On the behaviour of clamped plates under large compression
Spectral Theory
2019-07-12 v1 Analysis of PDEs
Abstract
We determine the asymptotic behaviour of eigenvalues of clamped plates under large compression, by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical study of the extremal domains for the first eigenvalue, from which we see that these depend on the value of the compression, and start developing a boundary structure as this parameter is increased. The corresponding number of nodal domains of the first eigenfunction of the extremal domain also increases with the compression.
Keywords
Cite
@article{arxiv.1907.05052,
title = {On the behaviour of clamped plates under large compression},
author = {P. R. S. Antunes and D. Buoso and P. Freitas},
journal= {arXiv preprint arXiv:1907.05052},
year = {2019}
}
Comments
To appear on SIAM Journal on Applied Mathematics