Nonlinear vibration localisation in a symmetric system of two coupled beams

Abstract

We report nonlinear vibration localisation in a system of two symmetric weakly coupled nonlinear oscillators. A two degree-of-freedom model with piecewise linear stiffness shows bifurcations to localised solutions. An experimental investigation employing two weakly coupled beams touching against stoppers for large vibration amplitudes confirms the nonlinear localisation.

Control of isolated response curves through optimization of codimension-1 singularities

“…The presence of isolas have been reported in numerous numerical and experimental studies, with the first reports dating back to the 1950s [1]. They can be found in nonlinear mechanical systems affected by various nonlinearities: polynomial [69,50,64,30], contact and friction [66,29,40,76,67,77], hysteretic and piecewise linear elastic restoring forces [10,23,2,28], hertzian contact [62]. They were also uncovered in traf-fic flow [53], flight dynamics models [59] and systems controlled with rate-limited feedback [58].…”

On Harmonic Balance Method-based Lagrangian contact formulations for vibro-impact problems

“…The nonsmooth behaviour of contact interactions has widely been studied by means of the HBM. For instance, the HBM was used on phenomenological nonsmooth systems in order to observe sophisticated behaviours such as quasi-periodic orbits [7,36], sub-harmonic and super-harmonic resonances [2,9,20], detached solution branches [2,11,15] or vibration localization [11,31]. Several methodologies have also been developped in order to compute solutions to nonsmooth problems based on the HBM, without relying on an the AFT scheme.…”

“…When it comes to unilateral contact, several contact treatments exist in order to compute nonlinear forces. A large majority of the methodologies rely on a penalty-based contact treatment [2,6,7,9,11,18,20,23,31,36,43,44]. For some applications, the latter being too challenging from a numerical standpoint, an additional regularization is added [6,18,43,44] to smoothen the nonsmoothness of contact forces.…”

Bifurcation Analysis of a Four-Dimensional System of Two Symmetric Coupled Nonlinear Oscillators with Clearance

“…Concerning symmetric structures, Papangelo et al [2] studied multistability and localization of cyclic symmetric structures. Fontanela et al [3] investigated the nonlinear vibration localisation of two coupled beams modelled by a two degree-of-freedom piecewise smooth system using theoretical and experimental methods.…”