Interface Reduction in an Equivalent Linearization Algorithm for Nonlinearly Coupled Systems Under Random Excitation

Abstract

Stochastic excitation is a rarely discussed topic regarding the vibrational behavior of turbine blades. While the calculation of stochastic quantities describing the stochastic steady-state vibration response is comparatively straightforward in the linear case, it becomes much more challenging in the case of nonlinear couplings. A method suitable for calculating approximations of the stochastic steady-state vibration response is the equivalent linearization method. However, the efficiency of this method decreases with an increasing number of degrees of freedom. This is especially challenging if the number of nonlinearly coupled degrees of freedom is large, as in the case of an extended contact interface, such as a shroud contact. While the uncoupled part of the system can be reduced using a component mode synthesis, the remaining nonlinear interface degrees of freedom have to remain unreduced to evaluate the nonlinear forces. To address this problem, this paper presents an approach to reduce the interface degrees of freedom within the framework of the equivalent linearization method. The presented method is based on a representation of the dynamics of the contact interface by means of a reduced set of Legendre polynomials. However, the evaluation of the nonlinear force still takes place in physical coordinates. The presented procedure is demonstrated using a beam model with different contact pairings as well as a more realistic model of a bladed disk assembly.