On a New Cyclic Symmetry Formulation Accounting for Boundaries Undergoing Nonlinear Forces

Abstract

Although cyclic symmetry theory was initially developed for linear structures, the introduction of nonlinear forces on internal nodes of the fundamental sector does not affect the methodology. Nevertheless, the method is ill-suited when nonlinear forces are applied at the cyclic boundary. The purpose of this paper is to provide a complement to this theory and to propose a cyclic symmetry formulation for structures undergoing nonlinear forces at their cyclic boundary. A complete nonlinear cyclic formulation for such systems is derived in this work. The advantages of such an approach lie in the reduction of computational costs using the cyclic symmetry properties. The methodology is employed to characterize the dynamics of several mechanical systems. First, it is validated on simplified models of a cyclic system. Two nonlinearities are considered: a one-dimensional friction contact interface and a cubic nonlinearity. Both cases exhibit very different dynamics behaviors; yet, the results obtained with the new strategy are shown to be very accurate. Once the approach is validated, it is employed on an industrial finite element model of turbine bladed disk featuring contact interfaces between the blades' shrouds. The capability of the method to handle large systems is thus demonstrated. For all cases, periodic excitation are applied following either a traveling or standing wave shape for different engines orders.