SIMILARITY SOLUTIONS AND CONSERVATION LAWS FOR THE BEAM EQUATIONS: A COMPLETE STUDY
Type of document
articlePeer-reviewed
publishedVersion
Author
Halder , Amlan Kanti
Paliathanasis , Andronikos
Leach , Peter Gavin Lawrence
Rights
Creative Commons Attribution 4.0 International Licensehttp://creativecommons.org/licenses/by/4.0/
openAccess
Metadata
Show full item recordAbstract
We study the similarity solutions and we determine the conservation laws of various forms of beam equations, such as Euler-Bernoulli, Rayleigh and Timoshenko-Prescott. The travelling-wave reduction leads to solvable fourth-order odes for all the forms. In addition, the reduction based on the scaling symmetry for the Euler-Bernoulli form leads to certain odes for which there exists zero symmetries. Therefore, we conduct the singularity analysis to ascertain the integrability. We study two reduced odes of second and third orders. The reduced second-order ode is a perturbed form of Painlevé-Ince equation, which is integrable and the third-order ode falls into the category of equations studied by Chazy, Bureau and Cosgrove. Moreover, we derived the symmetries and its corresponding reductions and conservation laws for the forced form of the abovementioned beam forms. The Lie Algebra is mentioned explicitly for all the cases.
Collections
The following license files are associated with this item:
Except where otherwise noted, this item's license is described as Creative Commons Attribution 4.0 International License