The oscillating cylinder of a low-frequency inverted torsion pendulum is immersed into layers of noncohesive granular materials, including fine sand and glass beads. The relative energy dissipation and relative modulus of the granular system versus the amplitude and immersed depth of the oscillating cylinder are measured. A rheological model based on a mesoscopic picture is presented. The experimental results and rheological model indicate that small slides in the inhomogeneous force chains are responsible for the energy dissipation of the system, and the friction of the grains plays two different roles in the mechanical response of sheared granular material: damping the energy and enhancing the elasticity.