Equivalent Linearization of Bladed Disk Assemblies With Friction Nonlinearities Under Random Excitation

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Abstract The present article addresses the vibrational behavior of bladed disk assemblies with nonlinear shroud coupling under random excitation. In order to increase the service life and safety of turbine blades, intense calculations are carried out to predict the vibrational behavior. The use of friction dampers for energy dissipation and suppression of large amplitudes adds a nonlinearity to the mechanical system, which complicates the calculations. Depending on the stage, different types of excitation can occur in a turbine, from stationary to transient, synchronous to asynchronous as well as deterministic to random excitation. Random excitation in combination with the presence of nonlinearities makes the calculation of the vibrational behavior even more complex. So far, this problem has only been dealt with to a limited extent in the literature on turbomachinery. Nevertheless, there are in general different approaches and methods to address this problem most of which are strongly restricted with regard to the number of degrees of freedom. The focus of this paper is the application of an equivalent linearization method to calculate the stochastic response of an academic model of a bladed disk assembly under random excitation. The fundamental idea of the method is to linearize a nonlinear system in such a way that the most suitable equivalent linear system is found taking into account the approximated distribution of the response amplitude. To apply this method to a system with a friction nonlinearity, the linear part of the system is considered in state space and extended with additional nonlinear equations. The nonlinear contact is modelled with a Bouc-Wen formulation to reproduce the hysteretic character of a nonlinearity occurring in the presence of a friction damper. The classical Bouc-Wen formulation is standardized in such a way that the usual parameters can be replaced by physical ones such as the normal force or contact stiffness. The nonlinear force of the friction nonlinearity is linearized regarding the stochastic distribution of the system response. Both the excitation and the response are limited to mean-free, stationary stochastic processes, which means that the stochastic moments do not change over time. However, the spectrum of the excitation is not limited to being constant, as it is the case with Gaussian white noise. The equivalent linearization method could also deal with a narrowband or broadband excitation spectrum. Unlike previous papers on this topic, the calculations are performed on a full bladed disk assembly in which each sector is represented by a reduced order model with several degrees of freedom.