A Mixed Finite Volume Element Method for Time-Fractional Damping Beam Vibration Problem

Abstract

In this paper, the transverse vibration of a fractional viscoelastic beam is studied based on the fractional calculus, and the corresponding scheme of a viscoelastic beam is established by using the mixed finite volume element method. The stability and convergence of the algorithm are analyzed. Numerical examples demonstrate the effectiveness of the algorithm. Finally, the values of different parameter sets are tested, and the test results show that both the damping coefficient and the fractional derivative have significant effects on the model. The results of this paper can be used for the damping modeling of viscoelastic structures.

Keywords

• time-fractional damping beam
• vibration equation
• mixed finite volume element method
• stability
• convergence
• numerical simulation