Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing Separable Non-$2\pi$-Periodic Solutions to the
  Navier-Lam\'{e} Equation in Cylindrical Coordinates Using the Buchwald
  Representation: Theory and Applications   In a previous paper [Adv. Appl. Math. Mech. 10 (2018), pp. 1025-1056], we
used the Buchwald representation to construct several families of separable
cylindrical solutions to the Navier-Lam\'{e} equation; these solutions had the
property of being $2\pi$-periodic in the circumferential coordinate. In this
paper, we extend the analysis and obtain the complementary set of separable
solutions whose circumferential parts are elementary $2\pi$-aperiodic
functions. Collectively, we construct eighteen distinct families of separable
solutions; in each case, the circumferential part of the solution is one of
three elementary $2\pi$-aperiodic functions. These solutions are useful for
solving a wide variety of dynamical problems that involve cylindrical
geometries and for which $2\pi$-periodicity in the angular coordinate is
incompatible with the given boundary conditions. As illustrative examples, we
show how the obtained solutions can be used to solve certain forced-vibration
problems involving open cylindrical shells and open solid cylinders where (by
virtue of the boundary conditions) $2\pi$-periodicity in the angular coordinate
is inappropriate. As an addendum to our prior work, we also include an
illustrative example of a certain type of asymmetric problem that can be solved
using the particular $2\pi$-periodic subsolutions that ensue when there is no
explicit dependence on the circumferential coordinate.

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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: dg-ga