We study some spring mass models for a structure having a small unilateral contact with a small parameter ε. We valid 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: $T_\varepsilon \sim \varepsilon^{-1}$ as usual; or, for a new critical case, we can only expect: $T_\varepsilon \sim \varepsilon^{-1/2}$.