FINITE DIFFERENCES FOR PLATES MODAL ANALYSIS

Resumo

Plates are flat structural members with a thickness much less than the other two dimensions,
loaded in the direction perpendicular to the plane containing these two larger lengths. In case the
thickness does not exceed 1/10 of the other dimensions, these structures are called thin plates. In this
case, it is possible to adopt the so-called classical thin plate theory of plate dynamics, developed by
Lagrange / Sophie-Germain, in which Kirchhoff's hypotheses are given as valid. Due to the difficulty of
obtaining analytical solutions for the differential equations that govern this structural model, and to the
advancement of software and computational hardware, numerical methods have been used in the
modeling of this type of structural system. Our objective in this paper is to present modal analysis of
aircraft plates using a computer implementation of the Central Finite Differences Method. The
numerical results will be compared to solutions available in the literature. The numerical method of
finite differences is an approach to obtain the approximation of the solution of differential equations.
The basic idea of this method is to transform the resolution of a differential equation into a system of
algebraic equations, replacing the derivatives by differences.