Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates

IF 1 3区数学 Q1 MATHEMATICS

Journal of Spectral Theory Pub Date : 2019-07-24 DOI:10.4171/JST/355

E. Berchio, A. Falocchi

引用次数: 8

Abstract

We study the spectrum of non-homogeneous partially hinged plates having structural engineering applications. A possible way to prevent instability phenomena is to maximize the ratio between the frequencies of certain oscillating modes with respect to the density function of the plate; we prove existence of optimal densities and we investigate their analytic expression. This analysis suggests where to locate reinforcing material within the plate; some numerical experiments give further information and support the theoretical results.

查看原文本刊更多论文

最大化非均匀部分铰接板的特征值比率

本文研究了具有结构工程应用的非均质部分铰接板的谱。防止不稳定现象的一种可能方法是使某些振荡模式的频率与板的密度函数之间的比值最大化;证明了最优密度的存在性，并研究了它们的解析表达式。通过分析，提出了在板内安装补强材料的位置;一些数值实验提供了进一步的信息和支持理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.