  The fully dynamic PDE model, describing the longitudinal oscillations on
magnetizable piezoelectric beams, with two boundary feedback controllers is
known to have exponentially stable solutions. Finding the maximal decay rate
and optimal feedback sensor amplifiers are crucial for the fast suppression of
oscillations on these beams. In this paper, a Lyapunov-based approach is
adopted to obtain a maximal decay rate with (i) two separate sensor feedback
amplifiers for exact exponential stabilization and (ii) a unique feedback
amplifier for the simultaneous exponential stabilization. For case (i),
feedback amplifiers come out of an optimization process where the safe range of
amplifiers are explicitly determined in terms of material constants to achieve
the fastest exponential decay rate possible. It is also shown that for certain
material parameter combinations, feedback amplifiers may not exist. The case
(ii) is a special case of case (i), and a safe range of amplifiers can also be
established. However, for a wider class of realistic material parameters the
feedback amplifiers can not be established to achieve the desired maximal decay
rate. To show the strength of our results, several numerical experiments are
provided.
