A new numerical scheme with Wavelet-Galerkin followed by spectral deferred correction for solving string vibration problems

In this paper, the nonlinear governing equations for longitudinal and transverse vibrations of axially moving strings are presented first and a new numerical scheme with Wavelet-Galerkin method followed by spectral deferred correction (SDC) is developed to solve such governing equations. A string vibration problem with exact solution is used to demonstrate the accuracy and efficiency of the proposed method by comparing it to the traditional methods with a classic finite element method (FEM) followed by Runge-Kutta or SDC, Wavelet-Galerkin followed by Runge-Kutta. Moreover, the proposed method is applied in solving for the coupled nonlinear string vibration of the main drive chain system of escalator and the results show a good agreement with experimental and multi-body dynamic (MBD) simulation results, which demonstrates the validity of the proposed method for solving coupled nonlinear string vibration problems. (C) 2019 Elsevier Ltd. All rights reserved.