Year: 2025
Type: article
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.
DOI: 10.11948/20240285
Author: Yi Gong
Institution: Shanghai Customs College
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411533694