Free Vibration of Tapered Timoshenko Beams By Deformation Decomposition

This paper deals with the free vibration of tapered Timoshenko beams. The simultaneous differential equations governing the free vibration of tapered Timoshenko beams are derived by decomposing the deformations of the beam into components as transverse deflection, bending rotation and shear distortion. The governing differential equations are first integrated by the Runge–Kutta method and then solved by the determinant search method, combined with the Regula–Falsi method, to obtain the natural frequencies of the beam along with their corresponding mode shapes. In the numerical examples, the effects of various parameters on the frequencies and mode shapes of the beam are extensively discussed.