Branch dependent shear coefficients and their influence on the free vibration of Mindlin plates

For the plate that is simply-supported on all of its edges, each of the three frequency branches contributes to the motion of the plate independently of the other two branches. Hence, only one of the branches is active for a given vibration mode, which allows one to solve for unique natural frequencies for each of the branches and to quantify their accuracy as well as to study the motion of each branch separately. This is not, however, the case for plates with other support conditions. In these cases, the vibrational motion corresponding to each of the branches of the frequency spectrum contributes to a given vibration mode. This, in turn, alters the implementation of Mindlin theory for these plates. Results for natural frequency predictions are compared to those of other studies in the literature as well as to those of the classical case when a single shear correction coefficient is employed. It is shown that natural frequency predictions are improved for the plate with all of its edges simply-supported, while the accuracy of the mode shape is improved for other boundary conditions.