Vibrations of mechanical systems undergoing regularized unilateral contact conditions through the wavelet balance method

Simon Jones (1) , Mathias Legrand (1)

1 Structural Dynamics and Vibration Laboratory [Montréal]

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, 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.

Mots clés: wavelet analysis; Petrov-Galerkin method; weak formulation; unilateral contact conditions; nonsmooth dynamics

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Simon Jones, Mathias Legrand. Vibrations of mechanical systems undergoing regularized unilateral contact conditions through the wavelet balance method. 2013. ⟨hal-00806545v1⟩