Some aspects of analysis of transverse free vibrations of uniform beams loaded with axial force

Influence of constant compressive axial force on free transverse vibrations of uniform beams is considered. Three technical beam theories are applied and appropriate analytical solutions are obtained. Hamilton's variation principle is utilized for derivation of well -known differential equations of motion of Timoshenko beam, while Bernoulli-Euler and Rayleigh theories are considered as special cases. Furthermore, simple two-dimensional plane stress finite element with drilling degree of freedom is employed for numerical analysis. Appropriate code is developed and verified via comparison with commercial finite element software Abaqus, as well as with analytical results. Parametric analysis of influence of the axial force on the modal characteristics of considered beams is performed and discussed in detail.