A wave approach to show the existence of detached resonant curves in the frequency response of a beam with an attached nonlinear energy sink

摘要

A wave approach is used to study the nonlinear vibrations of a beam with an attached mass acting as a nonlinear energy sink (NES). Non-ideal boundary supports are considered. The influence on the NES efficiency of both the boundary torsional stiffness and the nonlinear cubic stiffness attaching the mass is studied. Frequency response functions under harmonic forcing are calculated and the proposed approach is shown to be in excellent agreement with results from numerical time integration, with the advantage of reduced computational costs. For some particular tuning parameters, detached resonant curves are found by tracking an imposed phase condition that identifies the resonant peaks. These isolated solutions can critically affect the NES desired behavior. (C) 2018 Elsevier Ltd. All rights reserved.