scholarly journals Kolmogorov Unstable Stellar Oscillations

1983 ◽  
Vol 66 ◽  
pp. 297-321
Author(s):  
J. Perdang
Keyword(s):  
Numerical Analysis ◽  
Internal Resonance ◽  
Degrees Of Freedom ◽  
High Surface ◽  
Broad Band ◽  
Resonance Effects ◽  
Stellar Oscillations ◽  
Noise Type ◽  
Non Linear ◽  
Equipartition Of Energy

AbstractWe survey the mathematics of non-linear Hamiltonian oscillations with emphasis being laid on the more recently discovered Kolmogorov instability. In the context of radial adiabatic oscillations of stars this formalism predicts a Kolmogorov instability even at low oscillation energies, provided that sufficiently high linear asymptotic modes have been excited.Numerical analysis confirms the occurrence of this instability. It is found to show up already among the lowest order modes, although high surface amplitudes are then required (ǀδrǀ/R ~ 0.5 for an unstable fundamental mode – first harmonic coupling). On the basis of numerical evidence we conjecture that in the Kolmogorov unstable regime the enhanced coupling due to internal resonance effects leads to an equipartition of energy over all interacting degrees of freedom. We also indicate that the power spectrum of such oscillations is expected to display two components: A very broad band of overlapping pseudo-linear frequency peaks spread out over the asymptotic range, and a strictly non-linear 1/f-noise type component close to the frequency origin.It is finally argued that the Kolmogorov instability is likely to occur among non-linearly coupled non-radial stellar modes at a surface amplitude much lower than in the radial case. This lends support to the view that this instability might be operative among the solar oscillations.

An XYZ Parallel Kinematic Flexure Mechanism With Geometrically Decoupled Degrees of Freedom

2011 ◽  
Author(s):  
Shorya Awtar ◽  
John Ustick ◽  
Shiladitya Sen
Keyword(s):  
Degrees Of Freedom ◽  
Element Analysis ◽  
Motion Direction ◽  
Form Analysis ◽  
Flexure Mechanism ◽  
Non Linear ◽  
Decoupled Motion ◽  
Motion Range ◽  
Parallel Kinematic ◽  
Cross Axis

We present the constraint-based design of a novel parallel kinematic flexure mechanism that provides highly decoupled motions along the three translational directions (X, Y, and Z) and high stiffness along the three rotational directions (θx, θy, and θz). The geometric decoupling ensures large motion range along each translational direction and enables integration with large-stroke ground-mounted linear actuators or generators, depending on the application. The proposed design, which is based on a systematic arrangement of multiple rigid stages and parallelogram flexure modules, is analyzed via non-linear finite element analysis. A proof-of-concept prototype of the flexure mechanism is fabricated to validate its large range and decoupled motion capability. The analyses as well as the hardware demonstrate an XYZ motion range of 10 mm × 10 mm × 10 mm. Over this motion range, the non-linear FEA predicts a cross-axis error of less than 3%, parasitic rotations less than 2 mrad, less than 4% lost motion, actuator isolation less than 1.5%, and no perceptible motion direction stiffness variation. Ongoing work includes non-linear closed-form analysis and experimental measurement of these error motion and stiffness characteristics.

A Two-Dimensional Linear Assumed Strain Triangular Element for Finite Deformation Analysis

2005 ◽  
Vol 73 (6) ◽  
pp. 970-976 ◽  
Author(s):  
Fernando G. Flores
Keyword(s):  
Finite Deformation ◽  
Degrees Of Freedom ◽  
Yield Function ◽  
Triangular Element ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Stress Strain ◽  
Metric Tensor ◽  
Assumed Strain ◽  
Non Linear

An assumed strain approach for a linear triangular element able to handle finite deformation problems is presented in this paper. The element is based on a total Lagrangian formulation and its geometry is defined by three nodes with only translational degrees of freedom. The strains are computed from the metric tensor, which is interpolated linearly from the values obtained at the mid-side points of the element. The evaluation of the gradient at each side of the triangle is made resorting to the geometry of the adjacent elements, leading to a four element patch. The approach is then nonconforming, nevertheless the element passes the patch test. To deal with plasticity at finite deformations a logarithmic stress-strain pair is used where an additive decomposition of elastic and plastic strains is adopted. A hyper-elastic model for the elastic linear stress-strain relation and an isotropic quadratic yield function (Mises) for the plastic part are considered. The element has been implemented in two finite element codes: an implicit static/dynamic program for moderately non-linear problems and an explicit dynamic code for problems with strong nonlinearities. Several examples are shown to assess the behavior of the present element in linear plane stress states and non-linear plane strain states as well as in axi-symmetric problems.

Theorical Analysis of Leakage in High Pressure Pipe Using Acoustic Emission Method

2012 ◽  
Vol 445 ◽  
pp. 917-922 ◽  
Author(s):  
Saman Davoodi ◽  
Amir Mostafapour
Keyword(s):  
High Pressure ◽  
Acoustic Emission ◽  
Degrees Of Freedom ◽  
Oil And Gas ◽  
Pipe Wall ◽  
Leak Detection ◽  
Stress Waves ◽  
Motion Equation ◽  
Non Linear ◽  
Acoustic Emission Test

Leak detection is one of the most important problems in the oil and gas pipelines. Where it can lead to financial losses, severe human and environmental impacts. Acoustic emission test is a new technique for leak detection. Leakage in high pressure pipes creates stress waves resulting from localized loss of energy. Stress waves are transmitted through the pipe wall which will be recorded by using acoustic sensor or accelerometer installed on the pipe wall. Knowledge of how the pipe wall vibrates by acoustic emission resulting from leakage is a key parameter for leak detection and location. In this paper, modeling of pipe vibration caused by acoustic emission generated by escaping of fluid has been done. Donnells non linear theory for cylindrical shell is used to deriving of motion equation and simply supported boundary condition is considered. By using Galerkin method, the motion equation has been solved and a system of non linear equations with 6 degrees of freedom is obtained. To solve these equations, ODE tool of MATLAB software and Rung-Kuta numerical method is used and pipe wall radial displacement is obtained. For verification of this theory, acoustic emission test with continues leak source has been done. Vibration of wall pipe was recorded by using acoustic emission sensors. For better analysis, Fast Fourier Transform (FFT) was taken from theoretical and experimental results. By comparing the results, it is found that the range of frequencies which carried the most amount of energy is same which expresses the affectivity of the model.

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