Analysis of free and forced vibrations of a viscoelastic micro-beam, using Kelvin-Voigt fractional viscoelastic model

In recent years, with the growing of fractional calculus, applications of fractional calculus in engineering sciences have been emerged. One of the applications that attracted many researchers in recent years is modelling of viscoelastic materials by using the fractional calculus. In this paper, an Euler-Bernoulli micro beam that has been modeled by fractional Kelvin-Voigt, is investigated. The beam is modeled based on linear strains, Modified Couple Stress theory (MCST) and Kelvin-Voigt fractional viscoelastic model. By the using of Hamilton principle partial fractional differential equations are derived. Equations of motions are solved by the using of Finite Element Method and Finite Difference Method. Time domain is discretized based on Finite Difference Method and space domain is discretized by utilizing the Finite Element Method. Simulations show that, fractional derivative has large effect on amplitude and response of free and forced vibration of beam and can increase or decrease the damping of the beam. Moreover, effects of beam length and viscoelastic parameter have been shown. Results of this paper can be used for improving viscoelastic model of materials.