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

摘要

The effect of the shear correction coefficient on the branches of the frequency spectrum for the free vibrations of plates using Mindlin plate theory is studied. Each of the three branches of the frequency spectrum for the Mindlin plate is identified through comparison with the frequency spectrum of the infinite elastodynamic plate. The use of branch dependent shear correction coefficients is proposed, in order to bring each of the three branches of the Mindlin plate into best agreement with their corresponding elastodynamic branches. The general solution presented is applied to plates with simply-supported, simply-supported/clamped, and simply-supported/free edges and representative results for the frequency spectrum and modal plots for each of the boundary conditions is discussed. It is shown that the use of branch dependent shear correction coefficients improves the frequency predictions for the free vibrations of Mindlin plates when compared to other studies in the literature. The branches of the frequency spectrum contribute differently to the calculation of the natural frequencies of the vibration modes of the plate for the various boundary conditions considered. The insight gained into the interactions of the frequency branches improves upon the physical understanding and interpretation, as well as the analysis of the free vibration of the Mindlin plate, even for the classical case when a single shear correction coefficient is employed.