Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear and nonlinear equations for beams and degenerate plates with
  multiple intermediate piers   A full theory for hinged beams and degenerate plates with multiple
intermediate piers is developed. The analysis starts with the variational
setting and the study of the linear stationary problem in one dimension.
Well-posedness results are provided and the possible loss of regularity, due to
the presence of the piers, is underlined. A complete spectral theorem is then
proved, explicitly determining the eigenvalues on varying of the position of
the piers and exhibiting the fundamental modes of oscillation. The obtained
eigenfunctions are used to tackle the study of the nonlinear evolution problem
in presence of different nonlinearities, focusing on the appearance of linear
and (a suitable notion of) nonlinear instability, with a twofold goal: finding
the most reliable nonlinearity describing the oscillations of real structures
and determining the position of the piers that maximizes the stability of the
structure. The last part of the paper is devoted to the study of degenerate
plate models, where the structure is composed by a central beam moving
vertically and by a continuum of cross-sections free to rotate around the beam
and allowed to deflect from the horizontal equilibrium position. The torsional
instability of the structure is investigated, taking into account the impact of
different nonlinear terms aiming at modeling the action of cables and hangers
in a suspension bridge. Again, the optimal position of the piers in terms of
stability is discussed. The stability analysis is carried out both by means of
analytical tools, such as Floquet theory, and numerical experiments. Several
open problems and possible future developments are presented.

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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg