12. Linear Modal Analysis of a Horizontal-Axis Wind Turbine Blade

In this work, mode shapes and modal frequencies of a horizontal axis wind turbine blade are found. The blade is modeled as a pre-twisted beam under bend-bend-twist deformations, and the strain, gravitational potential and kinetic energy expressions are found. These expressions are then simplified for linear theory, and further by using the assumed modes method in which assumed modes are chosen independently for flapwise, edgewise, and twist deflections from a cantilevered uniform beam. Lagrange’s equations of motion are applied to the assumed modal coordinates, and coupled linear equations are thus found. Modal analysis is applied to the assumed modal equations to find the resonance frequencies, and the resulting mode shapes are recombined to express the mode shapes in the bend-bend-twist coordinates. The approach was applied to a uniform twisted rectangular beam, and the first three mode shapes are found to be combinations of the in-plane and out-of-plane bending. The results of the modal analysis are compared with results from a finite element analysis, and the mode shapes and frequencies are consistent. The method is also applied to NREL’s 5 MW wind turbine blade to find its bend-bend-twist mode shapes and natural frequencies.