Last modified: 2018-04-13

#### Abstract

In continuation of previous works, this paper deals with the vibratory response of loosely supported tubes under cross-flow in the following situation: (i) the cross-flow generates turbulent forces (TF) and fluid-elastic forces (FEF); (ii) both are defined in a dimensionless way: reduced spectra for TF, impulse response functions for FEF (derived from the quasi-unsteady model), each one being function of the reduced frequency; (iii) the mechanical restraint is loose due to small gaps between the tube and the rigid supports; (iv) the systems are unstable (or close to be) under FEF when no support is acting; (v) the parameters of each configuration (geometry, TF, FEF) are fixed except the flow velocity and the gaps' size that may vary since being two key-factors.

The objective of the paper is to clarify the competition between TF and FEF that arises in the tube vibro-impacting motion, and to produce dimensionless results when possible. First, the model equations are reviewed and formulations specific to single shock oscillators, mostly analytical, are gathered for anticipating general trends. It is particularly shown how the decreasing slope of TF spectrum and the different terms of the FEF impulse function impact the dynamics. Moreover the dynamics of multi-modal systems is much more complicated than the one of single shock oscillators. So in a second part, the paper studies, from extensive time-history simulations, how the general trends first identified are distorted using beam models. Lessons are drawn and finally the paper focuses on a pragmatic way to perform a minimal set of calculations to identify allowable domains regarding the impact damage, in terms of flow velocity and gap size.