Three-dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation Academic Article

abstract

• AbstractWe consider threedimensional elastic frames constructed out of EulerBernoulli beams and describe a simple process of generating joint conditions out of the geometric description of the frame. The corresponding differential operator is shown to be selfadjoint. In the special case of planar frames, the operator decomposes into a direct sum of two operators, one coupling outofplane displacement to angular (torsional) displacement and the other coupling inplane displacement with axial displacement (compression). Detailed analysis of two examples is presented. We actively exploit the symmetry present in the examples and decompose the operator by restricting it onto reducing subspaces corresponding to irreducible representations of the symmetry group. These quotient operators are shown to capture particular oscillation modes of theframe.

authors

• Berkolaiko, Gregory

published proceedings

• STUDIES IN APPLIED MATHEMATICS

author list (cited authors)

• Berkolaiko, G., & Ettehad, M.

citation count

• 4

complete list of authors

• Berkolaiko, Gregory||Ettehad, Mahmood

publication date

• May 2022

publisher

• Wiley  Publisher

keywords

• Elastic Frames
• Irreducible Representations
• Oscillation Modes

Digital Object Identifier (DOI)

• 10.1111/sapm.12485

start page

• 1586

end page

• 1623

volume

• 148

issue

• 4

URL

• http://dx.doi.org/10.1111/sapm.12485