Table of Contents

Tower Modes

The standard axisymmetric tower model in Bladed has one proximal node at the base and one distal node at the top. This implies that the mode shape functions are represented by a combination of attachment modes with fixed-free boundary conditions and normal modes with fixed-fixed boundary conditions. These mode shapes represent the deflection in the fore-aft and side-side directions as well as the torsional deflection and axial elongation. The tower modes are defined in terms of their modal frequency, modal damping and mode shape.

A multi-member tower uses the same approach, but in this case an arbitrary structure consisting of any number of straight interconnected members is permitted. Since the tower is not assumed to be axisymmetric, the modes are generally three-dimensional and contain all six degrees of freedom at each node, and there may be a foundation at more than one node (proximal nodes).

Mass and inertia of the nacelle and rotor: For the calculation of the tower support structure modes, the nacelle and rotor are modelled as lumped mass and inertia located at the nacelle centre of gravity and rotor hub, respectively. As the normal modes do not couple to other components it appears that only the frequency of the attachment modes are affected. This means that the mass and inertia of the nacelle and rotor only affect the resulting frequency of the attachment modes.

Mode Naming

In the context of tower structures, mode names are determined based on the largest deflection in the mode shape vector and the corresponding degree of freedom. For towers, there are four different mode names:

  • Side-Side: This mode exhibits the largest deflection in the y-direction.
  • Fore-Aft: In this mode, the largest deflection occurs in the x-direction.
  • Torsional: The largest deflection is around the z-direction (torsion).
  • Axial: This mode corresponds to the largest deflection in the z-direction.

Additionally, whether a mode is an attachment mode or a normal mode is appended to its name. Attachment modes, despite being point loads (both forces and moments), also fall into these four categories. For example, a moment around the x-axis would produce a deflection in the y-direction, resulting in a side-side mode.

Note on the Difference between Normal and Attachment modes for Towers

For the support structure, the interpretation of the definition of normal modes can sometimes cause confusion.

The conventional free vibration modes of a support structure include the modes where the top of the tower is free to move with no external forces on it. In Bladed, normal modes only include the modes from the eigen-analysis using the fixed-fixed boundary condition as shown here. However, Bladed also includes the attachment modes which are more realistic, as in reality the tower top will move due to the application of external forcing from the structure above it.

This means that if the free vibration modes for the tower structure are calculated with only the tower base constrained, they will not match the mode frequencies calculated by Bladed.

Bladed also calculates coupled vibration modes in the Campbell diagram, shows how the normal and attachment modes combine into coupled vibration modes at a specific operating point. Typically, these coupled modes correspond well to normal modes calculated in other software, with the tower base constrained and the tower top free to move.

Note on Comparing Coupled and Uncoupled Modes for Floating Turbines

For a floating turbine with soft moorings, the deflection shape of the tower when a load is applied to the top in the Campbell diagram calculation doesn’t correspond to the first attachment mode, as the structure is fixed at the modal reference node during the modal analysis. So, the cantilever attachment mode shapes calculated in modal analysis are not seen individually in the Campbell diagram deflections. When a load is applied to the tower top of a floating turbine, the deflection in the tower will take a form that is a combination of various normal and attachment modes, so the first coupled tower mode will be a combination of various uncoupled modes.