Natural frequency of offshore wind turbines on rigid and flexible monopiles in cohesionless soils with linear stiffness distribution

•Wind turbine structure supported by rigid and flexible monopiles are considered.•Soil-pile interaction is modeled based on beam on elastic foundation concept for cohesionless soil with linearly varying modulus of subgrade reaction along depth.•Rayleigh method is applied to derive natural frequency of the structure with both rigid and flexible monopiles.•Excellent agreement was found between the present method and FE model.•The effect of different foundation parameters are investigated on dynamic characteristics. A simplified method is introduced to obtain the fundamental frequency of offshore wind turbines supported by monopile foundations. Soil-pile interaction is modeled based on Winkler approach and concept of beam on elastic foundation. The soil is considered to have linearly varying modulus of subgrade reaction along depth which is a typical assumption for cohesionless soils. Rayleigh method which is based on conservation of total energy of the system is utilized. Firstly the natural frequency of the system with rigid pile is derived and then an innovative procedure is introduced to take pile flexural stiffness into consideration. Comparison between results of the present method with those of a numerical FE model for a typical 2MW wind turbine structure shows excellent agreement for rigid pile and flexible pile with small value of slenderness ratio. The agreement is also good for flexible pile with higher slenderness ratios. A parametric study is carried out to investigate the effect of important parameters of foundation including pile slenderness ratio, pile aspect ratio and pile mass on the system natural frequency.