5 Vibration Analyses Using Finite Element Method

The objectives of this chapter are to furnish the readers with elementary knowledge of the finite element method (FEM) and to provide guided tours on using commercial finite element software to perform vibration analyses. The simplest type of finite element is used to illustrate the relationship among the Lagrangian dynamics, the lumped-parameter modeling, and the finite element modeling. Then, a complete finite element analysis for beams is formulated and implemented using MatLab as the programming language. The use of commercial finite element analysis software is presented by illustrated tutorials using SolidWorks. This chapter is not intended as an in-depth treatment of the subject. Students are expected to gain further understanding of both the finite element theory and any particular software through more extensive and dedicated resources and references.