes the spatiotemporal solution into independent subnetworks through variable separation. In addition, enhancement strategies incorporating hybrid constraints, hybrid activation functions, and two-stage optimization were designed specifically for the ST-PINN. To validate the advantage of the ST-PINN, numerical simulations are conducted for the free vibration analysis of three types of variable cross-section cantilever beams. Furthermore, the capability of ST-PINN to identify damping coefficients and variable cross-section distributions under limited data conditions is systematically investigated. Results demonstrate that ST-PINN delivers more accurate solutions at lower computational cost than PINN across all cases, confirming the proposed technique effectively resolves numerical stiffness issues in dynamic analysis and parameter identification. The ST-PINN provides a unified, interpretable, and computationally efficient approach for dynamic analysis and parameter identification in structural dynamics.