Spectral Optimization of Torsional Eigenvalues for a Nonhomogeneous Fish-Bone Plate with Piers

Abstract Motivated by stability issues for suspension bridges, the analysis focuses on the maximization of the torsional eigenvalues of a nonhomogeneous multi-span fish-bone plate with respect to the mass density. The incorporation of internal piers significantly impacts the spectral properties of the system. After a general spectral theorem, a characterization of the densities maximizing the first and the second torsional eigenvalue is provided, starting from the corresponding results for the nonhomogeneous Dirichlet problem. In the case where the mass of the central span is equal to its length, more explicit insight is then given, taking into account the role of the position of the piers and discussing the scenario for higher-order eigenvalues, as well.