Blades and Towers Modal Analysis Code (BModes): Verification of Blade Modal Analysis Capability

BModes is a finite-element code we developed to provide coupled modes for flexible blades, rotating or non-rotating, and for towers, onshore or offshore (supported either on floating platforms or on monopile foundations). Both the blade and the tower allow a tip attachment, which is modeled as a rigid body with mass, six moments of inertia, and a mass centroid that may be offset from the blade or tower axis. Examples of tip attachments are aerodynamic brakes for blades and nacelle-rotor subassemblies for towers. Allowable supports for the tower include tension wires, floating platforms, and shallow-water monopiles with elastic foundation. Coupled modes (implying coupling of flap, lag, axial, and torsion motions) have several applications. Examples are: modeling of major flexible components for modal-based aeroelastic codes such as FAST [1], validation of turbine models using experimental data, modal-based fatigue analysis, and understanding of aeroelastic-stability behavior of turbines. This paper presents verification of the blade modal analysis capability of BModes. Verification begins with simple uniform beams, rotating and non-rotating, and progresses to realistic blades. BModes-computed modes for all models are compared with analytical modes, if possible to obtain, and with modes generated by RCAS [2]. All results, presented in terms of frequencies and mode shapes, show excellent agreement. I. Introduction BModes is a finite-element code that allows high-fidelity modal analysis of a turbine blade or a tower. Both the blade, rotating or non-rotating, and the tower can have arbitrary distribution of structural properties along their length. Both allow tip attachment, which is assumed to be a rigid body with mass, six moments of inertia, and a mass centroid that may be offset from the blade or the tower axis. Examples of tip attachments are aerodynamic brakes for blades and nacelle-rotor subassemblies for towers. In addition, the blade may have precone and an arbitrary pitch-control setting. For the tower, BModes allows three configurations: a land-based tower, an offshore monopile-supported tower, or an offshore floating-platform-supported tower. The land-based tower may optionally have tension support wires. BModes yields coupled modes for both the blade and the tower. A coupled mode implies presence of flexural, axial, and torsion motions in a natural mode of vibration. For the blade, flexural motion means flap and lag bending, whereas for the tower it means fore-aft and side-to-side bending. Knowledge of coupled modes is crucial to several applications. Examples are: modeling of major flexible components for modal-based aeroelastic codes, validation of turbine models using experimental data, modal-based fatigue analysis, and in-depth interpretation of aeroelasticstability behavior of turbines, both onshore and offshore. Obtaining rotating-blade coupled modes involves solving a complex boundary-value problem, and only a few codes rigorously handle this. BModes is accurate because it uses a finite-element approach in conjunction with analytical linearization and a special finite-element assembly that properly captures Coriolis and centrifugal effects. The finite-element method (FEM) is based on a 15- degree of freedom (dof) element with three internal and two boundary nodes. Because BModes is a finite-element based, it has the capability to handle a complex range of boundary conditions. The structural properties along the blade length are specified in terms of the flap bending, lag bending, torsion, and axial stiffness; mass; section moments of inertia; and chordwise offsets of section shear center, tension center, and center-of-mass along the blade. These properties may be obtained from experimental tests, blade manufacturer, or a properties-extractor code, such as PreComp [3] or BPE [4]. Currently, BModes can handle only metallic or