Free Vibration Analysis of Flexural-Shear Plates Under the Action of Axial Forces

Abstract

The governing differential equations for vibration of flexural-shear plates considering the effects of flexural, shear deformation and axial forces are established. The general solutions of a one-step flexural-shear plate are derived and used to obtain the eigenvalue equations of a multi-step flexural-shear plate with various boundary conditions. The new exact approach which combines the transfer matrix method and closed form solutions of a uniform flexural-shear plate with various boundary conditions is presented. A numerical example demonstrates that the calculated natural frequencies and mode shapes of a tall building that is treated as a two-step flexural-shear plate are in good agreement with the experimentally measured data. It is also shown that the effect of shear deformation on the fundamental natural frequency can be ignored, but its effect on the higher natural frequencies should be considered. On the contrary, the effect of axial force (N) on the higher natural frequencies is not significant, and its effect on the fundamental natural frequency is dependent on the ratio of N to the critical buckling force N_c.