On nonlinear normal modes to derive reduced order models of cylindrical shells with 1:1 internal resonance

Abstract

In this work, based on nonlinear normal modes theory, it is derived the nonlinear reduced order model of a cylindrical shell with 1:1 internal resonance. For this, from Donnell's nonlinear theory and the Galerking method, the full discretized dynamical model of a simply supported cylindrical shell is obtained, considering a transversal displacement field with 1:1 internal resonance. Next, the nonlinear normal modes of the full dynamical model are obtained through invariant manifolds methodology to obtain an equivalent reduced order model. A comparative analysis of nonlinear resonance curves is performed between the full nonlinear dynamical model and its respective reduced order model obtained by nonlinear normal modes. The numerical results demonstrate that nonlinear normal modes reduced models can adequately approximate overall dynamics limited to a certain magnitude of vibration and the chosen pairs of the master coordinates.