Numerical model of compliant tower oscillations

U svrhu provedbe dinamičke analize rešetkastih offshore konstrukcija temeljenih na morskom dnu (eng. compliant tower), razvijen je numerički algoritam za proračun polja pomaka konstrukcije uslijed hidrodinamičkog djelovanja mora. Stohastička narav rasprostiranja valova u moru je uvedena u analizu putem funkcije gustoće snage spektra valova. Opterećenje konstrukcije morskim valovima se potom definira koristeći Morisonov model djelovanja sile. Kinematički parametri valova su definirani linearnom teorijom. Utjecaj vjetra na raspodjelu strujanja mora u vertikalnom smjeru je uzet u obzir kroz kontekst Ekmanove spirale. Rešetkasta konstrukcija je modelirana prostornim Euler-Bernoulijevim konačnim elementima. Inicijalizacija dinamičkog proračuna započinje utvrđivanjem polja pomaka nastalog uslijed statičkog djelovanja uzgona, korisnog i stalnog tereta. Integracija jednadžbi gibanja se provodi Newmarkovom β metodom. U svrhu izrade numeričkih primjera, prikazani algoritam je implementiran u programsko okruženje MathCAD 15. Numerički primjeri uključuju analizu slobodnih i prisilnih oscilacija konstrukcije te FFT analizu zapisa pomaka težišta operativne površine konstrukcije.For the purpose of conducting a dynamic analysis of compliant towers, a numerical algorithm was developed for calculating the structure of the movement field caused by hydrodynamic action of the sea. The stochastic nature of wave spreading in the sea is introduced into the analysis through the function of power spectral density of waves. The structure’s wave load is then defined by applying the Morison model of force action. Kinematic parameters of waves are defined by the linear theory. The wind impact on the distribution of marine circulation in the vertical direction is taken into account in the context of the Ekman spiral. The compliant tower is modelled with spatial Euler–Bernoulli final elements. The initiation of the dynamic calculation starts with the determining the movement field resulting from static activity of buoyant force, dead and permanent loads. The integration of the equations of motion is performed by applying the Newmark-β method. To develop numeric parameters, the presented algorithm is implemented in the MathCAD 15 programming environment. The numerical parameters include the analysis of free and forced oscillations of the structure and the FFT analysis of the records of the centre of gravity shift of the structure’s operating surface