Equations of motion for cracked beams and shallow arches
Analysis of PDEs
2021-10-22 v1
Abstract
Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that "absorbs" the boundary conditions at the cracks. Then the equations of motion are derived from the first principles using the Extended Hamilton's Principle, accounting for non-conservative forces. The variational formulation of the equations is stated in terms of the subdifferentials of the bending and axial potential energies. The equations are given in their abstract (weak), as well as in classical forms.
Keywords
Cite
@article{arxiv.2110.11197,
title = {Equations of motion for cracked beams and shallow arches},
author = {Semion Gutman and Junhong Ha and Sudeok Shon},
journal= {arXiv preprint arXiv:2110.11197},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:2110.06406