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We study the dynamics of an elastic structure composed of a cylindrical rod in contact with a bead at one extremity. Wave propagation within the cylindrical rod is considered linear and dispersionless while the bead-rod contact shows a highly nonlinear behavior as expected from the Hertz's model of contact. The resonance curves of the nonlinear contact depend on the excitation amplitude, where a downshift of the resonance frequency with increasing excitation amplitude is observed. The prediction of the resonance frequency shift by the Hertz's model is compared to the experimental results and shows a disagreement. A better agreement is found by considering the losses with a viscoelastic model, namely the Kuwabara and Kono or Brilliantov model. The observation of the nonlinear effects linked to the resonance of the mass-spring system can lead to the design of nonlinear elastic metamaterials, where the wave propagation is controlled by nonlinear isolated resonators. (C) 2018 Elsevier Ltd. All rights reserved.