Nonlinear Dynamic Identification of Beams Resting on Nonlinear Viscoelastic Foundations Based on the Time-Delayed Transfer Entropy and Improved Surrogate Data Algorithm

In this work, the transfer entropy and surrogate data algorithm were introduced to identify the nonlinearity level of the system by using a numerical solution of nonlinear response of beams. A homogeneous Euler-Bernoulli beam was subjected to a time-varying concentrated load and resting on a nonlinear foundation. The Galerkin method was applied to discretize the dimensionless differential governing equation of the forced vibration, and then the fourth-order Runge-Kutta method was used to obtain the time-history response of the lateral displacement. In order to simulate different nonlinearity levels, different ratios between nonlinear parameters and linear parameters of foundation, as well as different Young’s moduli, were used. A nonlinearity index was proposed. In the case of different nonlinearity levels, the nonlinearity index was used to analyze the difference between the transfer entropy calculated from the original data and the transfer entropy calculated from the surrogate data. By comparing and analyzing the nonlinearity index values under different ratios, it was found that the nonlinearity index values generally increased with the increase of the ratio and the sum of nonlinearity index values had a positive correlation with the ratio. By comparing the nonlinearity index values of the transfer entropy results of beams with different Young's moduli, it was found that the sum of the nonlinearity index values generally decreased with the increase of Young's modulus. The numerical results demonstrate that the present approach could effectively quantify the nonlinearity in the response of a beam resting on a nonlinear foundation.