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This book develops a full theory for hinged beams and degenerate
plates with multiple intermediate piers with the final purpose of
understanding the stability of suspension bridges. New models are
proposed and new tools are provided for the stability analysis. The
book opens by deriving the PDE's based on the physical models and
by introducing the basic framework for the linear stationary
problem. The linear analysis, in particular the behavior of the
eigenvalues as the position of the piers varies, enables the
authors to tackle the stability issue for some nonlinear evolution
beam equations, with the aim of determining the "best position" of
the piers within the beam in order to maximize its stability. The
study continues with the analysis of a class of degenerate plate
models. The torsional instability of the structure is investigated,
and again, the optimal position of the piers in terms of stability
is discussed. The stability analysis is carried out by means of
both analytical tools and numerical experiments. Several open
problems and possible future developments are presented. The
qualitative analysis provided in the book should be seen as the
starting point for a precise quantitative study of more complete
models, taking into account the action of aerodynamic forces. This
book is intended for a two-fold audience. It is addressed both to
mathematicians working in the field of Differential Equations,
Nonlinear Analysis and Mathematical Physics, due to the rich number
of challenging mathematical questions which are discussed and left
as open problems, and to Engineers interested in mechanical
structures, since it provides the theoretical basis to deal with
models for the dynamics of suspension bridges with intermediate
piers. More generally, it may be enjoyable for readers who are
interested in the application of Mathematics to real life problems.
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