  We investigate how the kinetic energy acquired by a dense granular system
driven by an external vibration depends on the input energy. Our focus is on
the dependence of the granular behavior on two main parameters: frequency and
vibration amplitude. We find that there exists an optimal forcing frequency, at
which the system reaches the maximal kinetic energy: if the input energy is
increased beyond such a threshold, the system dissipates more and more energy
and recovers a colder and more viscous state. Quite surprisingly, the
nonmonotonic behavior is found for vibration amplitudes which are sufficiently
small to keep the system always in contact with the driving oscillating plate.
Studying dissipative properties of the system, we unveil a striking difference
between this nonmonotonic behavior and a standard resonance mechanism. This
feature is also observed at the microscopic scale of the single-grain dynamics
and can be interpreted as an instance of negative specific heat. An
analytically solvable model based on a generalized forced-damped oscillator
well reproduces the observed phenomenology, illustrating the role of the
competing effects of forcing and dissipation.
