Free flexural vibration of symmetric beams with inertia induced cross section deformations

Beams with large thin-walled cross sections are not generally following the classical beam theories such as Euler-Bernoulli and Timoshenko theories. In free vibration, the cross section is deformed by the inertia induced body loads. These deformations may have significant effect on the beam modal frequencies, especially in applications involving non-structural masses. This paper presents a method to include the effect into vibration modal results obtained by the classical beam theories. Generalized mass and stiffness of the classical results are modified according to kinetic-, and strain energies of the cross section deformation. The method is validated in typical engineering case studies against fine mesh Finite Element Method and excellent agreement is found.