  Existing smart composite piezoelectric beam models in the literature mostly
ignore the electro-magnetic interactions and adopt the linear elasticity
theory. However, these interactions substantially change the controllability
and stabilizability at the high frequencies, and linear models fail to
represent and predict the governing dynamics since mechanical nonlinearities
are pronounced in certain applications such as energy harvesting. In this
paper, first, a consistent variational approach is used by considering
nonlinear elasticity theory to derive equations of motion for a single-layer
piezoelectric beam with and without the electromagnetic interactions (fully
dynamic and electrostatic). This modeling strategy is extended for the
three-layer piezoelectric smart composites by adopting the two widely-accepted
sandwich beam theories. For both single-layer and three-layer models, the
resulting infinite dimensional equations of motion can be formulated in the
state-space form. It is observed that the fully dynamic nonlinear models are
unbounded boundary control systems (same in linear theory) ${\bf \dot
y}(t)=(\mathcal A +\mathcal N) {\bf y} (t) + \mathcal B u(t)$, the
electrostatic nonlinear models are unbounded bilinear control systems ${\bf
\dot y}(t)=(\mathcal A +\mathcal N){\bf y} (t) + (\mathcal B_1+ \mathcal B_2
{\bf y}) u(t)$ in sharp contrast to the linear theory. Finally, we propose
$\mathcal B^*-$type feedback controllers to stabilize the single piezoelectric
beam models. The filtered semi-discrete Finite Difference approximations is
adopted to illustrate the findings.
