Open AccessModal Analysis of Circular Symmetrical Plates by Means of Generalized Finite Difference Method
Author(s) -
Alaa E. Mansour
Publication year - 2019
Publication title -
mir transporta
Language(s) - English
Resource type - Journals
ISSN - 1992-3252
DOI - 10.30932/1992-3252-2019-17-3-88-98
Subject(s) - finite element method , discretization , curvilinear coordinates , finite difference , finite difference method , mathematics , truss , polar coordinate system , modal , computation , convergence (economics) , mathematical analysis , computer science , structural engineering , engineering , geometry , algorithm , chemistry , polymer chemistry , economics , economic growth
In this paper, a simplified modal analysis procedure of circular plates procedures (on polar domains) through generalized (modernized) finite difference method (abbreviated next as – FDM) is developed.Generally, circular plates are widely used for a plenty of modern civilian and industrial utilities, machine design and many other purposes. They form a spectrum of elements starting with trains’ bogies along with engine pistons, dampers and up to slabs and roofs over circular-shaped buildings, train stationsand other transportation facilities. Nowadays, FDM predominates the numerical solutions of partial differential equations (abbreviated next as – PDE) not less than the method of finite elements (abbreviated next as – FEM). This is wide-famous mathematical-discretization method that is economic to compute and simple to code, less regarding to computation tools in hands and how powerful/less powerful they are, since it bases on replacing each derivative by a difference algebraic quotient in a classical formulation. In a sense, a finite difference formulation offers a more direct approach to the numerical solution of the PDE especially in polar coordinates domain problems considering curvilinear dimensions that even FEM does not.The generalized approach of FDM considers many parameters less regarded by the classical one. Consequently, the use of classical approach negatively affects the accuracy of calculation (convergence to the exact solution values) and the tendency of results, the thing been healed by the generalized approach.