Soil dynamics

Up to now, the effect of the flexibility of the foundation and its supporting soil has not been dealt with in this thesis. Soil is a non-linear material in which the stifness progressively decreases with increasing shear stress until, at a sufficient high stress level, plastic deformation takes place. Furthermore, when subjected to cyclic loading, soil exhibits damping which increases with increasing shear amplitude. Soil damping comprises two parts: internal and radiation. The internal damping (also called material, structural or hysteric damping) is mainly caused by viscous and frictional effects within the soil. The radiation damping is an elastic property associated with stress waves being propagated away from an area. Obviously, the soil properties vary from place to place, and many of the properties vary in time too.

In this chapter it is assumed that the flexibility of the foundation and its supporting soil can be modeled by a torsional spring plus viscous damper in the two bending directions. This assumption will be (in)validated in Section 4.2 where the results from a full-scale modal test on the Lagerwey LW-50/750 wind turbine are described.

The flexibility of the soil makes the mechanical wind turbine structure less stiff than if the wind turbine were on a fixed base. This reduces the eigenfrequencies of the wind turbine in transverse vibration which in turn tends to increase the dynamic response of the mechanical structure. Figure 3.19 illustrates that the lowest modes are most affected because they tend to involve the highest proportion of soil response in the mode shape. In this figure the relative frequency shift as function of the foundation spring stiffness is depicted for Tower2f (i.e. tower plus foundation modeled as a torsional spring, see Appendix I.2.3 for a detailed description of the Tower2f module). This shift is defined as:

Eigenfrequencies of Tower2f

Eigenfrequencies of Tower2

In other words: the relative frequency shift converges to zero with increasing foundation spring stiffness, since it then will approximate the infinitely rigid foundation modeled in Tower2. The dashed vertical line in the figure indicates the measured value of foundation spring stiffness at the location in Nieuwe-Tonge. This value is experimentally determined by Jacobs [116]. Obviously, small inaccuracies in the determination of this value will have significant impact on the model quality.

Figure 3.19: Effect of foundation spring stiffness Cf on the first four uncoupled eigenfrequencies of the Lagerwey LW-50/750 tower. Solid line: first mode, dashed line: second mode, dashed-dotted line: third mode, dotted line: fourth mode, dashed vertical line: Cf = 19.4 • 10 9 [Nm/rad], and dashed-dotted vertical lines: - 25% and + 25% error bound respectively.

Figure 3.19: Effect of foundation spring stiffness Cf on the first four uncoupled eigenfrequencies of the Lagerwey LW-50/750 tower. Solid line: first mode, dashed line: second mode, dashed-dotted line: third mode, dotted line: fourth mode, dashed vertical line: Cf = 19.4 • 10 9 [Nm/rad], and dashed-dotted vertical lines: - 25% and + 25% error bound respectively.

Renewable Energy Eco Friendly

Renewable Energy Eco Friendly

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable.

Get My Free Ebook


Post a comment