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On the first frequency of reinforced partially hinged plates
- Publication Year :
- 2019
-
Abstract
- We consider a partially hinged rectangular plate and its normal modes. The dynamical properties of the plate are influenced by the spectrum of the associated eingenvalue problem. In order to improve the stability of the plate, it seems reasonable to place a certain amount of stiffening material in appropriate regions. If we look at the partial differential equation appearing in the model, this corresponds to insert a suitable weight coefficient inside the equation. A possible way to locate such regions is to study the eigenvalue problem associated to the aforementioned weighted equation. In the present paper we focus our attention essentially on the first eigenvalue and on its minimization in terms of the weight. We prove the existence of minimizing weights inside special classes and we try to describe them together with the corresponding eigenfunctions.<br />Comment: 25 pages, 5 figures
- Subjects :
- Mathematics - Analysis of PDEs
35J40, 35P15, 74K20
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1904.09173
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1142/S0219199719500743