Premium
Forced vibrations of a turbine blade undergoing regularized unilateral contact conditions through the wavelet balance method
Author(s) -
Jones S.,
Legrand M.
Publication year - 2014
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4807
Subject(s) - wavelet , mathematics , vibration , convergence (economics) , unilateral contact , harmonic balance , mathematical analysis , balance (ability) , fourier series , turbine blade , galerkin method , contact force , turbine , mathematical optimization , computer science , finite element method , structural engineering , engineering , classical mechanics , physics , acoustics , mechanical engineering , artificial intelligence , nonlinear system , quantum mechanics , economics , physical medicine and rehabilitation , economic growth , medicine
SUMMARY The 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, although wavelet bases that can sparsely define nonsmooth solutions may be superior. This hypothesis is investigated using a full three‐dimensional blade with unilateral contact conditions on a set of N c discrete contact points located at its tip. The unilateral contact conditions are first regularized, and a distributional formulation in time is introduced, allowingL 2( S 1 ) Ntrial functions to properly approximate in the time domain the solution to the governing equations. The mixed wavelet Petrov–Galerkin solutions are found to yield consistent or better results than HBM, with higher convergence rates and seemingly more accurate contact force prediction. Copyright © 2014 John Wiley & Sons, Ltd.