Flexural vibrations of a rod of variable stiffness and distributed mass

A general approach to constructing mathematical models of the transverse vibrations of structures for different dynamic forces is considered. The variable flexural stiffness and the distributed mass are taken into account for the case when their ratio is expressed by a quadratic dependence on the dimensionless radius of inertia of the cross section. The free flexural vibrations and dynamic loads in an elastic rod, modelled by the structure of a lattice tower, are considered as an example. The effect of the model parameters on the value of the first natural frequency is investigated taking into account the presence of an inertial load. Expressions are obtained for the dynamic coefficients when the load is suddenly applied.