The effect of longitudinal motion and other parameters on the bending eigenfrequencies of a simple frame

Abstract

Using the variational Hamilton's principle, the equations for free motion of a simple two-bar frame carrying a concentrated mass with rotational inertia at its joint are established. The effect on the bending eigenfrequencies of the longitudinal motion, alone or in combination with other parameters, is thoroughly discussed. These parameters are the translational and rotational inertia of the joint mass, the length and slenderness ratios of the two bars, and the stiffness ratio. The variety of the numerical results presented herein provides a better insight into the actual flexural motion of frames when the effect of longitudinal motion is taken into account.