On the Behavior of Clamped Plates under Large Compression | Zendy

Pedro R. S. Antunes | Zendy; Davide Buoso | Zendy; Pedro Freitas | Zendy

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On the Behavior of Clamped Plates under Large Compression

Author(s) -

Pedro R. S. Antunes,

Davide Buoso,

Pedro Freitas

Publication year - 2019

Publication title -

siam journal on applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.954

H-Index - 99

eISSN - 1095-712X

pISSN - 0036-1399

DOI - 10.1137/19m1249606

Subject(s) - eigenfunction , eigenvalues and eigenvectors , mathematics , compression (physics) , domain (mathematical analysis) , boundary value problem , mathematical analysis , boundary (topology) , laplace operator , physics , quantum mechanics , thermodynamics

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.

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