Vibrations of a simply supported beam with a fractional derivative order viscoelastic material model - Supports movement excitation

Abstract

The paper presents vibration analysis of a simply supported beam with a fractional order viscoelastic material model. The Bernoulli-Euler beam model is considered. The beam is excited by the supports movement. The Riemann –Liouville fractional derivative of order 0 < α ≤ 1 is applied. In the first stage, the steady-state vibrations of the beam are analyzed and therefore the Riemann –Liouville fractional derivative with lower terminal at -∞ is assumed. This assumption simplifies solution of the fractional differential equations and enables us to directly obtain amplitude-frequency characteristics of the examined system. The characteristics are performed for various values of fractional derivative of order a and values of the Voigt material model parameters.