| Volume 15, Number 2, 2025, Pages - DOI：10.11948/JAAC-2024-0285 |
| A Hermite Finite Element Method for the Vibration Problem of the Rayleigh-Bishop beam |
| Yi Gong |
| Keywords:Rayleigh-Bishop beam, pseudohyperbolic equation, hermite finite element. |
| Abstract: |
| 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. |
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