Issue 51

D. Vasconcelos et alii, Frattura ed Integrità Strutturale, 51 (2020) 24-44; DOI: 10.3221/IGF-ESIS.51.03 40 Modal Analysis On one hand, due to the reinforcement of the platform, its rigidity increased. On the other, the mass of the global structure is composed of the steel of the structure and of the water present inside the ballasts. The rise in the steel mass is compensated by a decrement in the mass of water, thus the structure’s mass remains constant. Considering Eqn. 1, which is the formula used for the determination of the natural frequency of a simplified mass-spring system, as the stiffness increases, with the mass remaining constant, the natural frequencies will also increase. n k w m  (1) Fig. 23 shows the deformation shapes and Tab. 6 displays the values of the natural frequencies of interest for the final platform. Figure 23 : Deformation Shapes from the Modal Analysis; a) Mode 1 – Side to Side; b) Mode 1 - Fore-Aft; c) Mode 2 – Torsion; d) Mode 2 - Fore-Aft; e) Mode 2 - Side-to-Side. Table 6 : Mode description and respective frequency. Mode Description Frequency [Hz] Mode 1 – Side-to-Side 0.6896 Mode 1 – Fore-Aft 0.70212 Mode 2 - Torsion 1.8263 Mode 2 – Side-to-Side 2.1473 Mode 2 – Fore-Aft 2.5376 a) b) d) c) e)