Nonlinear forced transient response of rotating ring on the elastic foundation by using adaptive ANCF curved beam element

Based on the Euler-Bernoulli beam theory, nonlinear axial Lagrangian strain and simplified curvature, the nonlinear differential equations of motion for rotating ring on the elastic foundation (RREF) are established by absolute nodal coordinate formulation curved beam element. In non-rotating state, the double modes at the same frequency are observed. In rotating state, the first-order critical angular speed, the frequency of forward traveling wave and backward traveling wave are obtained. Then, the nonlinear forced transient response (radial deformation rate) of the RRE under the action of concentrated load at bottom point is analyzed. In order to improve computational efficiency, the adaptive ANCF curved beam element is proposed, and reasonable range of two key parameters, i.e., element length and rotation angle of adjacent nodal tangential vector are determined. And it is used to analysis the influences of internal pressure, radial and tangential elastic support stiffness, and Young's modulus on nonlinear transient response characteristics of RREF. In order to study the standing wave phenomenon for a period, the RREF-hub contact model is established and used to analyze the nonlinear transient response of RREF at the first-order critical angular speed.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This article employs the Euler-Bernoulli beam theory to establish nonlinear differential equations for the rotating ring on an elastic foundation (RREF) based on Lagrangian strain and simplified curvature. The study investigates the nonlinear motion and response of the RREF under various conditions, such as rotating and non-rotating states, and the influences of internal pressure, elastic support stiffness, and Young's modulus. The proposed adaptive curved beam element improves computational efficiency and allows for more accurate analysis of the RREF's characteristics.