Nonlinear Dynamic Analysis of Cracked Cantilever Beam using Reduced Order Model

In this work, a reduced order model is obtained for a cracked turbine rotor blade modeled here as a cantilever beam. Accurate dynamical model of this system using a numerical tool such as Finite Element (FE) would typically possess large number of degrees of freedom due to refinement of the mesh near crack and contact, which makes the system computationally intensive especially for long term analysis. We describe a lower order macromodel by using subspace based projection of the full order system to fewer dominant nonlinear normal modes (NNM) of the system, called proper orthogonal modes (POM). Breathing crack is modeled as piecewise linear system with bilinear natural frequency while geometric nonlinearities are incorporated in a cubic Duffing's term. We find that the reduced order model was able to match the original FEM data to the desired accuracy with only first two POD modes of the system and capture the change in frequency introduced by the damage. Two orders of magnitude reduction in the simulation time is obtained. Robustness of the macromodel is checked under different loading conditions viz. changed forcing frequency, pressure loading and damping. Complex nonlinear dynamic effects such as chaos and bifurcations were shown to be captured qualitatively. (C) 2016 The Authors. Published by Elsevier Ltd.