Alternate model of Chladni figures for the circular homogenous thin plate case with open boundaries

7th International Congress of Engineering Physics

物理学;工业技术

Trejo-Mandujano, H.A.^1 ; Mijares-Bernal, G.^1 ; Ordoñez-Casanova, E.G.^2

Departamento de Física y Matemáticas, Universidad Autónoma de Ciudad Juárez, Chihuahua, Mexico^1

Departamento de Industrial y Manufactura, Universidad Autónoma de Ciudad Juárez, Chihuahua, Mexico^2

关键词: Circular plates;    Fresnel;    Huygens;    Hydrogen atoms;    Open boundaries;    Open boundary condition;    Solution model;    Thin plate;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/582/1/012022/pdf
DOI  :  10.1088/1742-6596/582/1/012022

学科分类：工业工程学

来源: IOP

【 摘 要 】

The wave equation is a direct but a complex approach to solve analytically for the Chladni figures, mainly because of the complications that non-smooth and open boundary conditions impose. In this paper, we present an alternate solution model based on the principle of Huygens-Fresnel and on the ideas of Bohr for the hydrogen atom. The proposed model has been implemented numerically and compared, with good agreement, to our own experimental results for the case of a thin homogenous circular plate with open boundaries.