  We study the dynamical behavior of a single degree of freedom mechanical
system with a particle damper. The particle (granular) damping was optimized
for the primary system operating condition by using an appropriate gap size for
a prismatic enclosure. The particles absorb the kinetic energy of the vibrating
structure and convert it into heat through the inelastic collisions and
friction. This results in a highly nonlinear mechanical system. Considering
linear signal analysis, state space reconstruction, Poincar\'e sections and the
determination of maximal Lyapunov exponents, the motion of the granular system
inside the enclosure is characterized for a wide frequency range. With the
excitation frequency as control parameter, either regular and chaotic motion of
the granular bed are found and their influence on the damping is analyzed.
