see https://www.ila.uni-stuttgart.de/nlvib From p. 105 in their book. Solved excercises are distribted along with their program and found in the folder: nlvib/EXAMPLES
Table 5.1 Solved exercises with their learning goals
| No. | System | Learn that: |
|---|---|---|
| 1 | Duffing | Computational agrees with analytical HB |
| 2 | Single-DOF, unilateral spring | Zeroth and higher harmonics can be relevant |
| 3 | Beam, dry friction | HB can save a lot of computational effort |
| 4 | Beam, cubic spring | Dynamic scaling can be beneficial |
Table 5.2 Homework problems with their learning goals
| No. | System | Learn to… |
|---|---|---|
| A | Linear single-DOF | …use path continuation |
| B | Duffing | …use more path continuation, and run a harmonic convergence study |
| C | Two-DOF, cubic spring | …implement Hill’s method for stability analysis |
| D | Two-DOF, unilateral springs | …implement a new nonlinearity, implement combined static–dynamic loading, and compute a subharmonic response |
| E | Van der Pol | …implement another new nonlinearity, implement limit cycle analysis (self-excitation), and continue w.r.t. a nonlinearity parameter |
| F | Beam, dry friction | …implement a condensation of the HB equations to the nonlinear part |
https://github.com/LCSETH/SSMtool
See the accompanying paper Analytic Prediction of Isolated Forced Response Curves from Spectral Submanifolds https://arxiv.org/abs/1812.06664
https://github.com/LCSETH/SteadyStateTool https://arxiv.org/abs/1810.10103
And Recipes for Continuation(incl. coco toolbox for matlab) https://epubs.siam.org/doi/book/10.1137/1.9781611972573