Abstract: A wind turbine blade is considered as a cantilever beam with variable sections, which can be divided to arbitrary segments. Each satisfies the governing differential equations of biaxial bending coupled with torsional variations. The material properties involved can be anisotropic. Solutions to them are represented as functions of 10 free degrees at both end nodes. Nodal displacements of the same cross-section from two adjacent segments are connected by the continuity conditions, resulting in a transfer function correlating the nodal freedoms at one cross-section with those at any other. Finally, a group of homogeneous equations that contain only ten unknown variables is established by applying the boundary conditions at the fixed and the free tip ends of the blade. A nontrivial solution condition results in the frequency equation to be solved. Compared with finite element and other numerical methods, this transfer function method has several advantages such as fewer variable, easier to implement into a computer program, more quickly to obtain a solution and higher accuracy achievable with the same cost in time and computer sources. The method is then applied to evaluate frequencies of a large blade with optimized laminate structure. The result shows that not only the weight of the blade after optimization can be significantly reduced, but also its stiffness and frequency characteristics can meet the operating requirements.

Key words: composite material, wind turbine blade, natural frequency, transfer function, structural optimization