Closed form solution for the first natural frequency of offshore wind turbine jackets supported on multiple foundations incorporating soil-structure interaction

Offshore Wind Turbines (OWTs) are dynamically sensitive structures and as a result estimating the natural frequency of the whole system taking into effect the flexibility of the foundation is one of the major design considerations. The natural frequency is necessary to predict the long-term performance as well as the fatigue life. Currently, jackets supported on multiple foundations (such as piles or suction caissons) are being considered to support WTG (Wind Turbine Generators) for deeper water developments. This paper presents a practical method to compute the natural frequency of a jacket supporting WTG by incorporating Soil-Structure-Interaction (SSI) based on closed form solutions. The formulation presented can be easily programmed in a spreadsheet type program and can serve as a convenient way to obtain the natural frequency with the least amount of input. The basis of this method is the Euler-Bernoulli beam theory where foundations are idealized with a set of linear springs. In this method, a 3-Dimensional jacket is first converted into a 2-Dimensional problem along the orthogonal planes of vibration which are essentially the principal axes of the foundation geometry. Subsequently, the jacket is converted into an equivalent beam representing it's stiffness and a formulation is presented to find an equivalent beam for the entire tower-jacket system. Using energy methods, an equivalent mass of the RNA (Rotor Nacelle Assembly)-tower-jacket system is also calculated and the fixed base frequency of the jacket is estimated. To consider the flexibility effects of the foundation, a formulation for an equivalent rotational spring of the foundation is developed. A method to incorporate the mass of the transition piece is also presented. Finally, a step-by-step application of the methodology is presented by taking example problems from literature which also serves the purpose of validation and verification.