A Method for Use of Cyclic Symmetry Properties in Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks

Abstract

An effective method for analysis of periodic forced response of nonlinear cyclically symmetric structures has been developed. The method allows multiharmonic forced response to be calculated for a whole bladed disk using a periodic sector model without any loss of accuracy in calculations and modeling. A rigorous proof of the validity of the reduction of the whole nonlinear structure to a sector is provided. Types of bladed disk forcing for which the method may be applied are formulated. A multiharmonic formulation and a solution technique for equations of motion have been derived for two cases of description for a linear part of the bladed disk model: (i) using sector finite element matrices and (ii) using sector mode shapes and frequencies. Calculations validating the developed method and a numerical investigation of a realistic high-pressure turbine bladed disk with shrouds have demonstrated the high efficiency of the method.

A methodology for identification of dynamic parameters in assembled aircraft structures

“…Hurty [1], proposed the Component Mode System (CMS), many years ago. More recently the Harmonic Balance Method has been used for different purposes [2][3][4][5][6][7]. A research conducted in the University of Coruna in collaboration with AIRBUS has taken a different approach providing good results and will be next described.…”

Modelling Friction Contacts in Structural Dynamics and its Application to Turbine Bladed Disks

“…In order to reduce the long computation times, reduction techniques are applied to equations (8) and then the nonlinear reduced model is solved with iterative methods, typical of non-linear algebraic equations. In the field of turbomachinery, in particular in the field of bladed disk dynamics, the first reduction technique consists in the application of the boundary conditions of cyclic symmetry (Petrov, 2004;Siewert et al, 2010).…”

An analytical calculation of the Jacobian matrix for 3D friction contact model applied to turbine blade shroud contact

“…where M, K and C are the mass, stiffness and viscous damping matrices of a single sector, (k) q(t) represents the cyclic displacement vector of the k th sector, which is equivalent to the displacements in the cylindrical coordinate system for a sector model and (k) f ext (t) is a travelling wave excitation [8,21,35]. A dot above q(t) indicates derivative with respect to time, t. Due to the spatial periodicity of the excitation wave, it is expressed as a Fourier series truncated after n h harmonics.…”