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This paper presents an extension of the recently published quadrilateral finite element to analyze the free vibration of plates vibrating in air or in interaction with the fluid. The previously proposed four-node element is based on the strain approach and the Reissner-Mindlin plate theory. The developed finite element, which contains the three essential external degrees of freedom at each of the four corner nodes, is based on assumed functions of the strain field that satisfy the compatibility equations. A comparison is presented with experimental and numerical data available in the literature to demonstrate the performance of the current element. The dynamic characteristics (natural frequencies and associated modes) of a rectangular plate simply supported or clamped totally submerged in water, a cantilever square plate, and a vertical plate partially submerged are numerically computed by the proposed element. The frequencies obtained by this element are of excellent accuracy compared to numerical, analytical, or experimental solutions from the literature.
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