Effects of Boundary Conditions on the Structural Dynamics of Wind Turbine Blades—Part 1: Flapwise Modes

Abstract

Mode shapes and resonant frequencies of an individual wind turbine blade can be readily determined in either a laboratory or a blade test facility using experimental modal analysis. However, performing a modal test on a utility-scale wind turbine with several blades attached to a tower can be a challenge due to the number of sensors required, the size of these structures, the time required for testing, and cost. Therefore, understanding the influence of the coupled three-bladed turbine/tower system and identifying a correlation between the dynamic behavior of an assembled wind turbine to an individual blade or three-bladed turbine attached to a hub while disconnected from the tower is desirable. In this paper, which is the first part of a two-part paper, the influence of boundary conditions on flapwise mode shapes and resonant frequencies of wind turbine blades are numerically studied using a finite element beam analysis (a similar study was performed on edgewise modes of the turbine and is presented in the second part of this paper). In the current paper, translational and rotational springs are mounted to the hub of a three-bladed turbine and the sensitivity of dynamic characteristics (natural frequencies and mode shapes) to variations in the spring constants are investigated. Then, a model is developed of the three-bladed turbine installed on a tower and the dynamic characteristics of the assembly are compared to the three-bladed turbine with a free-free or fixed boundary condition at the hub. Furthermore, the mode contribution matrix of the assembled wind turbine is used to identify the necessary set of modal vectors of the tower and three-bladed turbine to accurately obtain the dynamic behavior of the final assembly. Many flapwise mode shapes of the assembled three-bladed wind turbine can be estimated by applying a fixed condition for a single blade (or a three-bladed turbine) instead of using a free-free boundary condition.