Fractional differential equation modeling of viscoelastic fluid in mass-spring-magnetorheological damper mechanical system

Autor: Luis J. Morales-Mendoza, V. M. López-Cruz, J. E. Escalante-Martínez, M. Rodríguez-Achach, J.R. Laguna-Camacho, Hector Daniel Lopez-Calderon, M.I. Cruz-Orduña, Diptiranjan Behera
Rok vydání: 2020
Předmět:
Zdroj: The European Physical Journal Plus. 135
ISSN: 2190-5444
DOI: 10.1140/epjp/s13360-020-00802-0
Popis: The mass-spring-damper system has the minimum complexity scenario which characterizes almost all the mechanical vibration phenomena. Also it is well known that a second-order differential equation can model its dynamics. However, if the damper has a magnetorheological fluid, then it shows viscoelastic properties in the presence of a magnetic field. Hence the mathematical model that best reflects the dynamics of this system is a fractional order differential equation. Naturally, here the Mittag–Leffler function appears in the analytical solution. Mathematical modeling of the mass-spring-magnetorheological damper mechanical system has been presented here. The main focus of the investigation is to show how the fractional order $$\gamma $$ changes by varying the viscosity damping coefficient $$\beta $$ . These observations have been made by varying current intensity in the range of 0.2–2 A. A Helmholtz coil has been used to produce the magnetic field. It is worth mentioning that, this work has a high pedagogical value in the connection of fractional calculus to mechanical vibrations as well as it can be used as a starting point for a more advanced treatment of fractional mechanical oscillations.
Databáze: OpenAIRE
Externí odkaz: