Free vibrations of beam with variable cross section, in the presence of elastic base constraints and eccentric mass with rotary inertia ad the tip

Abstract

Quite recently, dynamic behaviour of wind towers has been investigated by many authors. For example, a detailed study of an offshore tower with constant cross section has been offered in [1], and its free vibration frequencies have been detected, for a partially immersed structure with flexible base constraints and eccentric mass with rotary inertia at the tip. On the same footsteps, in this paper the free frequencies of an onshore tower have been calculated, the cross section is supposed to vary according to an exponential law, the base constraints are supposed to be both axially and rotationally flexible, and at the tip an eccentric mass with rotary inertia is taken into account. The solution method can be considered “exact”, as long as the differential equation of motion is deduced and solved, and various numerical examples are discussed.