The contribution of higher order modes in the dynamic response of slender vertical structures with application to wind turbine towers

Understanding the contribution of the vibration modes to the response of a tower-like structure subjected to base excitations is crucial for a safe and optimized design. The modal contributions to the structural response are generally assessed through modal participation factors and effective masses; however, relatively recent studies pointed out the variability of the modal contributions depending on the response effect (e.g., top displacement, base shear force, base bending moment). The formulation proposed here derives the shear force and the bending moment at the base of a tower-like structure by combining the influence function technique with the quasi-static equivalent forces technique. The resulting formulation of the tower response relies on the concept of modal contribution factors, which provides a straightforward indication of the modal contributions associated with a given response effect. The proposed methodology is applied to the case of wind turbine towers erected on temporary foundations at the port quayside without rotor nacelle assembly to assess the forces on the foundations due to the seismic loading on the towers. This technique may be of great relevance for assessing the tower integrity during installation and for the design of the temporary foundations at the quayside of harbors in seismic area, also considering the quick expansion of the offshore wind energy in countries prone to earthquakes.