Abstract
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 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 © 2014 John Wiley & Sons, Ltd.
Highlights
Predicting the vibratory responses of flexible structures which experience unilateral contact is becoming of high engineering importance primarily because of possible subsequent mechanical failure originated by fatigue
Whilst the DB6:DB6 formulation has many good attributes for solving nonsmooth contact problems, these results suggest a greater number of basis functions may be necessary to predict globally accurate solutions as compared to the Harmonic Balance Method (HBM) method
If the FFT method were incorporated into the code this would significantly reduce run times for HBM cases
Summary
Predicting the vibratory responses of flexible structures which experience unilateral contact is becoming of high engineering importance primarily because of possible subsequent mechanical failure originated by fatigue. This type of response is increasingly common in industrial applications due to implementation of light materials and thin designs involving larger displacements together with tighter operating clearances between components. Structural displacements and velocities which satisfy these non-penetration Signorini conditions are known to respectively feature absolute continuity and bounded variation only [41] This implies displacements are not necessarily differentiable everywhere in the defined domain and velocities may exhibit jumps; these types of problems are generally referred to as nonsmooth. Existence of solutions is still an open problem and intense research is devoted to the derivation of efficient timestepping solution methods [1, 28]
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