2. Benchmark solution

We are interested in the calculation of periodic solutions of the system thus characterizing the non-linear mode.

2.1. Calculation method

To solve the system, we use the EHMAN [1] method. We try to follow the branch of periodic solutions starting from the second mode of the linear system.

The stability of the periodic solution obtained is also calculated based on Floquet’s theory, by a Newmark diagram and an eigenvalue calculation.

2.2. Reference quantities and results

The reference quantities chosen are the frequency-energy pair and the stability of the periodic solution obtained.

The periodic solution is stable for the frequency-energy pair such as:

\(0.2578\mathit{Hz}<f<0.2580\mathit{Hz}\) and \(1.0J<E<1.3J\)

2.3. Uncertainties about the solution

Non-regression solution.

2.4. Bibliographical references

1. 5. 8. MOUSSI, Analysis of vibrating structures with localized nonlinearities at play using nonlinear modes. Doctoral thesis 2013.