The effect of axial inertia on the bending eigenfrequencies of a timoshenko two‐bar frame

The equations of free lateral vibrations of a uniform Timoshenko two‐bar frame including the effects of axial motion and joint mass with its rotational inertia are presented. The influence on the flexural eigenfrequencies of the axial motion alone or in combination with other parameters is fully assessed and thoroughly discussed. These parameters are: the translational and rotational inertia of the joint mass, the transverse shear deformation and rotatory inertia, the length, stiffness and slenderness ratios of the two bars of the frame. The variety of numerical results presented herein leads to the important finding that for framed structures the effect of axial inertia on the flexural eigenfrequencies alone or in combination with the foregoing parameters may be considerable. In particular, if the joint mass should be accounted for, the foregoing effect cannot be ignored, since it leads, in general, to considerable errors even for frames with relatively slender bars.