Linear and nonlinear equations for beams and degenerate plates with double piers

Motivated by the phenomena observed on the occasion of the famous Tacoma Narrows Bridge collapse in 1940, we deal with some nonlinear fourth-order differential equations related to the analysis of the dynamics of suspension bridges. Following a "structural" approach, we discuss the role of the position of intermediate piers in the stability of a hinged beam, making a comparison between different notions of stability. The analysis is carried out analytically, with some help from numerics. (Joint work with Filippo Gazzola)