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Journal of Applied Nonlinear Dynamics 13(3) (2024) 475--489 | DOI:10.5890/JAND.2024.09.005

N. Mohammadi$^{1}$, M. Mohammadi$^{2}$, A. A. Jafari$^{2}$

$^{1}$ Department of Mechanical Engineering, Islamic Azad University, Parand Branch, Parand, Tehran, Iran

$^{2}$ Department of Mechanical Engineering, Islamic Azad University, West Tehran Branch, Tehran, Iran

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Abstract

The current study investigates vortex-induced vibration analysis of bladeless wind turbines made of functionally graded materials (FGMs). The bladeless wind turbine is modeled as a clamped-free cantilever beam with a circular cross-section. The mechanical properties of the turbine are assumed to be graded along the length of the beam according to the power-law distribution. The distributed aerodynamic force on the turbine is modeled based on an oscillator semi-empirical model. In order to analyze free vibrations, the functionally graded (FG) turbine's natural frequencies are calculated by the Ritz method and compared to the results obtained by Abaqus FEA. Good agreement is observed between analytical results and numerical values. Using Hamilton's principle, the governing dynamics equation of the FG turbine is derived based on the Euler-Bernoulli beam theory. The partial differential equations of motion are transformed into the ordinary differential equations employing the Galerkin method. A set of coupled differential equations are then solved by the Runge-Kutta method. Eventually, the effects of some parameters of the system, such as the turbine's length, turbine's cross-section, power-law gradient index, and wind velocity, on the system's dynamic response are discussed. The results show that the gradient index and geometric ratios significantly affect the wind turbine's vibration.

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