Modal Analysis of Functionally
Graded Simply-Supported Plates
By Wes Saunders
Progress Report 1
Purpose
• To use Finite Element Analysis (FEA) to
perform a modal analysis on functionally
graded materials (FGM) to determine modes
and mode shapes.
Background
• FGMs
– FGMs are defined as an anisotropic material whose physical
properties vary throughout the volume, either randomly or
strategically, to achieve desired characteristics or functionality
– FGMs differ from traditional composites in that their material
properties vary continuously, where the composite changes at
each laminate interface.
– FGMs accomplish this by gradually changing the volume fraction
of the materials which make up the FGM.
• Modal Analysis
– 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.
Problem Description
• Cases
– (A) Isotropic steel plate
– (B) A linear FGM consisting of steel and aluminum
– (C) A power law (n=2) FGM of steel and aluminum
– (D) A power law (n=3) FGM of steel and aluminum
– (E) A power law (n=3) FGM of steel and alumina
– (F) A power law FGM of aluminum and zirconium,
relation given by the Vel 2004 paper
Methodology
• FEA
• Modal analysis performed by COMSOL
eigenfrequency platform.
Methodology (cont.)
• Mori-Tanaka estimation of material properties for FGMs
– Gives accurate depiction of material properties at certain
point in the thickness, dependent on volume fractions and
material properties of the constituent materials
– Get density (ρ), shear (K) and bulk (μ) moduli
– Use elasticity to get expressions for E and ν
Results
• Cases A compared
against plate theory
• Cases B-E checked by
convergence to Case A
• Case F is compared to
results in Vel 2004
paper.