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

Abstract

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 Nc discrete contact points located at its tip. The unilateral contact conditions are first regularized, and a distributional formulation in time is introduced, allowing L2(S1)N trial 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