Bending Waves, Plate and Beam theory?

Hi,



I am doing research on sound radiation of a plate due to bending waves. I have come across the Kirchhoff Plate theory, Euler beam theory and also the equations for the phase velocity of longitudinal, transverse shear and bending waves. What i am confused about is how these theories and equations are related to each other? I read journals that only state the three waves previously mentioned and provide the bending wave equation with them. However, when i research the plate and beam theory, there is also mention of the bending wave equations. Am i wrong in thinking that the plate and beam theory are used to derive the equation of a bending wave? Or is it that the bending wave equation was already known, and the plate/beam theory are used to determine how a bending wave reacts in solids? I hope this makes sense



Thanks