# DYNAMIC ANALYSIS OF ONSHORE WIND TURBINES FROM A LAGRAGEAN APPROACH

## Palavras-chave:

Onshore Wind Turbine, Operating Condition, SSI, Velocity of the Rotor## Resumo

Special structures, such as wind turbines, have characteristics and exhibit significantly

different behavior than conventional civil engineering structures. Wind turbines are generally flexible

structures and susceptible to considerable displacement due to external vibrations. Thus, it is of

significant importance to analyze the dynamic behavior of these structures. Considering this, the

present study aims to evaluate the dynamic performance of wind turbines through two approximate

models, investigating three different conditions and how each one will affect the results. The three

studied aspects are the influence of the operational condition (parked and rotating), the influence of

SSI and the influence of rotor speed. The NREL 5MW wind turbine will be the source of tower,

nacelle and rotor properties. The models use multi-degrees of freedom to represent an onshore wind

turbine of horizontal axes; in addition, the Euler-Lagrangian approach is used to process dynamic

analysis. The first model was developed using rotary blades modeled as continuous beams. The whole

model has 8 degrees of freedom. The blades are analyzed as a system of two degrees of freedom, that

is, it is possible to vibrate in the directions in the plane and out of the plane. They are connected in the

center of the tower-nacelle represented by a spring of mass corresponding to a system of two degrees

of freedom, that is to say, also can have vibrations in the directions in the plane and outside the plane.

The second model has the same characteristics as the first; however, a foundation shaped like a spring

with bi-directional rotational stiffness is included therein. In this way, it is possible, from this model,

to study the soil-structure interaction (SSI). Soil stiffness and damping properties were acquired from

the DNV/Risø standards and are used as a comparison. A wind load and an earthquake are used as a

source of vibration for the models. The main objective, then, is to evaluate the impact of three

different conditions through the dynamic response obtained from the two models. From the results, it

can be seen that the responses of the wind turbine in the operating condition are much larger than

those in the parked condition; SSI can greatly affect tower responses; however, does not have a

significant effect on the vibrations occurring in the plane of rotation of the blades. Finally, it is

realized that the amplitude of the response increases with the velocity of the rotor, in general.