Free vibrations of a longitudinally loaded column with rotary inertia elements

The influence of the rotary inertia and axial load on the natural frequency of non-linear two-member column is studied. The perturbation method is used for solving the problem. Numerical results concerning both the vibration frequency and modes are compared with those from experiment. For equal ratios of the mass per unit length to flexural rigidity for both members the rotary inertia does not affect the natural frequency. The critical load caused the divergence instability of the system is also found.