# 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

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 32 REFERENCES

## Applied asymptotic analysis

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

## Multiple Scale and Singular Perturbation Methods

VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

S. Junca
• 2010

S. Junca
• 2010
VIEW 2 EXCERPTS

VIEW 1 EXCERPT

VIEW 2 EXCERPTS

VIEW 2 EXCERPTS

VIEW 2 EXCERPTS