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.

中文翻译：

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最大化非均匀部分铰接板的特征值比

我们研究了具有结构工程应用的非均匀部分铰接板的范围。防止不稳定现象的一种可能方法是最大化某些振荡模式的频率与板的密度函数之间的比率；我们证明了最佳密度的存在，并研究了它们的解析表达式。该分析建议在板内放置增强材料的位置；一些数值实验提供了进一步的信息并支持了理论结果。