Océane Daoud is a Graduate Engineer at Empire Engineering. Here, Océane shares her insight into the principles of damping and why it’s critical for offshore wind foundation analysis.
As offshore wind turbines continue to push the boundaries of scale and engineering complexity, understanding the fundamental principles that govern their dynamic behaviour becomes increasingly critical. One concept that often receives insufficient attention in preliminary analyses, yet plays a pivotal role in the long-term performance of these structures, is damping.
The fundamentals of energy dissipation
Damping represents the ability of any object to dissipate energy. The most common approach to modeling damping in engineering applications is through viscous damping, where the damping force is directly proportional to the velocity of the system. This relationship allows us to quantify damping behaviour using two primary metrics: the damping coefficient, which quantifies this amount of damping in a structure and the damping ratio, which describes proximity of the damping to an ideal ‘critically damped’ system.
But why does this matter for offshore wind? As a dynamic system, the response of an OWT depends on the magnitude of the applied forces, proximity of forcing frequencies to the natural and resonant frequencies of the system, and the damping.
Let’s consider a simplified representation of a monopile foundation as a cantilever beam. This analogy, while basic, provides valuable insights into the dynamic behaviour of these massive structures. If this cantilever beam is allowed to oscillate freely after dynamic excitation, it will bend around its neutral axis inducing cyclic loading, and contributing significantly more fatigue damage than if it reached its steady-state without vibration. This relationship has direct implications for fatigue performance, which is often the governing design criterion for offshore wind foundations.
Theoretical models which include damping can help us determine this dynamic response and subsequent loading.
Free vibration response: understanding system behaviour
To fully appreciate damping effects, consider what happens when you apply a transverse load to a cantilever beam and then release it. The system enters a state of free vibration, and its response depends entirely on the amount of damping present.
When the damping ratio is less than one (which is typical for wind turbine foundations), the system oscillates around its steady state before eventually settling. In the rare cases where the damping ratio equals or exceeds one, the system reaches steady state directly without oscillation, settling at varying rates depending on the specific damping characteristics.
Understanding these response patterns is crucial for predicting how offshore wind foundations will behave following transient events such as extreme weather conditions or emergency shutdown scenarios.
The mass-spring-damper model: simplicity with power
Most dynamic systems, including offshore wind foundations, can be adequately represented using a mass-spring-damper system. This model breaks down complex structural behavior into three fundamental components:
- The spring element, which stores potential energy
- The mass component, which stores kinetic energy
- The damper, which dissipates energy
Figure 1. Mass-spring-damper system (image credit MDPI)
For our monopile, the cantilever beam’s structural behaviour can be represented by a single mass, spring and damper. Its dynamic behaviour can therefore be represented by a simple 2nd-order differential equation:
mẍ+cẋ+kx = 0
With m, the system’s mass, c the system’s damping coefficient and k the system’s stiffness coefficient.
This representation proves invaluable for determining steady-state responses, natural frequencies, and most critically for our purposes, resonant frequencies at which the system’s amplitude response peaks. For offshore wind foundations subjected to cyclic loading from wind and waves, understanding these characteristics is also essential for preventing catastrophic resonance conditions.
Figure 2: Displacement response of a driven, damped oscillator. With, the forcing frequency, the resonant frequency, and the damping ratio (image credit Pennsylvania State University)
Forced vibration and the resonance challenge
Most dynamic loading on monopiles, from both the rotor-nacelle assembly and environmental forces, can be considered as forced vibrations. In this case, the inclusion of damping in our analytical models significantly affects how the structure responds to forcing frequencies, particularly near its resonant frequencies.
For a critically damped structure, i.e. with a damping ratio equal to 1, a forcing frequency nearing or equal to the resonant frequencies of the system will have little impact on its response. However, such a damping configuration is impossible in OWTs. Critically damped systems present damping at a sufficiently high level to compensate for mass and stiffness effects on its motion. For a structure as heavy as an OWT foundation, a critically damped configuration would require the inclusion of highly effective passive or active damper systems, far from standard practice. Their damping ratios are therefore always far below 1.
As the damping ratio of a structure tends to zero, it experiences increasing oscillations as the excitation frequency approaches the resonant frequency, which become increasingly critical to its structural integrity. This phenomenon becomes particularly relevant when we consider the operational environment of offshore wind turbines, where structures are subjected to millions of loading cycles throughout their design life.
Evaluating this forced loading over the OWT’s design life is complex, especially given damping does not remain constant. Indeed, prior to installation of the tower and rotor-nacelle assembly onto the foundation, the structure’s mass, stiffness and damping is significantly lower than during operations. This means both its resonant frequencies and motion response will differ from most of its lifecycle. Due to long installation timelines, a monopile may remain in this state for many load cycles. Additionally, soil damping is highly dependent on soil composition, which typically varies between locations in a turbine site.
More importantly, the highest contributor to the damping of the OWT assembly is the aerodynamic damping, present due to blade motion through air. When an OWT is in parked configuration, where the blades are feathered and static, it is far less damped than in operational conditions. According to Rezaei et al., 2018, normal and unforeseen shutdowns of a wind turbine are likely to induce fatigue damage of up to 60% of total capacity, primarily driven by this significant reduction in damping and its influence on the structural responses. This change in damping has a much larger impact on the structure than the corresponding reduction in operational dynamic loads. As Integrated Load Analysis processes typically require a single damping value to represent entire clusters or sites, a value must be found to encompass all these complexities. This value is therefore typically overconservative for most positions and use cases.
The omnipresence of damping
In an offshore wind turbine, damping comes from many sources. It manifests itself in the following forms:
- Structural damping from geometry and material properties
- Soil damping between the seabed and the monopile
- Hydrodynamic damping between the monopile walls and the surrounding seawater
- Aerodynamic damping from the movement of blades in air
Each of these sources contributes to the overall damping characteristics of the foundation system, and can be linearly combined to provide a more holistic model.
Most importantly, typical MP design only considers the damping as a side-effect, to be calculated and assessed but not optimised. It has been shown that the fatigue life of an OWT has an almost linear relationship to the overall damping of the structure, and that even small changes in soil or structural damping can extend fatigue life significantly, particularly as it is driven by shutdown conditions. Implementing damping as a design metric can help produce better optimised monopile and jacket foundation designs and save overall costs. Current industry practice recommends the use of a single damping value to cover the structural, hydrodynamic and soil damping contribution for foundation design processes. As turbines have grown larger and stiffer, this value is becoming underconservative. However, the accurate determination of damping ratios and coefficients is complex and full of uncertainty, requiring computationally intensive processes with soil damping measurements contingent on expensive tests. A fine balance is hard to find between the over-conservativeness of computationally efficient design practices, which can incur large penalties to foundation costs, and under-conservativeness resulting from standardised damping values.
Moving forward with confidence
Understanding damping principles is fundamental to successful offshore wind foundation design, from basic mass-spring-damper representations to the complex reality of multiple damping sources affecting resonant response and fatigue life. Accurate estimations of fatigue damage throughout a turbine’s operational life are becoming increasingly relevant as OWTs near end of life, and lifetime extensions are being put forward. As the industry moves toward larger turbines and more sophisticated foundation systems, rigorous damping analysis becomes increasingly critical for predicting long-term structural performance and enabling engineers to push technological boundaries with confidence in their designs.
Reach out to Océane on LinkedIn or read more about Empire Engineering’s offshore wind expertise.