Dynamic instability in tapered beams under wind excitation

Dynamic modeling of beams under aerodynamic loading is extremely important in many engineering applications. So the objective of this paper is to present a new approach to model and simulate the time domain response of tapered cantilever beams with airfoil cross section to wind excitation. The extended Hamilton’s principles along with the Euler-Bernoulli assumptions are utilized to derive the Partial Differential Equation (PDE) governing the deflection of the beam. A new finite difference based algorithm is proposed for finding the mode-shapes as well as the natural frequencies of the beam. These mode-shapes are then used in a Galerkin projection procedure to convert the PDE governing the system’s behavior into strongly coupled nonlinear Ordinary Differential Equations (ODEs). The aerodynamic loadings are modeled using the open source code of XFOIL. The blade of an under developed 100KW wind turbine is considered as a case study. The results reveal that even a single mode approximation is accurate enough in predicting the beam’s dynamic exposed to wind excitation. It was also observed that the instability speed of beams with higher modal damping is considerably higher than those with lower modal damping. The knowledge resulting from this effort is expected to enable the analysis, optimization, and synthesis of tapered cantilever beams for improved dynamic performance.