Nonlinear response prediction of a high-dimensional nonlinear beam system under random parametric errors using neural networks

Abstract

This study presents a numerical investigation of how random parametric errors (RPEs) affect the nonlinear response of high-dimensional dynamical systems, with a particular focus on predicting the resulting vibration behavior. A case study is conducted on the vibration of a simply supported beam under uniformly distributed harmonic excitation. Initially, a high-dimensional nonlinear dynamical model of the beam is developed based on the Hamiltonian principle and the Galerkin method under the von Kármán assumption. The model is subsequently extended to incorporate RPEs, and the influence on the dynamic response of the simply-supported beam with varying RPE ranges is analyzed. Numerical simulations demonstrate that the minimum required truncation order increases as the PRE intensity grows. Finally, the transformer neural network is shown to exhibit high accuracy and robustness in predicting the chaotic vibration behavior of the system. This work provides a theoretical basis for investigating the vibrational characteristics and chaotic response prediction of simply-supported beams within high-dimensional nonlinear dynamical systems subjected to parametric errors.