scholarly journals Determination of Natural Frequencies and Mode Shapes of a Wind Turbine Rotor Blades using Timoshenko Beam Elements

2018 ◽  
Author(s):  
Evgueni Stanoev ◽  
Sudhanva Kusuma Chandrashekhara
Keyword(s):  
Finite Element ◽  
Numerical Integration ◽  
Timoshenko Beam ◽  
Rotor Blade ◽  
Natural Frequencies ◽  
Beam Element ◽  
Rotor Blades ◽  
Inertia Term ◽  
Mass Matrices ◽  
Kinetic Field

Abstract. In the simulation of a wind turbine, the lowest eigenmodes of the rotor blades are usually used to describe their elastic deformation in the frame of a multibody system. In this paper, a finite element beam model for the rotor blades based on the transfer matrix method is proposed. Both static and kinetic field matrices for the 3D Timoshenko beam element are derived by numerical integration of the differential equations of motion using RUNGE KUTTA 4th order procedure. The beam reference axis in the general case is at an arbitrary location in the cross section. The inertia term in the motion differential equation is expressed using appropriate shape functions for the Timoshenko beam. The kinetic field matrix is built by numerical integration applied on the approximated inertia term. The beam element stiffness and mass matrices are calculated by simple matrix operations from both field matrices. The system stiffness and mass matrices of the rotor blade model are assembled in the usual finite element manner in a global coordinate system with the accounting for structural twist angle and possibly pre-bending. The program developed for the above calculations and the final solution of the eigenvalue problem is accomplished using MuPAD, a symbolic math toolbox of MATLAB®. The calculated natural frequencies using generic rotor blade data are compared with the results proposed from FAST and ADAMS software.

scholarly journals Determination of natural frequencies and mode shapes of a wind turbine rotor blade using Timoshenko beam elements

2019 ◽  
Vol 4 (1) ◽  
pp. 57-69 ◽  
Author(s):  
Evgueni Stanoev ◽  
Sudhanva Kusuma Chandrashekhara
Keyword(s):  
Finite Element ◽  
Numerical Integration ◽  
Timoshenko Beam ◽  
Rotor Blade ◽  
Natural Frequencies ◽  
Beam Element ◽  
Rotor Blades ◽  
Inertia Term ◽  
Mass Matrices ◽  
Kinetic Field

Abstract. When simulating a wind turbine, the lowest eigenmodes of the rotor blades are usually used to describe their elastic deformation in the frame of a multi-body system. In this paper, a finite element beam model for the rotor blades is proposed which is based on the transfer matrix method. Both static and kinetic field matrices for the 3-D Timoshenko beam element are derived by the numerical integration of the differential equations of motion using a Runge–Kutta fourth-order procedure. In the general case, the beam reference axis is at an arbitrary location in the cross section. The inertia term in the motion differential equation is expressed using appropriate shape functions for the Timoshenko beam. The kinetic field matrix is built by numerical integration applied on the approximated inertia term. The beam element stiffness and mass matrices are calculated by simple matrix operations from both field matrices. The system stiffness and mass matrices of the rotor blade model are assembled in the usual finite element manner in a global coordinate system accounting for the structural twist angle and possible pre-bending. The program developed for the above-mentioned calculations and the final solution of the eigenvalue problem is accomplished using MuPAD, a symbolic math toolbox in MATLAB®. The natural frequencies calculated using generic rotor blade data are compared with the results proposed from the FAST and ADAMS software.

scholarly journals Finite element model of circularly curved Timoshenko beam for in-plane vibration analysis

2021 ◽  
Vol 49 (3) ◽  
pp. 615-626
Author(s):  
Azin Nadi ◽  
Mehdi Raghebi
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Element Model ◽  
Beam Element ◽  
Polar Coordinate System ◽  
Curved Beam ◽  
Plane Vibration ◽  
Curved Timoshenko Beam

Curved beams are used so much in the arches and railway bridges and equipments for amusement parks. There are few reports about the curved beam with the effects of both the shear deformation and rotary inertias. In this paper, a new finite element model investigates to analyze In-Plane vibration of a curved Timoshenko beam. The Stiffness and mass matrices of the curved beam element was obtained from the force-displacement relations and the kinetic energy equations, respectively. Assembly of the elemental property matrices is simple and without need to transformation matrix because of using the local polar coordinate system. The natural frequencies of curved Euler-Bernoulli beam with large thickness are not sufficiently accurate. In this case, using the curved Timoshenko beam element is necessary. Moreover, the influence of vibration absorber is discussed on the natural frequencies of the curved beam.

scholarly journals Failure Analysis of Gas Turbine Rotary Blade

2017 ◽  
pp. 1-6
Keyword(s):  
Finite Element ◽  
Gas Turbine ◽  
Rotor Blade ◽  
Rotor Blades ◽  
Centrifugal Forces ◽  
Analysis Software ◽  
Two Stage ◽  
Element Analysis ◽  
Finite Element Software ◽  
Super Alloy

In the present work the first stage rotor blade of a two- stage gas turbine has been analyzed for structural, thermal using ANSYS 9.0, which is a powerful Finite Element Software. In the present work, the first stage rotor blade of the gas turbine has been analyzed for the mechanical and radial elongations resulting from the tangential, axial and centrifugal forces. The gas forces namely tangential, axial were determined by constructing velocity triangles at inlet and exist of rotor blades. The rotor blade was then analyzed using ANSYS 9.0 for the temperature distribution. The material of the blade was specified as N155 but its properties were not given. This material is an iron based super alloy and structural and thermal properties at gas room and room temperatures. The turbine blade along with the groove is considered for the static, thermal, modal analysis. The first stage rotor blade of a two-stage gas turbine has been analyzed for structural, thermal using ANSYS 9.0 Finite Element Analysis software.

scholarly journals ACTIVE TWIST OF MODEL ROTOR BLADES WITH D-SPAR DESIGN

Transport ◽  
2007 ◽  
Vol 22 (1) ◽  
pp. 38-44 ◽  
Author(s):  
Andrejs Kovalovs ◽  
Evgeny Barkanov ◽  
Sergejs Gluhihs
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Rotor Blade ◽  
Element Model ◽  
Rotor Blades ◽  
Helicopter Rotor ◽  
3D Finite Element ◽  
3D Finite Element Model ◽  
Helicopter Rotor Blade ◽  
Active Twist

The design methodology based on the planning of experiments and response surface technique has been developed for an optimum placement of Macro Fiber Composite (MFC) actuators in the helicopter rotor blades. The baseline helicopter rotor blade consists of D‐spar made of UD GFRP, skin made of +450/‐450 GFRP, foam core, MFC actuators placement on the skin and balance weight. 3D finite element model of the rotor blade has been built by ANSYS, where the rotor blade skin and spar “moustaches” are modeled by the linear layered structural shell elements SHELL99, and the spar and foam ‐ by 3D 20‐node structural solid elements SOLID 186. The thermal analyses of 3D finite element model have been developed to investigate an active twist of the helicopter rotor blade. Strain analogy between piezoelectric strains and thermally induced strains is used to model piezoelectric effects. The optimisation results have been obtained for design solutions, connected with the application of active materials, and checked by the finite element calculations.

scholarly journals Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method

2021 ◽  
Vol 13 (11) ◽  
pp. 168781402110609
Author(s):  
Hossein Talebi Rostami ◽  
Maryam Fallah Najafabadi ◽  
Davood Domiri Ganji
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Variable Properties ◽  
The Third ◽  
Koch Snowflake

This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural frequencies. Displacement and natural frequency for each case presented and compared to other cases. Significant research achievements illustrate that if we change the Koch snowflake cross-section of the beam from the first iteration to the second, the area and moment of inertia will increase, and we have a 5.2% rise in the first natural frequency. Similarly, by changing the cross-section from the second iteration to the third, a 10.2% growth is observed. Also, the hollow cross-section is considered, which can enlarge the natural frequency by about 26.37% compared to a solid one. Moreover, all the clamped-clamped, hinged-hinged, clamped-free, and free-free boundary conditions have the highest natural frequency for the Timoshenko beam with the third iteration of the Koch snowflake cross-section in solid mode. Finally, examining important physical parameters demonstrates that variable density from a minimum value to the standard value along the beam increases the natural frequencies, while variable elastic modulus decreases it.

QUANTITATIVE IDENTIFICATION OF ROTOR CRACKS BASED ON FINITE ELEMENT OF B-SPLINE WAVELET ON THE INTERVAL

2009 ◽  
Vol 07 (04) ◽  
pp. 443-457 ◽  
Author(s):  
XUEFENG CHEN ◽  
BING LI ◽  
JIAWEI XIANG ◽  
ZHENGJIA HE
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Beam Element ◽  
Rotational Inertia ◽  
Spline Wavelet ◽  
B Spline ◽  
Rotor Systems ◽  
Crack Location ◽  
Contour Lines ◽  
Quantitative Identification

Based on finite element of B-spline wavelet on the interval (BSWI), the quantitative identification method of transverse crack for rotor systems was studied. The new model of BSWI Rayleigh–Euler rotary beam element considering gyroscopic effect and rotational inertia was constructed to solve the first three natural frequencies of the cracked rotor with high precision, and the first three frequencies solution surfaces of normalized crack location and size were obtained by using surface-fitting technique. Then the first three metrical natural frequencies were employed as inputs of the solution curve surfaces. The intersection of the three frequencies contour lines predicted the normalized crack location and size. The numerical and experimental examples were given to verify the validity of the beam element for crack quantitative identification in rotor systems. The new method can be applied to prognosis and quantitative diagnosis of cracks in the rotor system.

scholarly journals Effect of Dead Load on Dynamic Characteristics of Rotating Timoshenko Beams

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Yan-Qi Yin ◽  
Bo Zhang ◽  
Yue-ming Li ◽  
Wei-Zhen Lu
Keyword(s):  
Finite Element ◽  
Cantilever Beam ◽  
Dynamic Characteristics ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Experimental Result ◽  
Dead Load ◽  
Rotating Speed ◽  
Experimental Apparatus ◽  
The Dead

The dynamic characteristics of a rotating cantilever Timoshenko beam under dead load are investigated in this paper. Considering the predeformation caused by dead load and centrifugal force, governing equation of rotating cantilever Timoshenko beam is derived based on Hamilton’s principle, and the influence of the load on natural vibration is revealed. A suit of modal experimental apparatus for cantilever beam is designed and used to test the natural frequencies under the dead load, and the natural frequencies under rotation condition are calculated with a commercial finite element code. Both the experimental result and numerical result are utilized to compare with the present theoretical result, and the results obtained by present modeling method show a good agreement with those obtained from the experiment and finite element method. It is found that the natural frequencies of cantilever beam increase with both the dead load and the rotating speed.

scholarly journals Extension of the FGM Beam Finite Element by Warping Torsion

2019 ◽  
Vol 69 (2) ◽  
pp. 57-76
Author(s):  
Murín Justín ◽  
Hrabovský Juraj ◽  
Aminbaghai Mehdi ◽  
Kutiš Vladimír ◽  
Paulech Juraj ◽  
...  
Keyword(s):  
Finite Element ◽  
Cantilever Beam ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Material Properties ◽  
Torsion Effect ◽  
Mass Matrices ◽  
Effective Material Properties ◽  
Fgm Beam ◽  
Torsional Analysis

AbstractIn the contribution, our 3D FGM Timoshenko beam finite element with 12x12 stiffness and mass matrices for doubly symmetric open and closed cross-section [1] is extended by warping torsion effect (non-uniform torsion) to 14x14 finite element matrices. A longitudinal continuous variation of effective material properties is considered by the finite element equations derivation, which can be obtained by homogenization of the spatial varying material properties in real FGM beam. Results of numerical elastostatic non-uniform torsional analysis of the FGM cantilever beam of I-cross-section are presented and the accuracy and effectiveness of the new FGM beam finite element is discussed and evaluated.

Multistage Coupling of Eight Mistuned Bladed Disk on a Solid Shaft: Part 1—Free Vibration Analysis

2012 ◽  
Author(s):  
Romuald Rzadkowski ◽  
Artur Maurin
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Bladed Disk ◽  
Centrifugal Stiffening

Considered here was the effect of multistage coupling on the dynamics of a rotor consisting of eight mistuned bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study the global rotating mode shapes of eight flexible mistuned bladed discs on shaft assemblies were calculated, taking into account rotational effects such as centrifugal stiffening. The thus obtained natural frequencies of the blade, shaft, bladed disc and entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that mistuned systems cause far more intensive multistage coupling than tuned ones. The greater the mistuning, the more intense the multistage coupling.

The Finite Element Model Study of the Pre-Twisted Timoshenko Beam

2012 ◽  
Vol 446-449 ◽  
pp. 3587-3590
Author(s):  
Chang Hong Chen ◽  
Ying Huang ◽  
Jian Shan
Keyword(s):  
Finite Element ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Angular Displacement ◽  
Element Model ◽  
Beam Element ◽  
Element Stiffness Matrix ◽  
Straight Beam ◽  
The Relationship ◽  
Timoshenko Beam Element

The paper studies a new mechanical model of pre-twisted Timoshenko beam. But it is different from the conventional Timoshenko straight beam; the proposed new Timoshenko beam element takes separate interpolation polynomial functions both flexure bending displacement and angular displacement. According to the relationship between bending moment and shear, the relationship between of bending displacement and angle displacement is derived, more accurate to consider the effects of shear deformation, come up with a new initial reverse Timoshenko beam element stiffness matrix. Finally, by calculating the pre-twisted rectangle section beam example, and contrasting three-dimensional solid finite element using ANSYS, the comparative analysis results show that pre-twisted Timoshenko beam element stiffness matrix has good accuracy.

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