Self-taught Finite Element Method implementation to the assessing of natural frequencies and modal shapes in 2D rectangular plates

Abstract

This work presents a self-taught guide to the implementation of a Finite Element Model (FEM) to assess the natural frequencies and modal shapes of 2D rectangular plates. The study offers a practical way of understanding the FEM processing in commercial software available in the market and is motivated by the Computer Vibro-acoustic module of the Graduate Program in Mechanical Engineering of the Federal University of Santa Catarina, Brazil. A steel plate with dimensions of 200 mm x 500 mm x 2 mm is implemented, and the results obtained from this algorithm are compared with results given by a commercial software. Two configurations are tested and validated: a free plate, i.e., no boundary conditions, and a door-like plate whose boundary conditions are the door hinges and the door handle. The implementation is made for the direct and superposition methods in FEM, using both symbolic and numerical approaches in MATLAB software. Results obtained present acceptable errors in most frequency bands, thus validating the algorithm and enhancing the understanding of FEM modeling for vibro-acoustic applications.