Analytic Formulas for the Cantilever Structures' Natural Frequencies with Taking into Account the Dead Weight

The article has deal with investigations of free bending vibrations of uniform cantilever structures with taking into account the dead weight. The investigation uses the exact solution of the partial differential vibration equation with variable coefficients. The formulas for the natural frequencies of a rod structures are obtained in analytical form. An analytic relationship between the frequencies with and without taking into account the dead weight of the structures is established. The nature of the dependence of frequencies on the value of the longitudinal load is revealed. An example is considered, in which the values of the first three nature frequencies obtained by the author's method are given.