Time-fractional dependence of the shear force in some beam type problems with negative Young modulus

• Type: Article in International Scientific Journal
• Date: 2020

Authors

Cao Labora, DC (Author) Other; António Mendes Lopes (Author) FEUP; Tenreiro Machado, JAT (Author) Other

Journal

Title: Applied Mathematical Modelling

Vol. 80

Pages: 668-682

ISSN: 0307-904X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 2 Citations

Other information

Authenticus ID: P-00R-GBJ

DOI: 10.1016/j.apm.2019.11.054

Abstract (EN): Under the Euler-Lagrange equation, a time-fractional dependence for the shear force in a beam in the absence of a transverse load is analysed. The main assumption is that the beam is composed by a material with a negative Young modulus. The existence of such materials is documented in several recent studies. A strategy adopting analytical calculations involving Laplace transforms concludes that, up to a known constant, the shear force can be computed as the Riemann-Liouville time-fractional derivative of order 3/2 of the deflection of the beam. This identity presents an interesting connection with the Bagley-Torvik equation.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15