scholarly journals Resonance Zones in Action Space

2001 ◽  
Vol 56 (8) ◽  
pp. 537-556
Author(s):  
Jan Wiersig
Keyword(s):  
Degrees Of Freedom ◽  
Lattice Structure ◽  
Invariant Tori ◽  
Action Space ◽  
Cubic Lattices ◽  
Resonance Zone ◽  
Level Statistics ◽  
Energy Surfaces ◽  
Good Agreement ◽  
03.65 Sq

Abstract The classical and quantum mechanics of isolated, nonlinear resonances in integrable systems with N ≥ 2 degrees of freedom is discussed in terms of geometry in the space of action vari­ ables. Energy surfaces and frequencies are calculated and graphically presented for invariant tori inside and outside the resonance zone. The quantum mechanical eigenvalues, computed in the sem iclassical WKB approximation, show a regular pattern when transformed into the action space of the associated symmetry reduced system: eigenvalues inside the resonance zone are arranged on iV-dimensional cubic lattices, whereas those outside are, in general, non-periodically distributed. However, TV-dimensional triclinic (skewed) lattices exist locally. Both kinds of lattices are joined smoothly across the classical separatrix surface. The statements are illustrated with the help of two and three coupled rotors. The energy-level statistics of this system are found numerically to be in very good agreement with the Poisson distribution, despite of the complex lattice structure. PACS: 03.65.Sq, 05.45.-a

ELLIPSOIDAL BILLIARDS WITH ISOTROPIC HARMONIC POTENTIALS

2000 ◽  
Vol 10 (09) ◽  
pp. 2075-2098 ◽  
Author(s):  
JAN WIERSIG
Keyword(s):  
Harmonic Oscillator ◽  
Energy Dependence ◽  
Invariant Tori ◽  
Low Energy ◽  
Action Space ◽  
Harmonic Potential ◽  
Classical Dynamics ◽  
Isotropic Harmonic Oscillator ◽  
Energy Surfaces ◽  
Action Variables

The classical dynamics of the triaxial ellipsoidal billiard with isotropic harmonic potential attracting to the center of the ellipsoid is discussed. The integrability preserving potential introduces an energy dependence to the foliation of energy shells into invariant tori. This foliation and the character of the corresponding motion is described in terms of 13 qualitatively different energy surfaces in the space of the action variables. Frequencies and the location of resonances are calculated. The consequences of the superintegrability of the low-energy case, the isotropic harmonic oscillator, for the energy surfaces in action space are investigated.

Estimation of the Thermodynamic Properties of Branched Hydrocarbons

2000 ◽  
Vol 122 (3) ◽  
pp. 147-152 ◽  
Author(s):  
Hui He ◽  
Mohamad Metghalchi ◽  
James C. Keck
Keyword(s):  
Thermodynamic Properties ◽  
Degrees Of Freedom ◽  
Statistical Thermodynamic ◽  
Motion Modes ◽  
Branched Alkanes ◽  
Branched Hydrocarbons ◽  
Wide Range ◽  
On Line ◽  
Kinetic Calculations ◽  
Good Agreement

A simple model has been developed to estimate the sensible thermodynamic properties such as Gibbs free energy, enthalpy, heat capacity, and entropy of hydrocarbons over a wide range of temperatures with special attention to the branched molecules. The model is based on statistical thermodynamic expressions incorporating translational, rotational and vibrational motions of the atoms. A method to determine the number of degrees of freedom for different motion modes (bending and torsion) has been established. Branched rotational groups, such as CH3 and OH, have been considered. A modification of the characteristic temperatures for different motion mode has been made which improves the agreement with the exact values for simple cases. The properties of branched alkanes up to 2,3,4,-trimthylpentane have been calculated and the results are in good agreement with the experimental data. A relatively small number of parameters are needed in this model to estimate the sensible thermodynamic properties of a wide range of species. The model may also be used to estimate the properties of molecules and their isomers, which have not been measured, and is simple enough to be easily programmed as a subroutine for on-line kinetic calculations. [S0195-0738(00)00902-X]

Bending stiffness of circular multilayer van der Waals material sheets

2022 ◽  
pp. 1-36
Author(s):  
Xiaojie Ma ◽  
Luqi Liu ◽  
Zhong Zhang ◽  
Yueguang Wei
Keyword(s):  
Lattice Structure ◽  
Van Der Waals ◽  
Bending Stiffness ◽  
Quantitative Prediction ◽  
Young’S Moduli ◽  
Different Types ◽  
Interlayer Shear Strength ◽  
Isometric Deformations ◽  
Good Agreement ◽  
Sinusoidal Function

Abstract We study the bending stiffness of symmetrically bent circular multilayer van der Waals (vdW) material sheets, which corresponds to the non-isometric configuration in bulge tests. Frenkel sinusoidal function is employed to describe the periodic interlayer tractions due to the lattice structure nature and the bending stiffness of sheets is theoretically extracted via an energetic consideration. Our quantitative prediction shows good agreement with recent experimental results, where the bending stiffness of different types of sheets with the comparable thickness could follow a trend opposite to their Young's moduli. Based on our model, we propose that this trend may experience a transition as the thickness decreases. Apart from the apparent effects of Young's modulus and interlayer shear strength, the interlayer distance is also found to have an important impact on the bending stiffness. In addition, according to our analysis on the size effect, the bending stiffness of such symmetrically bent circular sheets can steadily own a relatively large value, in contrast to the cases of isometric deformations.

Adhesion Force Between High Energy Surfaces in Vapor Atmosphere

1994 ◽  
Vol 366 ◽  
Author(s):  
Jerome Crassous ◽  
Jean-Luc Loubet ◽  
Elisabeth Charlaix
Keyword(s):  
Liquid Bridge ◽  
Adhesion Force ◽  
Van Der Waals ◽  
Surface Force ◽  
High Energy ◽  
Attractive Force ◽  
Experimental Measurements ◽  
Metallic Substrates ◽  
Energy Surfaces ◽  
Good Agreement

ABSTRACTWe report experimental measurements of the adhesion force between metallic substrates in undersaturated heptane vapor atmosphere, with a surface force apparatus. The attractive force between the substrates is strongly dependant of the condensation of a liquid bridge connecting the surfaces. The results show the importance of wetting phenomena for the maximum attractive force: we find that this maximum attraction varies as the power two-third of the curvature of the meniscus connecting the surfaces, in good agreement with the theory of Van der Waals wetting.

Modeling of Multibody Flexible Articulated Structures With Mutually Coupled Motions: Part II — Application and Results

1992 ◽  
Author(s):  
Jiechi Xu ◽  
Joseph R. Baumgarten
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Open Loop ◽  
Body Motion ◽  
Universal Joint ◽  
Open Loop System ◽  
Numerical Examples ◽  
Kinematic Properties ◽  
Good Agreement

Abstract The application of the systematic procedures in the derivation of the equations of motion proposed in Part I of this work is demonstrated and implemented in detail. The equations of motion for each subsystem are derived individually and are assembled under the concept of compatibility between the local kinematic properties of the elastic degrees of freedom of those connected elastic members. The specific structure under consideration is characterized as an open loop system with spherical unconstrained chains being capable of rotating about a Hooke’s or universal joint. The rigid body motion, due to two unknown rotations, and the elastic degrees of freedom are mutually coupled and influence each other. The traditional motion superposition approach is no longer applicable herein. Numerical examples for several cases are presented. These simulations are compared with the experimental data and good agreement is indicated.

Dynamic Characteristics of TEHD Tilt Pad Journal Bearing Simulation Including Multiple Mode Pad Flexibility Model

1993 ◽  
Author(s):  
Jinsang Kim ◽  
Alan Palazzolo
Keyword(s):  
Heat Transfer ◽  
Elastic Deformation ◽  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Variable Viscosity ◽  
Global Analysis ◽  
Analysis Method ◽  
Stiffness And Damping ◽  
Modal Coordinates ◽  
Good Agreement

Abstract An approach for incorporating the heat transfer and elastic deformation effects into dynamic coefficient calculation is presented. A global analysis method is used, which finds the equilibrium pad tilt angles at each eccentricity position and includes cross-film variable viscosity, heat transfer effects in the lubricant, elastic deformation, heat conduction effects in the pads, and elastic deformation effect in the pivots. Deflection modes are used to approximate deformation of the top surface of the pads. The dynamic coefficients of a single pad are calculated at the equilibrium state of the bearing, based on numerical perturbation with respect to the bearing degrees of freedom. These include journal position, pad rotation, pivot deformation, and modal coordinates. The stiffness and damping coefficients are calculated and show very good agreement with experimental and numerical results from the existing literature.

scholarly journals Response of a Warped Flexible Rotor with a Fluid Bearing

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Jim Meagher ◽  
Xi Wu ◽  
Chris Lencioni
Keyword(s):  
Experimental Data ◽  
Analytical Model ◽  
Degrees Of Freedom ◽  
Journal Bearing ◽  
Equation Of Motion ◽  
Diagnostic Information ◽  
Flexible Rotor ◽  
Vibration Data ◽  
Rotor Model ◽  
Good Agreement

A two-complex-degrees-of-freedom model is developed and compared to experimental data for various amounts of rotor bow and its orientation to mass imbalance of the rotor. The equation of motion is developed by adding constant forces that rotate with the rotor to a Bently-Muszynska two-mode isotropic rotor model with a plane journal bearing. Diagnostic information discernable from probes at the bearing is explored and compared to midspan response, where previous research has concentrated. The model presented also extends earlier work by representing the effect of a nonrigid bearing. Good agreement between the analytical model and experiment demonstrates that the analysis presented can be useful to diagnose and balance residual shaft bow from probes located at the bearings, where vibration data are typically more available than midspan probes.

A nuclear phenomenological study of the even–even Thorium Isotopes 228–232Th

2018 ◽  
Vol 27 (05) ◽  
pp. 1850040 ◽  
Author(s):  
S. B. Doma ◽  
H. S. El-Gendy
Keyword(s):  
Potential Energy Surfaces ◽  
Phenomenological Study ◽  
Transition Probability ◽  
Phenomenological Approach ◽  
Vibrational Energies ◽  
Boson Model ◽  
Electric Transition ◽  
Energy Surfaces ◽  
Good Agreement ◽  
Thorium Isotopes

The rotational and vibrational energies and the electric transition probability B [Formula: see text] of the even–even [Formula: see text]Th isotopes are studied empirically in framework of a nuclear phenomenological approach by using the SU(3) dynamical symmetries of the Interacting Boson Model-1 (IBM-1). Furthermore, the potential energy surfaces for these isotopes are plotted as functions of the deformation parameters [Formula: see text] and [Formula: see text]. Moreover, we introduce empirical fit formulas for rotational and vibrational energies, which used to calculate these energies for the thorium isotopes. The obtained results by applying the IBM-1 and the authors’ formulas are in good agreement with the corresponding experimental data for most of the nuclear states.

Prediction of Blade Flutter in a Tuned Rotor

1985 ◽  
Author(s):  
Jianmin Xu ◽  
Zhaohong Song
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Rotating Blades ◽  
Multiple Degrees Of Freedom ◽  
Strip Theory ◽  
Blade Flutter ◽  
Good Agreement

This paper is about blade flutter in a tuned rotor. With the aid of the combination of three dimensional structural finite element method, two dimensional aerodynamical finite difference method and strip theory, the quasi-steady models in which two degrees of freedom for a single wing were considered have been extended to multiple degrees of freedom for the whole blade in a tuned rotor. The eigenvalues solved from the blade motion equation have been used to judge whether the system is stable or not. The calculating procedure has been formed and using it the first stage rotating blades of a compressor where flutter had occurred, have been predicted. The numerical flutter boundaries have good agreement with the experimental ones.

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