Finite element modal analysis of free-free beams and plates: A study of transition from beam-like to plate-like behaviour

The finite element analysis (FEA) of the free vibrations of free-free aluminium alloy beams and plates of 5 mm thickness and of length-to-breadth ratios (aspect ratios) ranging from 20 for a beam down to 0.25 for a plate is presented. For each ratio, a total of 20 natural frequencies and mode shapes were predicted. The objective of the paper is to demonstrate that a transition zone for beam-like to plate-like behaviour can be approximately defined for the transverse vibrations of a beam-plate structure, which is a structure that is either a beam or plate. From the FEA results, the variations of the frequency parameters of the free-free vibrations of beam-plates with respect to the aspect ratios were obtained. It is shown that at small aspect ratios, the FEA results follow a zigzag trend which is a manifestation of platelike behaviour. But at high aspect ratios, the FEA results follow a smooth trend which is a manifestation of beam-like behaviour. It is also shown that the maximum difference between the frequency parameters of the plate-like and beam-like behaviour is 6 %. Furthermore, it is shown that the transition from plate-like to beam-like behaviour can be represented by a polynomial equation and curve.