Abstract

In this paper, by introducing two meaningful auxiliary variables, a mixed finite volume element scheme for the time-fractional damping beam vibration equation is established. The scheme can keep the local conservation of physical quantity and reduce the computational cost. Then the stability and convergence of the scheme are analyzed, and numerical examples show its effectiveness. In the end, we test the value of different sets of parameters to observe the influence of damping coefficient and order of fractional derivative on the model. The results of this paper can be used for modeling the damping of the viscoelastic structures.