Premium
Coupled bending–torsional dynamic stiffness matrix for beam elements
Author(s) -
Banerjee J. R.
Publication year - 1989
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.1620280605
Subject(s) - direct stiffness method , bending stiffness , stiffness matrix , cantilever , torsion (gastropod) , stiffness , beam (structure) , space frame , timoshenko beam theory , finite element method , structural engineering , vibration , bending , mathematics , mathematical analysis , physics , engineering , acoustics , medicine , surgery
Abstract Explicit expressions for the coupled bending–torsional dynamic stiffness matrix of a uniform beam element are derived in an exact sense by solving the governing differential equation of the beam. Implementation of the derived dynamic stiffness matrix in a space frame computer program is discussed with particular reference to an established algorithm to enable vibration analysis of coupled systems to be made. The application of the theory is demonstrated by an illustrative example wherein the results for a cantilever beam with a substantial amount of coupling between bending and torsion are highlighted. The correctness of the theory is confirmed to a high degree of accuracy by computed results and numerical checks.