Free Vibrations of the Slender Non-Prismatic Column Under the Specific Load Regarding the Joint Flexibility

The issue of the free vibrations of the non-prismatic rod subjected to the selected case of the specific load has been studied. In the carried out simulations, a flexibility of a constructional joints modelled by the translational and rotational springs at the point of mounting or on the free end of analysed system was taken into account. The shape of rod was approximated by linear function and by polynomial of degree 2, under the condition of constant volume of the column. After prior definition of total mechanical energy, a differential equations of motion as well as a boundary conditions were formulated on the basis of the Hamilton’s principle. The results of the numerical calculations refer to an influence of variable cross-section of the rod, joint flexibility and a geometry of a loading structure on the value of the frequency of free vibrations due to the external load (a characteristic curves) and on the critical load.