MATLAB-Based Finite Element Analysis in a Vibrations Class

This paper overviews MATLAB (R)-based assignments developed and implemented in a mechanical vibrations class which utilize finite element analysis (FEA) for structural vibration calculations. The course is dual level and includes upper-level undergraduates taking it as a technical elective, and graduate students taking it for graduate credit. In dual level courses, there are additional requirements for graduate credit as compared to the work required for undergraduate credit. The course is offered via ITV (Interactive Television). A primary component of the paper is an overview of a graduate student project that requires the students to produce a flexible FEA program to analyze beam vibration using the MATLAB user function capability. This work is intended to solidify for the students the basics of structural vibration analysis, including calculation of natural frequencies and mode shapes, and also forced harmonic response analysis. It also provides an introduction to some students on FEA. Those who already have FEA experience gain more insight into development of a structural model, including mass, stiffness, and damping matrices, than they may obtain from use of standard FEA software, such as ANSYS (R). Also, the students gain valuable programming experience, and better knowledge of the widely-used mathematical software tool, MATLAB. While undergraduates are not required to develop an FEA program, they utilize the finite element method through MATLAB functions developed by the instructor and provided to them, and the programming approach is outlined in lecture material. In some assignments, students compare finite element results to results based on other analysis methods to verify for them that the finite element analysis method is reliable. They also compare results from FEA implemented using MATLAB user functions to results from the commercial FEA software, ANSYS. The assignments provide some insight into important issues such as how results can be impacted by mesh density. This computational work complements a more traditional coverage of vibrations topics, which is the main basis of the course.