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The steady state response of geometrically non‐linear shallow arches
Author(s) -
Hitchings D.,
Ward P.
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620110807
Subject(s) - mathematical analysis , mathematics , arch , quadratic equation , curvature , equations of motion , finite element method , nonlinear system , differential equation , geometry , classical mechanics , physics , engineering , quantum mechanics , thermodynamics , civil engineering
The non‐linear steady state response of structures with curvature is investigated through the expository example of a shallow circular arch. A consistent mass finite element formulation is employed to derive the governing non‐linear differential equations. These equations are solved by assuming a single mode expansion reducing the governing equations to the single degree‐of‐freedom Duffing's equation with a quadratic term. The non‐symmetric amplitude‐frequency curve is derived and compared with results previously obtained by direct integration of the equations of motion.