*2.1. Description of the Approach*

The study combines numerical and experimental analyses to provide basic insights into the nonlinear dynamic response of a system with contact interfaces, under propagating waves due to an impulsive-type force.

The nonlinear response of an experimental test bench (Figure 1) to an impulsive force is then modelled in a one-dimensional framework, including two rough contact interfaces with nonlinear contact stiffness.

**Figure 1.** Experimental set-up.

The tested contact stiffness laws are first identified over a large contact pressure range, using both the experimental tests and results from the literature [15,18,28]. However, there is a lack, both experimentally and from the literature, of assessments of the stiffness trend within the lower pressure range (less than 0.14 MPa). By comparing the nonlinear time responses of the experimental system with the numerical results obtained by different stiffness–pressure curves, this gap is discussed.

The analysis was conducted in terms of the evolution of the amplitude of the fundamental and second harmonics and their frequencies, as a function of the force amplitude. In fact, due to the nonlinearity of the contact in compression, higher harmonics [26] appear in the spectrum of the vibrational response.

The numerical results derived from a specific nonlinear law, reconstructed from the available experimental data, are compared to other contact laws in the literature, in particular with respect to constant linear contact stiffness [29] and the power–law relation between stiffness and pressure [15].

In this article, the system remains in compression for all the configurations throughout the simulations. The "clapping" effect, which leads to a further strong nonlinearity [30] and denotes intermittent loss of contact at the interface, is not studied in this work.
