Forced oscillations of a body attached to a viscoelastic rod of fractional derivative type

TL;DR

This paper investigates the forced oscillations of a system comprising a body attached to a viscoelastic rod modeled with fractional derivatives, introducing a complex function to analyze system behavior.

Contribution

It develops a novel analytical framework using a complex function to solve and analyze systems with fractional derivative viscoelastic components.

Findings

Derived a key complex function for system analysis

Established solution methodology for fractional viscoelastic systems

Analyzed properties of the oscillation system

Abstract

We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate a single function of complex variable that plays a key role in finding the solution of the system and in determining its properties. This function could be defined for a linear viscoelastic bodies of integer/fractional derivative type.