The quantum character of buckling instabilities in thin rods
Abstract
Here the buckling of inextensible rods due to axial body forces is mapped to 1d, nonrelativistic, time-independent quantum mechanics. Focusing on the pedagogical case of rods confined to 2d, three simple and physically realizable applications of the mapping are given in detail; the quantum counterparts of these are particle in a box, particle in a delta-function well, and particle in a triangular well. A fourth application examines the buckling counterpart of a quantum many-body problem (in the Hartree approximation). Through a fifth application, given in the form of an exercise, the reader can explore the surprising consequences of adding a second transverse dimension to the rod buckling problem and imposing periodic boundary conditions.
Keywords
Cite
@article{arxiv.2002.05772,
title = {The quantum character of buckling instabilities in thin rods},
author = {T. A. Engstrom},
journal= {arXiv preprint arXiv:2002.05772},
year = {2020}
}
Comments
7 pages, 2 figures, accepted by Am. J. Phys