A HERMITE FINITE ELEMENT METHOD FOR THE VIBRATION PROBLEM OF THE RAYLEIGH-BISHOP BEAM

In this paper, a Hermite finite element method is proposed for the Rayleigh-Bishop equation which describes the vibration problem of the Rayleigh-Bishop beam. We first present the semi-discrete Galerkin finite element form for the Rayleigh-Bishop equation. Then by means of the cubic Hermite element, a full-discrete finite element scheme is established. Furthermore, a numerical algorithm based on the Hermite finite element method is proposed to solve the fourth-order Rayleigh-Bishop equation. Finally, a numerical example is given to illustrate the effectiveness of the proposed method. The Hermite finite element method is potentially applied to other vibration problems.