Approximate frequency analysis of isotropic shear beams using initial value method

Abstract

This study investigates the vibration of isotropic shear beams (ISBs) using the unified shear deformation theory for various shear stress distribution functions. The governing differential equations and boundary conditions are obtained using the principle of virtual work. Using the initial values method, the first five frequencies for various end conditions were calculated with four digits. Frequencies for different shear stress distributions can be easily determined using the approximate transfer matrices provided in this study. To verify the accuracy of the obtained results, we compared the frequencies with the findings in the existing literature.