Modeling Rotating Shafts Using Axisymmetric Solid Finite Elements with Matrix Reduction

1993 ◽  
Vol 115 (4) ◽  
pp. 484-489 ◽  
Author(s):  
R. W. Stephenson ◽  
K. E. Rouch
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Series Representation ◽  
Element Model ◽  
Beam Element ◽  
Two Dimensions ◽  
Matrix Reduction ◽  
Stiffness Matrices ◽  
Rotating Shafts ◽  
Element Type

An axisymmetric harmonic finite element representation is used to calculate shaft lateral critical speeds and perform stability analysis. Unlike a beam element model, an axisymmetric solid element representation allows the actual rotor geometry to be modeled. A Fourier series representation allows the three-dimensional shaft geometry to be modeled in two dimensions by only considering the radial and axial coordinates. Thus, the degrees of freedom of this element type are different from the usual two translations and two rotations at each node associated with bending of a three-dimensional beam element. A required gyroscopic matrix is also presented for completeness in analysis of rotating shafts. A matrix reduction technique is used to reduce the size of the shaft mass, gyroscopic, and stiffness matrices by condensing out slave degrees of freedom in terms of the retained master degrees of freedom. The formulation is applied to various examples for verification and to investigate the effect of selection of different master degrees of freedom for this element type on the results.

Dynamic Finite Element Analysis of a Highly Parallel Robotic Surface

2011 ◽  
Author(s):  
Chris Salisbury
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Angular Displacement ◽  
Three Dimensional ◽  
Element Analysis ◽  
Revolute Joints ◽  
Stiffness Matrices ◽  
Joint Forces ◽  
Ricatti Equation ◽  
Optimal Dynamic

A novel three-dimensional robotic surface is devised using triangular modules connected by revolute joints that mimic the constraints of a spherical joint at each triangle intersection. The finite element method (FEM) is applied to the dynamic loading of this device using three dimensional (6 degrees of freedom) beam elements to not only calculate the cartesian displacement and force, but also the angular displacement and torque at each joint. In this way, the traditional methods of finding joint forces and torques are completely bypassed. An effiecient algorithm is developed to linearly combine local mass and stiffness matrices into a full structural stiffness matrix for the easy application of loads. An analysis of optimal dynamic joint forces is carried out in Simulink® with the use of an algebraic Ricatti equation.

scholarly journals Tensile and bending behavior of thin-walled triaxial weave fabric composites

2019 ◽  
Vol 14 ◽  
pp. 155892501989356
Author(s):  
Xiaotao Zhou ◽  
Xiaofei Ma ◽  
Yesen Fan ◽  
Huanxiao Li
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Membrane Structure ◽  
Three Dimensional ◽  
Element Model ◽  
Beam Element ◽  
Shell Membrane ◽  
Weave Fabric ◽  
Fabric Composites ◽  
Thin Walled

The laminate model of thin-walled triaxial weave fabric composites (hereinafter referred to as shell-membrane structure) to calculate the equivalent tensile Young’s modulus and bending stiffness is derived. Three-dimensional beam element finite element model of shell-membrane structure under different loading angles is established, and the tensile and bending properties of shell-membrane structure were simulated, respectively. Both results of laminate model and three-dimensional beam element finite element model verify the “size effect,” indicating that the shell-membrane structure can be equivalent to linear material in the small deformation range. And the shell-membrane structure exhibits an in-plane quasi-isotropic property. These two methods are convenient for the mechanical properties solving in engineering applications.

Modeling of Blades as Equivalent Beams for Aeroelastic Analysis

2003 ◽  
Author(s):  
David J. Malcolm ◽  
Daniel L. Laird
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Wind Turbine ◽  
Three Dimensional ◽  
Element Model ◽  
Detailed Model ◽  
Stiffness Matrices ◽  
Aeroelastic Analysis ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

A procedure has been developed and tested to derive a set of one-dimensional beam properties that will duplicate the behavior of a full three-dimensional finite element model of a wind turbine blade. This allows the full features of a detailed model to be transferred to an aeroelastic code for dynamic simulation of the complete wind turbine. The process uses the NuMAD interface to generate an ANSYS® finite element model to which a set of six unit loads are applied at the tip. The displacement results are used in a series of MATLAB routines to extract the stiffness matrices of the desired beam elements. Tests have been carried out on a number of blades and the stiffness matrices incorporated into ADAMS® models of the blades and complete wind turbines.

Modal Analysis Method for Blisks Based on Three-Dimensional Blade and Two-Dimensional Axisymmetric Disk Finite Element Model

2016 ◽  
Vol 139 (5) ◽  
Author(s):  
Wangbai Pan ◽  
Guoan Tang ◽  
Meiyan Zhang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Modal Analysis ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Three Dimensional ◽  
Element Model ◽  
Computational Time ◽  
Engineering Practice ◽  
Analysis Method

In this paper, a novel and efficient modal analysis method is raised to work on blisk structures based on mixed-dimension finite element model (MDFEM). The blade and the disk are modeled separately. The blade model is figured by 3D solid elements considering its complex configuration and its degrees-of-freedom (DOFs) are condensed by dynamic substructural method. Meanwhile, the disk is structured by 2D axisymmetric element developed specially in this paper. The DOFs of entire blisk are tremendously reduced by this modeling approach. The key idea of this method is derivation of displacement compatibility to different dimensional models. Mechanical energy equivalence and summation further contribute to the model synthesis and modal analysis of blade and disk. This method has been successfully applied on the modal analysis of blisk structures in turbine, which reveals its effectiveness and proves that this method reduces the computational time expenses while maintaining the precision performances of full 3D model. Though there is limitation that structure should have proper coverage of blades, this method is still feasible for most blisks in engineering practice.

scholarly journals The stability of an infinite system of circular vortices

1927 ◽  
Vol 114 (768) ◽  
pp. 594-604 ◽  
Keyword(s):  
Infinite Number ◽  
Degrees Of Freedom ◽  
Infinite System ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Vortex Rings ◽  
Infinite Cylinder ◽  
Vortex Filaments ◽  
Straight Line ◽  
The Stability

A system of equal circular vortex filaments have their centres evenly spaced along a straight line, and their planes at right angles to this line. The present investigation is concerned with the stability or instability of such an arrangement. The corresponding problem in two dimensions has been dealt with by Kármán who considered the case of two infinite trails of parallel rectilinear vortices, with the object of applying his results to the resistance of an infinite cylinder moving in a fluid and to the state of motion in the rear of the cylinder. The infinite system of circular vortex filaments, on the other hand, may be supposed, in certain circumstances to be discussed in a later paper, to be generated in the rear of a three-dimensional body in motion in a fluid. The present investigation may therefore be regarded as a first step towards an examination of the three-dimensional problem analogous to that treated by Kármán for two dimensions. A special difficulty arises in an investigation of this type from the fact that the system of vortex rings, possessing an infinite number of degrees of freedom, are capable of adopting an infinite number of possible configurations about the position of equilibrium.

Performance Enhancement of Three-Dimensional Soil Structure Model via Optimization for Estimating Seismic Behavior of Buried Pipelines

2017 ◽  
Vol 11 (05) ◽  
pp. 1750019 ◽  
Author(s):  
Tsuyoshi Ichimura ◽  
Kohei Fujita ◽  
Atsushi Yoshiyuki ◽  
Pher Errol Quinay ◽  
Muneo Hori ◽  
...  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Performance Enhancement ◽  
Three Dimensional ◽  
Element Model ◽  
Optimization Method ◽  
Buried Pipelines ◽  
Ground Structure ◽  
3D Finite Element ◽  
Ground Structures

Damage to buried pipelines due to complex ground responses has been reported at residential development sites and valley plains with complex ground structures. Three-dimensional (3D) ground amplification analyses using 3D, nonlinear, finite-element methods may be effective in predicting such damage; however, it is often difficult to construct ground structures that are capable of reproducing observational characteristics. In this paper, we propose a 3D ground structure optimization method using a 3000[Formula: see text] forward finite-element dynamic analysis with approximately 0.27 million degrees of freedom, enabled by combining an automated 3D finite-element model-generation method and a fast 3D finite-element wave propagation analysis method. This optimization method is capable of estimating 3D ground structure models that can reproduce observational data characteristics. The effectiveness of the method is shown through an illustrative example.

A Discrete Element Approach for Modeling Cage Flexibility in Ball Bearing Dynamics Simulations

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Nick Weinzapfel ◽  
Farshid Sadeghi
Keyword(s):  
Reference Frame ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Element Model ◽  
Discrete Element ◽  
Discrete Elements ◽  
Step Size ◽  
Deep Groove ◽  
Bearing Dynamics

A model for deep-groove and angular-contact ball bearings was developed to investigate the influence of a flexible cage on bearing dynamics. The cage model introduces flexibility by representing the cage as an ensemble of discrete elements that allow deformation of the fibers connecting the elements. A finite element model of the cage was developed to establish the relationships between the nominal cage properties and those used in the flexible discrete element model. In this investigation, the raceways and balls have six degrees of freedom. The discrete elements comprising the cage each have three degrees of freedom in a cage reference frame. The cage reference frame has five degrees of freedom, enabling three-dimensional motion of the cage ensemble. Newton’s laws are used to determine the accelerations of the bearing components, and a fourth-order Runge–Kutta algorithm with constant step size is used to integrate their equations of motion. Comparing results from the dynamic bearing model with flexible and rigid cages reveals the effects of cage flexibility on bearing performance. The cage experiences nearly the same motion and angular velocity in the loading conditions investigated regardless of the cage type. However, a significant reduction in ball-cage pocket forces occurs as a result of modeling the cage as a flexible body. Inclusion of cage flexibility in the model also reduces the time required for the bearing to reach steady-state operation.

STATIC AND DYNAMIC BEHAVIOUR OF LAMINATED COMPOSITE BEAMS

2001 ◽  
Vol 01 (04) ◽  
pp. 545-560 ◽  
Author(s):  
M. A. RAMOS LOJA ◽  
J. INFANTE BARBOSA ◽  
C. M. MOTA SOARES
Keyword(s):  
Cross Sections ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Single Layer ◽  
Laminated Composite ◽  
Element Model ◽  
Composite Beams ◽  
Straight Beam ◽  
Transverse Stresses

A higher order shear deformation theory, assuming a non-linear variation for the displacement field, is used to develop a finite element model to predict static and free vibration behaviour of anisotropic multilaminated thick and thin beams. The model is based on a single-layer Lagrangean four-node straight beam element with fourteen degrees of freedom per node. It considers bending into two orthogonal planes, stretching and twisting to enable three-dimensional analysis of frames. The most common cross sections and symmetric and asymmetric lay-ups are studied. The behaviour of the model is tested on thin and thick isotropic and composite beams. Comparisons show that the model is accurate and versatile. The good performance of the present model is evident on the prediction of displacements, normal and transverse stresses and natural frequencies of thin and thick isotropic or anisotropic beam structures.

Nonlinear Analysis of Twisted Wind Turbine Blade

2016 ◽  
Vol 34 (3) ◽  
pp. 269-278 ◽  
Author(s):  
M. Yangui ◽  
S. Bouaziz ◽  
M. Taktak ◽  
M. Haddar ◽  
A. El-Sabbagh
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Rotation Speed ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Shell Element ◽  
Element Model ◽  
Angular Rotation ◽  
Triangular Shell Element

AbstractModal analysis is developed in this paper in order to study the dynamic characteristics of rotating segmented blades assembled with spar. Accordingly, a three dimensional finite element model was built using the three node triangular shell element DKT18, which has six degrees of freedom, to model the blade and the spar structures. This study covers the effect of rotation speed and geometrically nonlinear problems on the vibration characteristics of rotating blade with various pretwist angles. Likewise, the effect of the spar in the blade is taken into consideration. The equation of motion for the finite element model is derived by using Hamilton's principle, while the resulting nonlinear equilibrium equation is solved by applying the Newmark method combined with the Newton Raphson schema. Results show that the natural frequencies increase by taking account of the spar, they are also proportional to the angular rotation speed and influenced by geometric nonlinearity and pretwist angle.

HEISENBERG QUANTIZATION FOR SYSTEMS OF IDENTICAL PARTICLES

1993 ◽  
Vol 08 (21) ◽  
pp. 3649-3695 ◽  
Author(s):  
JON MAGNE LEINAAS ◽  
JAN MYRHEIM
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Classical System ◽  
Two Dimensions ◽  
Identical Particles ◽  
Natural Approach ◽  
Fermion Systems ◽  
Special Cases ◽  
Continuous Interpolation

We show that the algebraic quantization method of Heisenberg and the analytical method of Schrödinger are not necessarily equivalent when applied to systems of identical particles. Heisenberg quantization is a natural approach, but inherently more ambiguous and difficult than Schrödinger quantization. We apply the Heisenberg method to the examples of two identical particles in one and two dimensions, and relate the results to the so-called fractional statistics known from Schrödinger quantization. For two particles in d dimensions we look for linear, Hermitian representations of the symplectic Lie algebra sp(d, R). The boson and fermion representations are special cases, but there exist other representations. In one dimension there is a continuous interpolation between boson and fermion systems, different from the interpolation found in Schrödinger quantization. In two dimensions we find representations that can be realized in terms of multicomponent wave functions on a three-dimensional space, but we have no clear physical interpretation of these representations, which include extra degrees of freedom compared to the classical system.

Sign in / Sign up

Export Citation Format

Share Document