Unstable Vibrations of a Wind Turbine Tower With Two Blades

2012 ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Yukio Ishida
Keyword(s):  
Wind Turbine ◽  
Equations Of Motion ◽  
Single Mode ◽  
Single Frequency ◽  
Dual Mode ◽  
Response Curves ◽  
Moments Of Inertia ◽  
System Parameters ◽  
Wind Turbine Tower ◽  
The Asymmetry

Unstable vibrations of a two-blade wind turbine tower are theoretically investigated. The theoretical model is a five-degree-of-freedom (5DOF) system, however, the equations of motion are derived separately for 3DOF subsystem (I) and 2DOF subsystem (II). Parametric excitation due to the asymmetry of the moments of inertia of the blade rotor is included only in subsystem (I). Frequency equations are derived and natural frequency diagrams are calculated to clearly demonstrate both the rotational speeds where unstable regions appear and which type of unstable vibrations may occur. It is found that at most, five unstable regions may appear depending on the values of the system parameters in subsystem (I). Two types of unstable vibrations may occur; single mode including a single frequency and dual mode including two frequencies. The influences of the asymmetry of moments of inertia, tower rigidity, and installation position of the blade rotor on the response of the system are also theoretically investigated. Van der Pol’s method is applied to determine the expressions for the response curves. The influences of the blade rotor unbalances on the translational, inclinational and torsional vibrations of the tower are shown. It is found that the amplitudes of the response curves corresponding to single and dual mode are infinite and finite at their boundaries, respectively. The validity of the theoretical analysis is confirmed by numerical simulations.

Influence of Earthquake Directions on Wind Turbine Tower under Seismic Action

2011 ◽  
Vol 243-249 ◽  
pp. 3883-3888 ◽  
Author(s):  
Lai Wang ◽  
Xi Tong Dong
Keyword(s):  
Finite Element ◽  
Wind Turbine ◽  
Equations Of Motion ◽  
Element Model ◽  
Dynamic Responses ◽  
Dominant Factor ◽  
Seismic Action ◽  
Bending Stress ◽  
Wind Turbine System ◽  
Wind Turbine Tower

Influence of earthquake directions on wind turbine tower under seismic action are numerically investigated in this paper. First, equations of motion and an integrated finite element model of a wind turbine system consisting of a rotor, a nacelle and a tower shaft are established. Second, the finite element modal analysis is discussed. Third, relationships between upper displacements in x, y directions and bottom bending stress when the angle is 0, 30, 45, 60, 90 degree respectively between earthquake directions and concentrated eccentric mass direction (x direction) are analyzed by adjusted Taft seismic wave .The results show that: seismic responses of a wind turbine tower are remarkable and seismic action may be the dominant factor in the design of wind turbine towers that located at a seismically active zone. Under different earthquake directions structure’s dynamic responses are different, 90 degree with regard to x direction is the most unfavorable direction. Both maximum upper displacements in x, y directions and bottom bending stress appear at 90 degree direction with regard to x direction.

Parametric Instability and Localization of Vibrations in Three-Blade Wind Turbines

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Yukio Ishida
Keyword(s):  
Wind Turbine ◽  
Wind Turbines ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Parametric Instability ◽  
Vertical Wind Shear ◽  
Coupled System ◽  
Basins Of Attraction ◽  
Response Curves ◽  
Softening Behavior

Nonlinear vibration characteristics of three-blade wind turbines are theoretically investigated. The wind turbine is modeled as a coupled system, consisting of a flexible tower with two degrees-of-freedom (2DOF), and three blades, each with a single degree of freedom (SDOF). The blades are subjected to steady winds. The wind velocity increases proportionally with height due to vertical wind shear. The natural frequency diagram is calculated with respect to the rotational speed of the wind turbine. The corresponding linear system with parametric excitation terms is analyzed to determine the rotational speeds where unstable vibrations appear and to predict at what rotational speeds the blades may vibrate at high amplitudes in a real wind turbine. The frequency response curves are then obtained by applying the swept-sine test to the equations of motion for the nonlinear system. They exhibit softening behavior due to the nonlinear restoring moments acting on the blades. Stationary time histories and their fast Fourier transform (FFT) results are also calculated. In the numerical simulations, localization phenomena are observed, where the three blades vibrate at different amplitudes. Basins of attraction (BOAs) are also calculated to examine the influence of a disturbance on the appearance of localization phenomena.

A Circuit Model for Lightning Surge of Wind Turbine Tower with an Internal Conductor

2015 ◽  
Vol 135 (3) ◽  
pp. 200-206 ◽  
Author(s):  
Yoki Ikeda ◽  
Naoto Nagaoka ◽  
Yoshihiro Baba
Keyword(s):  
Wind Turbine ◽  
Circuit Model ◽  
Wind Turbine Tower

Seismic response analysis of steel–concrete hybrid wind turbine tower

2021 ◽  
pp. 107754632110075
Author(s):  
Junling Chen ◽  
Jinwei Li ◽  
Dawei Wang ◽  
Youquan Feng
Keyword(s):  
Wind Turbine ◽  
Response Spectrum ◽  
Ground Motions ◽  
Time History ◽  
Seismic Action ◽  
Response Spectrum Method ◽  
Spectrum Method ◽  
Wind Turbine Tower ◽  
Ground Types ◽  
Nonlinear Time History

The steel–concrete hybrid wind turbine tower is characterized by the concrete tubular segment at the lower part and the traditional steel tubular segment at the upper part. Because of the great change of mass and stiffness along the height of the tower at the connection of steel segment and concrete segment, its dynamic responses under seismic ground motions are significantly different from those of the traditional steel tubular wind turbine tower. Two detailed finite element models of a full steel tubular tower and a steel–concrete hybrid tower for 2.0 MW wind turbine built in the same wind farm are, respectively, developed by using the finite element software ABAQUS. The response spectrum method is applied to analyze the seismic action effects of these two towers under three different ground types. Three groups of ground motions corresponding to three ground types are used to analyze the dynamic response of the steel–concrete hybrid tower by the nonlinear time history method. The numerical results show that the seismic action effect by the response spectrum method is lower than those by the nonlinear time history method. And then it can be concluded that the response spectrum method is not suitable for calculating the seismic action effects of the steel–concrete hybrid tower directly and the time history analyses should be a necessary supplement for its seismic design. The first three modes have obvious contributions on the dynamic response of the steel–concrete hybrid tower.

3 [email protected] kHz single mode single-frequency end pumped pulsed Nd:YAG ring laser

2014 ◽  
Author(s):  
A.S. Davtian ◽  
Z. V. Gorelova ◽  
V.P. Pokrovskyi ◽  
S.S. Sobolev ◽  
S.S. Terekhov
Keyword(s):  
Ring Laser ◽  
Single Mode ◽  
Single Frequency

Second Order Averaging Study of an Autoparametric System

1993 ◽  
Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj ◽  
Patricia Davies
Keyword(s):  
Dynamical Behavior ◽  
Period Doubling ◽  
Nonlinear Effects ◽  
Single Mode ◽  
Pitchfork Bifurcation ◽  
Second Order ◽  
System Response ◽  
Response Curves ◽  
Vibratory System ◽  
First Order

Abstract The autoparametric vibratory system consisting of a primary spring-mass-dashpot system coupled with a damped simple pendulum serves as an useful example of two degree-of-freedom nonlinear systems that exhibit complex dynamic behavior. It exhibits 1:2 internal resonance and amplitude modulated chaos under harmonic forcing conditions. First-order averaging studies of this system using AUTO and KAOS have yielded useful information about the amplitude dynamics of this system. Response curves of the system indicate saturation and the pitchfork bifurcation sets are found to be symmetric. The period-doubling route to chaotic solutions is observed. However questions about the range of the small parameter ε (a function of the forcing amplitude) for which the solutions are valid cannot be answered by a first-order study. Some observed dynamical behavior, like saturation, may not persist when higher-order nonlinear effects are taken into account. Second-order averaging of the system, using Mathematica (Maeder, 1991; Wolfram, 1991) is undertaken to address these questions. Loss of saturation is observed in the steady-state amplitude responses. The breaking of symmetry in the various bifurcation sets becomes apparent as a consequence of ε appearing in the averaged equations. The dynamics of the system is found to be very sensitive to damping, with extremely complicated behavior arising for low values of damping. For large ε second-order averaging predicts additional Pitchfork and Hopf bifurcation points in the single-mode response.

Collapse analysis of wind turbine tower under the coupled effects of wind and near-field earthquake

Wind Energy ◽  
2018 ◽  
Vol 22 (3) ◽  
pp. 407-419 ◽  
Author(s):  
Jian Fan ◽  
Qian Li ◽  
Yanping Zhang
Keyword(s):  
Wind Turbine ◽  
Near Field ◽  
Wind Turbine Tower ◽  
Collapse Analysis

scholarly journals Response of Base-Isolated Liquid Storage Tanks

2004 ◽  
Vol 11 (1) ◽  
pp. 33-45 ◽  
Author(s):  
M.B. Jadhav ◽  
R.S. Jangid
Keyword(s):  
Seismic Response ◽  
Seismic Isolation ◽  
Equations Of Motion ◽  
Approximate Model ◽  
Storage Tanks ◽  
Step Method ◽  
Earthquake Excitation ◽  
System Parameters ◽  
Liquid Storage ◽  
Isolation Systems

Seismic response of liquid storage tanks isolated by elastomeric bearings and sliding system is investigated under real earthquake ground motions. The continuous liquid mass of the tank is modeled as lumped masses known as sloshing mass, impulsive mass and rigid mass. The coupled differential equations of motion of the system are derived and solved in the incremental form using Newmark's step-by-step method with iterations. The seismic response of isolated tank is studied to investigate the comparative effectiveness of various isolation systems. A parametric study is also carried out to study the effect of important system parameters on the effectiveness of seismic isolation for liquid storage tanks. The various important parameters considered are: (i) aspect ratio of the tank and (ii) the time period of the isolation systems. It was observed that both elastomeric and sliding systems are found to be effective in reducing the earthquake forces of the liquid storage tanks. However, the elastomeric bearing with lead core is found to perform better in comparison to other systems. Further, an approximate model is proposed for evaluation of seismic response of base-isolated liquid storage tanks. A comparison of the seismic response evaluated by the proposed approximate method and an exact approach is made under different isolation systems and system parameters. It was observed that the proposed approximate analysis provides satisfactory response estimates of the base-isolated liquid storage tanks under earthquake excitation.

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