Unusual characteristics of free bending waves in thick plates with fluid loading

Abstract

Exact, steady‐state solutions, representing straight‐crested free bending waves, were calculated for the infinite Timoshenko‐Mindlin plate with fluid loading. In general there are three different types waves, two of which are roughly similar to plate waves in vacuum, and a third wave which is unique to fluid‐loaded plates. The unusual behavior of this third free bending wave is the subject of this paper. Calculated solutions are presented as loci of complex free bending wave numbers for steel plates and plates of a softer material for different conditions of fluid loading. The principal finding of this paper is that the loci of free bending wave number, and the character of the waves, change drastically with fluid density. Behavior under one fluid loading condition thus cannot be easily extrapolated to predict behavior in a different fluid. As a result of this work, it is concluded that nearfield solutions to plate radiation problems are more complicated than previously thought. One result of particular interest is that free bending waves in steel plates with water on one side are qualitatively different from those occurring with water on both sides. The results therefore have a very practical value.