Forced vibrations of a turbine blade undergoing regularized unilateral contact conditions through the wavelet balance method

Abstract

International audienceThe method of weighted residuals can efficiently enforce time-periodic solutions of flexible structures experiencing unilateral contact. The Harmonic Balance Method (HBM) based on Fourier expansion of the sought solution is a common formulation, though wavelet bases that can sparsely define nonsmooth solutions may be superior. This hypothesis is investigated using an axially vibrating rod with unilateral contact conditions. A distributional formulation in time is introduced allowing $L^2(S^1)^N$ trial functions to approximate the second-order equations. The mixed wavelet Petrov-Galerkin solutions are found to yield consistent or better results than HBM, with similar convergence rates and seemingly more accurate contact force prediction.<br> <a href="https://hal.archives-ouvertes.fr/hal-01403614/">Related Matlab scripts</a

Nonsmooth Modal Analysis: From the Discrete to the Continuous Settings

“…For unilateral contact problems, HBM has mostly been implemented in conjunction with regularizing techniques [15,20,39,55,73] and the contact forces are directly included in the governing ODE (11). A variant of HBM in which the truncated Fourier series is replaced by wavelets has been proposed to compute periodic solutions of a turbine blade with regularized contact conditions [48]. HBM with regularized friction has been investigated in [47].…”

The harmonic balance method with arc-length continuation in blade-tip/casing contact problems

“…On the other hand, blade-tip/casing contacts yield discontinuous velocity and acceleration fields for which a Fourier-based numerical strategy may be ill-suited due to the Gibbs phenomenon [24,25]. This last observation motivated the development of other frequency methods relying on other basis of functions such as wavelets [26].…”

Minimising Clearance Consumption: A Key Factor for the Design of Blades Robust to Rotor/Stator Interactions?

“…Such reduction may only be achieved through a closing of operating blade-tip/casing clearances which leads to more frequent structural contacts that may initiate the aforementioned interaction phenomena. In this context, the development of blades and bladed components robust to structural contacts is a growing field of investigation and motivated many recent numerical investigations [2,3,4]. The redesign operation that was previously carried out introduced a few optimization criteria [1] related to non-linear structural simulations between the blade of interest and a perfectly rigid casing on which was deposited an abradable coating.…”