Simple models for natural frequencies and mode shapes of towers supporting utilities

Effect of internal stiffening rings and wall thickness on the structural response of steel wind turbine towers

“…Lemak and Studnicka [15] investigated the effect of the spacing and stiffness of ring stiffeners on the behaviour of a cylindrical steel shell subjected to wind loading. Murtagh et al [16] demonstrated simple approximate methods of obtaining natural frequencies, and mode shapes of towers supporting utilities. The fundamental natural frequencies and mode shapes were extracted by analytical formulation and subsequently compared to the FEA model, and the values were observed to be in close agreement.…”

A parametric study of a tower controlled by a pendulum tuned mass damper: beam modelling

“…1. The theoretical BEAM+PTMD approach is also considered by some authors [9,10] assuming the dynamic contribution of wind rotor as compression-tension axial forces due to rotor angular velocity and gravitational force. The gravitational force causes parametric excitation on the blade, i.e., Mathieu's equation [11].…”

An investigation into the effect of scour on the natural frequency of an offshore wind turbine

“…The nacelle was modelled as a lumped mass at the top node of the tower (M Top ) with a rotational inertia (J) as specified in Table 1 and includes the contribution from the mass of the rotor and the blades. The discretized modelling approach can give a very good approximation of the natural frequencies of the system and removes the need for more computationally intensive finite element analysis of the continuous system (Murtagh et al, 2004). The gyroscopic effect of blade rotation on the frequency of the turbine was not modelled.…”