A Note on the Frequency and Normal Mode Equations of Uniform Timoshenko Beams

균일단면(均一斷面) Timoshenko보의 진동수방정식(振動數方程式) 및 기준함수(基準函數)에 관하여

The practical utilization of the frequency and normal mode equations of uniform Timoshenko beams such as those presented by Huang is not simple due to their highly trancendental nature. In this note largely simplified equations obtained for the fixed-fixed and the free-free boundary conditions, the modes of which are separable into symmetric modes and antisymmetric ones, are given. Numerical results obtains for six common-type boundary conditions show that the quantitative measure of the effect of rotary inertia and shear deformation on the natural frequency is greatly dependent upon the boundary conditions as well as the order number.