Brownian dynamics simulation has been employed to study the dynamic behavior of particles in three-dimensional ordered porous media subject to a sinusoidal force field. The media comprises interconnected spherical cavities arranged in a simple cubic lattice. The thermal noise assists the particles to undergo cavity hopping, leading to a displacement behavior analogous to stochastic resonance, when the imposed field is strong enough but not aligned with the aperture lines, and the oscillation frequency is not too high. The periodic mean trajectory depends on the strength, frequency, and orientation of the imposed field. At sufficiently large field strength, the periodic particle displacement can become nonsinusoidal due to the strong hindrance and pinning effect of the cavity wall.