Dynamic Response Prediction of a Cantilever Beam Under Different Boundary Constraints and Excitation Conditions Based on an Improved Physics‐Informed Neural Network

ABSTRACT

The cantilever beam structures, like wind turbine towers, space masts, solar wings, and high‐rise chimneys and buildings, are widely used engineering structures. It is crucial to fast and accurately predict their dynamic responses under complicated excitations. This paper establishes an improved physics‐informed neural network (PINN) called Fourier transformation‐PINN (FT‐PINN) for predicting the dynamic response of a cantilever beam subject to different boundary constraints and excitation conditions. The core idea of the FT‐PINN is to use the Latin hypercube sampling strategy for generating model training points and introduce multiple sets of control equations with different frequencies through Fourier expansion to achieve high solving accuracy and efficiency for partial differential equations. Two loss functions, including the mean square error and mean absolute error, are included in the FT‐PINN for comparison. Four test cases are designed to evaluate the performance of the FT‐PINN and classic PINN in solving dynamic equations of a cantilever beam structure with different boundary and excitation conditions. It is validated that the FT‐PINN model proposed in this paper has higher accuracy and efficiency than the classic PINN. This also provides a new approach for using PINN to handle local sharp gradients and complex high‐frequency problems in vibration equations.