1. Modal Analysis of Functionally Graded Rectangular Plates Wes Saunders Engineering Project Proposal

2. Purpose To use Finite Element Analysis (FEA) to perform a modal analysis on functionally graded materials (FGM) to determine modes and mode shapes.

3. Background Modal analysis involves imposing an excitation into the structure and finding when the structure resonates, and returns multiple frequencies, each with an accompanying displacement field. Functionally graded materials (FGM) are defined as an anisotropic material whose physical properties vary continuously throughout the volume, either randomly or strategically, to achieve desired characteristics or functionality.

4. Methodology Using COMSOL Finite Element software, a modal analysis will be performed to determine modes and mode shapes The project will begin by looking at basic isotropic plates using modal analysis, before progressing onto simply graded materials (i.e. linear, power law), then finally looking at a FGM.

5. Results Frequencies (modes) Displacement fields (mode shapes) for each frequency, plotted as such:

6. Milestones TaskCompletion Date Familiarize self with COMSOL software9/30/11 Perform modal analysis for a well known isotropic plate case in COMSOL and compare to exact solution 10/7/11 Perform analysis for a linearly graded material for test case10/7/11 Perform analysis for a power law graded material for test case10/11/11 Determine the governing equation for first FGM property variation, complete FGM model in COMSOL 10/14/11 Perform modal analysis on first FGM model and compare to known solution 10/21/11 Complete first progress report10/21/11 Determine the governing equation for second and third FGM property variation, complete FGM models in COMSOL 11/11/11 Complete second progress report11/11/11 Perform modal analysis on second and third FGM models. Compare to first FGM model 11/25/11 Complete final write-up draft12/2/11 Submit final write-up of project12/16/11