Investigation of boundary condition effects on the stability of FGP beams in thermal environment

In this paper, stability and instability of Functionally Graded Piezoelectric (FGP) beams
is investigated based on the Timoshenko beam theory. The material properties of the beam
are considered to change gradually through thickness of the beam by a simple power law. By
using the principle of minimum total potential energy, governing equations of the beam are
derived. Stability behavior of the beam is predicted by solving the governing equations of the
FGP beam. The results show that the homogeneity of boundary conditions plays a critical
role in the stability of the FGP beam. While non-homogeneous boundary conditions lead
to stable behavior of the FGP beam; homogeneous boundary conditions cause instability in
the beam. By solving the eigenvalue equation of the FGP beam, the buckling load of the
beam is obtained for the beams that have unstable behavior. Finally, the effects of various
parameters on the buckling load of the unstable beam, such as power law index, temperature,
applied voltage and aspect ratio are investigated, and the results are compared with the
Euler-Bernoulli beam theory.