On the Behavior of Clamped Plates under Large Compression
| Autor: | Pedro R. S. Antunes, Pedro Freitas, Davide Buoso |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Eextremal domains
Applied Mathematics Mathematical analysis eigenvalues Mathematics::Spectral Theory biharmonic operator 01 natural sciences Robin boundary condition Pplate with tension 010101 applied mathematics Plate with compression Eeigenvalues asymptotics Compression (functional analysis) extremal domains Biharmonic equation Biharmonic operator Aasymptotics plate with compression 0101 mathematics rayleighs conjecture Laplace operator plate with tension Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 1095-712X 0036-1399 |
| DOI: | 10.1137/19m1249606 |
| Popis: | We determine the asymptotic behavior 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. This work was partially supported by the Funda ̧c ̃ao para a Ciˆencia e a Tecnologia(Portugal) through the program “Investigador FCT” with reference IF/00177/2013 and the projectExtremal spectral quantities and related problems(PTDC/MAT-CAL/4334/2014). info:eu-repo/semantics/publishedVersion |
| Databáze: | OpenAIRE |
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