**Numerical and Experimental Analysis of Nonlinear Vibrational Response due to Pressure-Dependent Interface Sti**ff**ness**

**Dorra Nouira 1,2, Davide Tonazzi <sup>2</sup> , Anissa Meziane <sup>1</sup> , Laurent Baillet <sup>3</sup> and Francesco Massi 2,\***


Received: 9 June 2020; Accepted: 7 July 2020; Published: 10 July 2020

**Abstract:** Modelling interface interaction with wave propagation in a medium is a fundamental requirement for several types of application, such as structural diagnostic and quality control. In order to study the influence of a pressure-dependent interface stiffness on the nonlinear response of contact interfaces, two nonlinear contact laws are investigated. The study consists of a complementary numerical and experimental analysis of nonlinear vibrational responses due to the contact interface. The laws investigated here are based on an interface stiffness model, where the stiffness property is described as a nonlinear function of the nominal contact pressure. The results obtained by the proposed laws are compared with experimental results. The nonlinearity introduced by the interface is highlighted by analysing the second harmonic contribution and the vibrational time response. The analysis emphasizes the dependence of the system response, i.e., fundamental and second harmonic amplitudes and frequencies, on the contact parameters and in particular on contact stiffness. The study shows that the stiffness–pressure trend at lower pressures has a major effect on the nonlinear response of systems with contact interfaces.

**Keywords:** nonlinear dynamic response; second harmonics; experiments; numerical modelling; interface stiffness
