Publications on vibration of the beams are most relevant to FGM beams
with material properties varying in one spatial direction only, such as the
thickness or longitudinal direction. There are practical circumstances,
in which the unidirectional FGMs may not be so appropriate to resist
multi-directional variations of thermal and mechanical loadings. Optimizing durability and structural weight by changing the volume fraction of
FGM’s component materials in many different spatial directions is a matter of practical significance, being scientifically recognized by the world’s
scientists, especially Japanese researchers in recent years. Thus, structural analysis with effective material properties varying in many different
directions in general and the vibration of FGM beams with effective material properties varying in both the thickness and longitudinal directions of
beams (2D-FGM beams) in particular, has scientific significance, derived
from the actual needs. It should be noted that when the material properties
of the 2D-FGM beam vary in longitudinal direction, the coefficients in the
differential equation of beam motion are functions of spatial coordinates
along the beam axis. Therefore analytical methods are getting difficult to
analyze vibration of the 2D-FGM beam. Finite element method (FEM),
with many strengths in structural analysis, is the first choice to replace
traditional analytical methods in studying this problem. Developing the
finite element models, that means setting up the stiffness and mass matrices, used in the analysis of vibrations of the 2D-FGM beam is a matter of scientific significance, contributing to promoting the application of
FGM materials into practice. From the above analysis, author has selected
the topic: Finite element models in vibration analysis of two-dimensional
functionally graded beams as the research topic for this thesis.