Natural frequencies of a plate, or a membrane, with an air layer.

Abstract

Natural frequencies of a plate, or a membrane, with an air layer which is open-ended along the edge is analyzed, and the effect of the air layer on the plate, or on the mem -brane, is revealed.These results of the analysis are confirmed by the related experi -ment.The air layer acts as a aerodynamic spring when a propagation velocity of the plate vibration is faster than that of the sound pressure in the horizontal direction in the air layer.In the reverse case, the air layer acts as a negative stiffness. Hence, under the former condition, the natural frequencies increase inversely to the decreasing depth of the air layer.Under the latter condition, the natural frequencies decrease. It is, therefore, concluded that the effect of the air layer on the plate vibration, or the mem -brane vibration, reverses at the coincidence frequency.