ME3263 Introduction to Sensors and Data Analysis (Fall 2018)

Lab #4 Predicting Natural Frequencies with the Finite Element Method

What is the Finite Element Method?

The Euler-Lagrange dynamic beam equation is an example of a partial differential equation (PDE). These equations are common in many engineering applications e.g. solid mechanics, electromagnetics, fluid mechanics, and quantum mechanics. The finite element method solves PDEs. The FEM process involves two steps to create matrices for a computer algorithm solution. First, the PDE is integrated from the strong form to the weak form. Second, an approximation of the variable "shapes" within each "element" is created to convert the integrals and derivatives into matrices (1). For elements with nodes only at vertices, such as cubes (hexahedrons) or pyramids (tetrahedrals), the "shape" function is linear for displacement.