LIMIT CYCLES OF A DOUBLE OSCILLATOR EXCITED BY DRY FRICTION

2011 ◽  
Vol 21 (10) ◽  
pp. 3043-3046 ◽  
Author(s):  
SERGEY STEPANOV
Keyword(s):  
Fixed Points ◽  
Numerical Method ◽  
Limit Cycles ◽  
Dry Friction ◽  
Coulomb Friction ◽  
Three Dimensional ◽  
Slip Mode ◽  
Two Dimensional ◽  
Parametric Investigation ◽  
Friction Laws

A two-mass oscillator with one mass lying on the driving belt with dry Coulomb friction is considered. A numerical method for finding all limit cycles and their parametric investigation, based on the analysis of fixed points of a two-dimensional map, is suggested. As successive points for the map we chose points of friction transferred from stick mode to slip mode. These transfers are defined by two equalities and yield a two-dimensional map, in contrast to three-dimensional maps that we can construct for regularized continuous dry friction laws.

scholarly journals A Fast Two-Dimensional Numerical Method for the Wake Simulation of a Vertical Axis Wind Turbine

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 49
Author(s):  
Zheng Yuan ◽  
Jin Jiang ◽  
Jun Zang ◽  
Qihu Sheng ◽  
Ke Sun ◽  
...  
Keyword(s):  
Velocity Distribution ◽  
Numerical Method ◽  
Three Dimensional ◽  
Particle Method ◽  
Vortex Method ◽  
Vertical Axis ◽  
Two Dimensional ◽  
Vertical Axis Wind Turbine ◽  
Wake Effect ◽  
Array Design

In the array design of the vertical axis wind turbines (VAWT), the wake effect of the upstream VAWT on the downstream VAWT needs to be considered. In order to simulate the velocity distribution of a VAWT wake rapidly, a new two-dimensional numerical method is proposed, which can make the array design easier and faster. In this new approach, the finite vortex method and vortex particle method are combined to simulate the generation and evolution of the vortex, respectively, the fast multipole method (FMM) is used to accelerate the calculation. Based on a characteristic of the VAWT wake, that is, the velocity distribution can be fitted into a power-law function, a new correction model is introduced to correct the three-dimensional effect of the VAWT wake. Finally, the simulation results can be approximated to the published experimental results in the first-order. As a new numerical method to simulate the complex VAWT wake, this paper proves the feasibility of the method and makes a preliminary validation. This method is not used to simulate the complex three-dimensional turbulent evolution but to simulate the velocity distribution quickly and relatively accurately, which meets the requirement for rapid simulation in the preliminary array design.

scholarly journals Improved Reliability of Bladed Disks due to Friction Dampers

1997 ◽  
Author(s):  
Walter Sextro ◽  
Karl Popp ◽  
Ivo Wolter
Keyword(s):  
Dry Friction ◽  
Three Dimensional ◽  
Line Contact ◽  
Two Dimensional ◽  
Centrifugal Forces ◽  
Friction Damper ◽  
Blade Vibration ◽  
Friction Dampers ◽  
Bladed Disk ◽  
Bladed Disk Assembly

Friction dampers are installed underneath the blade platforms to improve the reliability. Because of centrifugal forces the dampers are pressed onto the platforms. Due to dry friction and the relative motion between blades and dampers, energy is dissipated, which results in a reduction of blade vibration amplitudes. The geometry of the contact is in many cases like a Hertzian line contact. A three-dimensional motion of the blades results in a two-dimensional motion of one contact line of the friction dampers in the contact plane. An experiment with one friction damper between two blades is used to verify the two-dimensional contact model including microslip. By optimizing the friction dampers masses, the best damping effects are obtained. Finally, different methods are shown to calculate the envelope of a three-dimensional response of a detuned bladed disk assembly (V84.3-4th-stage turbine blade) with friction dampers.

scholarly journals Tiling Efflorescence of Expanding Kernels in a Fixed Periodic Array

2021 ◽  
Vol 3 (1) ◽  
pp. 13-34
Author(s):  
Robert J Marks II
Keyword(s):  
Fourier Analysis ◽  
Fixed Points ◽  
Limit Cycles ◽  
Circular Cone ◽  
Two Dimensional ◽  
Periodic Functions ◽  
Fundamental Properties ◽  
Art And Architecture ◽  
The Trinity ◽  
Func Tion

Continually expanding periodically translated kernels on the two dimensional grid can yield interesting, beau- tiful and even familiar patterns. For example, expand- ing circular pillbox shaped kernels on a hexagonal grid, adding when there is overlap, yields patterns includ- ing maximally packed circles and a triquetra-type three petal structure used to represent the trinity in Chris- tianity. Continued expansion yields the flower-of-life used extensively in art and architecture. Additional expansion yields an even more interesting emerging ef- florescence of periodic functions. Example images are given for the case of circular pillbox and circular cone shaped kernels. Using Fourier analysis, fundamental properties of these patterns are analyzed. As a func- tion of expansion, some effloresced functions asymp- totically approach fixed points or limit cycles. Most interesting is the case where the efflorescence never repeats. Video links are provided for viewing efflores- cence in real time.

scholarly journals Implementation of numerically exact Coulomb friction for discrete element simulations in three dimensions

2021 ◽  
Vol 249 ◽  
pp. 14005
Author(s):  
Shouta Sakamaki ◽  
Dominik Krengel ◽  
Jan Mueller ◽  
Jian Chen ◽  
Hans-Georg Matuttis
Keyword(s):  
Coulomb Friction ◽  
Three Dimensional ◽  
Discrete Element ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Discrete Element Simulations

As a follow-up of an earlier work on the numerically exact Coulomb friction in two-dimensional simulations, we present here the relations and implementation for three-dimensional discrete element particles.

A numerical method based on three-dimensional Legendre wavelet method for two-dimensional time-fractional diffusion equation

2021 ◽  
pp. 2150008
Author(s):  
Sarkout Abdi ◽  
Aram Azizi ◽  
Mahmoud Shafiee ◽  
Jamshid Saeidian
Keyword(s):  
Numerical Method ◽  
Operational Matrix ◽  
Three Dimensional ◽  
Fractional Diffusion ◽  
Finite Domain ◽  
Two Dimensional ◽  
Linear System Of Equations ◽  
Fractional Diffusion Equations ◽  
Spatial Dimensions ◽  
Legendre Wavelet Method

In this paper, an efficient numerical method is proposed to handle two-dimensional fractional diffusion equations on a finite domain. The proposed method combines the product of Legendre wavelet bases for two spatial dimensions and a time direction. The operational matrix of the proposed method is obtained. Tikhonov regularization is employed to stabilize the system in cases where the final linear system of equations is large. The convergence analysis of the method is studied and some numerical examples are presented to investigate the efficiency and accuracy of the method.

Three-Dimensional Finite Element Analysis of Dovetail Attachments With and Without Crowning

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
J. R. Beisheim ◽  
G. B. Sinclair
Keyword(s):  
Stress Analysis ◽  
Coulomb Friction ◽  
High Stress ◽  
Three Dimensional ◽  
Contact Stresses ◽  
Three Dimensions ◽  
Element Analysis ◽  
Friction Laws ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The stress analysis of dovetail attachments presents some challenges. These stem from the high stress gradients present, the contact inequalities attending conforming contact, and the nonlinearities inherent in Coulomb friction laws. Obtaining converged contact stresses in the presence of these phenomena is demanding, especially in three dimensions. In Beisheim and Sinclair (2003, ASME J. Turbomach., 125, pp. 372–379), a submodeling approach with finite elements is employed to meet these challenges when friction is not present. Here we extend this approach to treat contact when friction is present. Converged stresses are obtained by using two successive submodels. Comparing these stresses with two-dimensional analysis elucidates some of the truly three-dimensional aspects of the stress analysis of dovetail attachments. Further comparisons of contact stresses when crowning is added indicate the possible alleviation of fretting fatigue that may be afforded by this means.

Validation of Numerical Analysis to Estimate Airfoil Aerodynamic Characteristics at Low Reynolds Number Region

2015 ◽  
Author(s):  
Donghwi Lee ◽  
Taku Nonomura ◽  
Akira Oyama ◽  
Kozo Fujii
Keyword(s):  
Reynolds Number ◽  
Numerical Method ◽  
Low Reynolds Number ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Eddy Simulation ◽  
Low Reynolds

In this study, two-dimensional laminar simulation (2-D Lam), two-dimensional Reynolds Averaged Navier-Stokes simulation with the Spalart-Allmaras turbulence model (2-D RANS(SA)), and implicit three-dimensional large-eddy simulation (3-D LES) are performed for NACA0012, NACA0006, and Ishii airfoils at Rec = 3.0 × 104. The relation between a predictability of airfoil aerodynamic characteristics and a dependence of airfoil geometry shape of each numerical method is evaluated at the low Reynolds number. Although little discrepancy is observed for the lift coefficient predictability, significant differences are presented in terms of the separation and reattachment points predictability depending on the numerical methods. The 2-D Lam simulation can predict the lift coefficients as well as the separation and reattachment points qualitatively as similar to the 3-D LES results except for the high angle of attack which is accompanied by the massive separation. The 2-D RANS(SA), the weak nonlinearity and stall phenomena for the lift coefficients are observed. A good predictability of the separation point are shown, however, it cannot be estimated the reattachment points due to the trend to predict widely for the separation region. The predictabilities of each numerical method appear regardless of the airfoil shapes.

A Numerical Method to Solve the Static Problem of a Catenary Riser

2004 ◽  
Author(s):  
Lauro Massao Yamada da Silveira ◽  
Clo´vis de Arruda Martins
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Numerical Method ◽  
Order Term ◽  
Three Dimensional ◽  
Static Problem ◽  
Computer Code ◽  
Bending Stiffness ◽  
Two Dimensional ◽  
Cable Model

The static configuration of a catenary riser can be obtained, with a good approximation, by a perfectly flexible cable model. However, such a model cannot deal with all the boundary conditions, as for an ideal cable there is no continuity of curvature at the touchdown point, at the top and at the points where there is change in the submerged weight. At the touchdown region, for instance, the cable model overestimates the maximum curvature. For real risers, the bending stiffness effect is relevant only at small boundary layers around the points where the cable model cannot represent well the curvature continuity. This represents a big problem in the numerical integration of the differential equation of the riser, as the leading order term is very small. One approach that can be adopted is to use firstly a perfect cable model and correct later the results with analytical expressions obtained from a boundary layer method. For a two-dimensional formulation it was already shown that this approach is very good. For a three-dimensional formulation, however, such expressions are very difficult to derive and the problem must be solved numerically. This work presents a numerical method to solve the differential equation of a catenary riser, including the bending stiffness. The results obtained are compared to analytical boundary layer solutions, for a two-dimensional case, and to a full nonlinear well-known commercial computer code.

Sign in / Sign up

Export Citation Format

Share Document