Modal Analysis of a Clamped-Free Plate in a Duct

When a rigid wall is replaced by a cavity covered by a flexible plate, the plate can cause broadband sound reflection in a duct. In this paper, analytical formulations in previous studies are extended to the plate with clamped-free boundary conditions. A set of static beam functions, which are a combination of sine series and third-order polynomial, is employed as the trial functions of the plate vibration velocity. Optimization is carried out in order to obtain the widest sound reflection bandwidth. Further studies with regard to the plate under several different classical boundary conditions based on the validated model show that, a clamped-free plate in the duct has the narrowest sound reflection bandwidth. In order to understand the precise mechanism of the spectra change, the behavior of each clamped-free plate mode is also analyzed. It is found that the weak first modal response in a clamped-free plate leads to its performance degradation.