Theory of free-vibration acoustic resonance for a two-dimensional grid-framework structure has been developed within the framework of micropolar elasticity and calculus of variations. Numerical analysis based on the Ritz method revealed the excitation of micro-rotational standing wave in a resonant state. It is also revealed that resonance frequency of the structure show a weak but finite size dependence, which is due to the breakdown of scale-invariant symmetry of the action integral.