Vibration Modal Analysis of a Thin Folded Elastic Structure using a Levy-type Solution

In this technical note, an approximated analytical Levy-type solution for the system of differential equations that governs the vibration of a thin folded structure is presented. The folded structure is composed of thin plates and thin curved circular panels attached by their straight sides. Hinged and arbitrary boundary conditions at curved edges and straight edges, respectively, were used. In order to test the proposed analytical approach, numerical experiments using commercial finite element method (FEM) software were developed for a particular folded structure commonly found in Air Motion Transformer loudspeakers. It is found that the first two natural frequencies of this structure obtained with the analytical approach differed by less than 2% from those obtained using FEM. In addition, the analytical mode shape is almost identical to that obtained by FEM.