A novel Fourier time-sequential PINN approach for multi-frequency analysis of nonlinear aerothermoelastic problems

Abstract

Panel structures on supersonic vehicles experience severe thermal and aerodynamic loads, leading to nonlinear aerothermoelastic responses that can jeopardize structural safety. Analyzing these responses is particularly challenging because of strong nonlinearity and rich frequency content, especially in long-duration numerical simulations. This work introduces a novel Fourier time-sequential physics-informed neural network (FT-PINN) for aerothermoelastic analysis. By incorporating a primitive function, FT-PINN transforms integro-differential governing equations into partial differential equations. Solution accuracy over long-duration time periods for dynamic analysis is maintained through time-sequential training, normalization, and hard-constraint techniques, while random Fourier feature mapping enhances the model ability to capture complex nonlinear and multi-frequency behaviors. Numerical experiments demonstrate that FT-PINN accurately predicts aerothermoelastic responses under various loading conditions, including thermal buckling, limit cycle oscillations, and both quasi-periodic and chaotic motions. The proposed method reduces relative L <inf>2</inf> error by two to three orders of magnitude compared to existing PINN approaches. It also effectively handles cases involving viscoelastic damping, non-uniform thickness and time-varying parameters, further highlighting its applicability and versatility.