The Method of Strained Coordinates for Vibrations with Weak Unilateral Springs

@inproceedings{Junca2009TheMO,
  title={The Method of Strained Coordinates for Vibrations with Weak Unilateral Springs},
  author={St'ephane Junca and Bernard Rousselet},
  year={2009}
}
We study some spring mass models for a structure having a unilateral spring of small rigidity $\epsilon$. We obtain and justify an asymptotic expansion with the method of strained coordinates with new tools to handle such defects, including a non negligible cumulative effect over a long time: $T_{\epsilon} \sim {\epsilon}^{-1}$ as usual; or, for a new critical case, we can only expect: $T_{\epsilon} \sim {\epsilon}^{-1/2}$. We check numerically these results and present a purely numerical… CONTINUE READING