  This study presents numerical simulations of the resonance of a finite-length
granular chain of dissipative grains driven by a harmonically vibrated tube.
Multiple gradual resonant modes, namely, non-resonance mode, partial-resonance
mode, and complete-resonance mode, are identified. With a fixed vibration
frequency, increased vibration acceleration leads to a one-by-one increase in
the number of grains participating in resonance, which is equal to the number
of grain-wall collisions in a vibration period. Compared with the
characteristic time of the grain-grain and the grain-wall collisions, the time
of free flight plays a dominant role in grain motion. This condition results in
the occurrence of large opening gaps between the grains and independent
grain-grain and gain-wall collisions. A general master equation that describes
the dependence of the system energy on the length of the granular chain and the
number of grain-wall collisions is established, and it is in good agreement
with the simulation results. We observe a gradual step-jump increase in system
energy when the vibration acceleration is continuously increased, which is
dedicated to an individual energy injection. Moreover, two typical phase
diagrams are discussed in the spaces of $\phi-\it{\Gamma}$ and $N-\it\Gamma$.
