A High-Accuracy Model Reduction for Analysis of Nonlinear Vibrations in Structures With Contact Interfaces

Abstract

A highly accurate and computationally efficient method is proposed for reduced modeling of jointed structures in the frequency domain analysis of' nonlinear steady-state forced response. The method has significant advantages comparing with the popular variety of mode synthesis methods or forced response matrix methods and can be easily implemented in the nonlinear forced response analysis using .standard finite element codes. The superior qualities of the new method are demonstrated on a set of major problems of nonlinear forced re.'iponse analysis of bladed disks with contact interfaces: (i) at biade roots, (ii) between interlock shrouds, and (iii) at underpiatform dampers. The numerical properties of the method are thoroughly studied on a number of special test cases

Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications

“…To reduce the size of the problem, a model reduction based on a FRF matrix representation is applied, and the harmonic coefficients are calculated with a Newton-Raphson iterative solver. The FRF matrix is obtained by calculating its exact value at a particular frequency point, and including a second term which describes its variation in a wide range of frequency [28]. Thanks to this approach the accuracy of the contact displacement calculation is significantly improved, without the need to include too many modes in the truncated modal expansion.…”

“…The approach used for the numerical analysis, is based on an exisiting multi-harmonic balance (MHBM) solver coupled with a model reduction technique, included in the code FORSE (FOrced Response SuitE) and discussed in detail in [21,22,28]. This flexible methodology can be applied to predict the nonlinear dynamic response of large FE models, which contain nonlinear joints and are subject to harmonic excitation.…”

“…For this reason, a combination of the harmonic balance method (HBM) [18,[23][24][25] which is based on a fundamental harmonic or multi-harmonic approximation of the nonlinear forces, together with model reduction techniques [26][27][28] has emerged as a widely used approach to solve vibration problems.…”

The influence of joints on friction induced vibration in brake squeal

“…The scalability of approaches using the HB method with or without reduction techniques (e.g. component mode synthesis [37]) is discussed and shown in [31,38,39,40]. Besides the scalability of the HB method, these works show the method's ability to handle few, but arbitrary nonlinearities for large FE-models.…”

Reduced-order modelling using nonlinear modes and triple nonlinear modal synthesis

“…Frequency-based techniques such as the HBM have proved very efficient in the past to study the forced response of nonlinear systems, especially when dealing with localised nonlinearities since they allow an exact condensation of the problem on the nonlinear degrees of freedom (DOF) [22,23]. However, these methods are still struggling to handle large finite element models comprising thousands of nonlinear variables.…”