Veering and Strong Coupling Effects in Structural Dynamics

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Elisabetta Manconi ◽  
Brian Mace
Keyword(s):  
Strong Coupling ◽  
Parameter Space ◽  
Structural Dynamics ◽  
Critical Points ◽  
Degrees Of Freedom ◽  
Variable Parameter ◽  
Rate Of Change ◽  
Continuous Systems ◽  
General Terms ◽  
Gyroscopic Coupling

Mode veering is the phenomenon associated with the eigenvalue loci for a system with a variable parameter: two branches approach each other and then rapidly veer away and diverge instead of crossing. The veering is accompanied by rapid variations in the eigenvectors. In this paper, veering in structural dynamics is analyzed in general terms. First, a discrete conservative model with stiffness, mass, and/or gyroscopic coupling is considered. Rapid veering requires weak coupling: if there is instead strong coupling then there is a slow evolution of the eigenvalue loci rather than rapid veering. The uncoupled-blocked system is defined to be that where all degrees-of-freedom (DOFs) but one are blocked. The skeleton of the system is the loci of the eigenvalues of the uncoupled-blocked system as the variable parameter changes. These loci intersect at certain critical points in the parameter space. Following a perturbation analysis, veering is seen to comprise rapid changes of the eigenvalues in small regions of the parameter space around the critical points: for coupling terms of order ε veering occurs in a region of order ε around the critical points, with the rate of change of eigenvalues being of order ε−1. This is accompanied by rapid rotations in the eigenvectors. The choice of coordinates in the model and application to continuous systems is discussed. For nonconservative systems, it is seen that veering also occurs under certain circumstances. Examples of 2DOFs, multi-DOFs (MDOFs), and continuous systems are presented to illustrate the results.

Effective Locality QCD calculations and the Gribov copy problem

2020 ◽  
Vol 35 (27) ◽  
pp. 2050230 ◽  
Author(s):  
T. Grandou ◽  
R. Hofmann
Keyword(s):  
Gauge Field ◽  
Strong Coupling ◽  
Degrees Of Freedom ◽  
Green's Functions ◽  
Green’S Functions ◽  
Strong Coupling Limit ◽  
Unexpected Result ◽  
Remarkable Property ◽  
Gauge Invariant

Standard functional manipulations have been proven to imply a remarkable property satisfied by the fermionic Green’s functions of QCD and dubbed effective locality. Resulting from a full gauge invariant summation of the gauge field degrees of freedom, effective locality is a non-perturbative property of QCD. This unexpected result has lead to suspect that the famous Gribov copy problem had been somewhat overlooked. It is argued that it is not so. The analysis is conducted in the strong coupling limit, relevant to the Gribov problem.

Transverse Vibrations of Cantilever Beams Having Unequal Breadth and Depth Tapers

1977 ◽  
Vol 44 (4) ◽  
pp. 737-742 ◽  
Author(s):  
B. Downs
Keyword(s):  
Stress Distribution ◽  
Cross Section ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Natural Frequencies ◽  
Distribution Patterns ◽  
Continuous Systems ◽  
Cantilever Beams ◽  
Transverse Vibrations ◽  
Discretization Technique

Natural frequencies of doubly symmetric cross section, isotropic cantilever beams, based on both Euler and Timoshenko theories, are presented for 36 combinations of linear depth and breadth taper. Results obtained by a new dynamic discretization technique include the first eight frequencies for all geometries and the stress distribution patterns for the first four (six) modes in the case of the wedge. Comparisons are drawn wherever possible with exact solutions and with other numerical results appearing in the literature. The results display outstanding accuracy and demonstrate that it is possible to model with high precision the dynamic behaviour of continuous systems by discretization on to a strictly limited number of degrees of freedom.

scholarly journals Design and Analysis of a 5-Axis Gantry CNC Machine Tool

2020 ◽  
Vol 318 ◽  
pp. 01019
Author(s):  
Esra Yuksel ◽  
Emre Özlü ◽  
Ahmet Oral ◽  
Fulya Tosun ◽  
Osman Fatih İğrek ◽  
...  
Keyword(s):  
Machine Tool ◽  
Structural Dynamics ◽  
Critical Points ◽  
Fe Analysis ◽  
Cnc Machine Tool ◽  
Heavy Duty ◽  
Cnc Machine ◽  
Velocity Measurements ◽  
Final Performance ◽  
Measurement Results

In this study, design and analysis of a gantry-type 5-axis CNC machine tool is presented with experimental results on a manufactured prototype. Critical points in the design of a large-scaled and heavy-duty machine tool is discussed. Moreover, FE analysis results is also presented with detailed discussion. The measurement results on structural dynamics is shown together with the FE results. Furthermore, the final performance of the machine tool is demonstrated thorough position and velocity measurements of the axes.

scholarly journals On the Emergence of the Microcanonical Description from a Pure State

2003 ◽  
Vol 18 (17) ◽  
pp. 2947-2993 ◽  
Author(s):  
N. D. Hari Dass ◽  
S. Kalyana Rama ◽  
B. Sathiapalan
Keyword(s):  
Pure State ◽  
Degrees Of Freedom ◽  
Coarse Graining ◽  
Resonant Absorption ◽  
Decay Rates ◽  
Quantum Mechanical ◽  
Classical Statistical Mechanics ◽  
General Terms ◽  
Black Hole Information ◽  
Usual Formalism

We study, in general terms, the process by which a pure state can "self-thermalize" and appear to be described by a microcanonical density matrix. This requires a quantum mechanical version of the Gibbsian coarse graining that conceptually underlies classical statistical mechanics. We make use of some extra degrees of freedom that are necessary for this. Interaction between these degrees and the system can be understood as a process of resonant absorption and emission of "soft quanta." This intuitive picture allows one to state a criterion for when self thermalization occurs. This paradigm also provides a method for calculating the thermalization rate using the usual formalism of atomic physics for calculating decay rates. We contrast our prescription for coarse graining, which is somewhat dynamical, with the earlier approaches that are intrinsically kinematical. An important motivation for this study is the black hole information paradox.

scholarly journals BROAD HISTOGRAM METHOD FOR CONTINUOUS SYSTEMS: THE XY-MODEL

1999 ◽  
Vol 10 (01) ◽  
pp. 95-113 ◽  
Author(s):  
JOSÉ D. MUÑOZ ◽  
HANS J. HERRMANN
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Large Temperature ◽  
Xy Model ◽  
Continuous Systems ◽  
Histogram Method ◽  
Temperature Range ◽  
Cpu Time

We propose a way of implementing the Broad Histogram Monte Carlo method to systems with continuous degrees of freedom, and we apply these ideas to investigate the three-dimensional XY-model with periodic boundary conditions. We have found an excellent agreement between our method and traditional Metropolis results for the energy, the magnetization, the specific heat and the magnetic susceptibility on a very large temperature range. For the calculation of these quantities in the temperature range 0.7<T<4.7 our method took less CPU time than the Metropolis simulations for 16 temperature points in that temperature range. Furthermore, it calculates the whole temperature range 1.2<T<4.7 using only 2.2 times more computer effort than the Histogram Monte Carlo method for the range 2.1<T<2.2. Our way of treatment is general; it can also be applied to other systems with continuous degrees of freedom.

Interpolated mappings for musical instruments

2002 ◽  
Vol 7 (2) ◽  
pp. 85-96 ◽  
Author(s):  
Camille Goudeseune
Keyword(s):  
Degrees Of Freedom ◽  
Cross Coupling ◽  
Musical Instruments ◽  
Rate Of Change ◽  
Synthesis Parameter ◽  
Proportional Integral ◽  
Synthesis Parameters ◽  
Derivative Control

Software-based musical instruments have controls for input, a sound synthesizer for output, and mappings connecting the two. An effective layout of controls considers how many degrees of freedom each has, as well as the overhead of selecting each one while performing. An isolated mapping from one control to one synthesis parameter needs an appropriate choice of proportional, integral or derivative control (the control's value, or that value's rate of change, drives the synthesis parameter's value, or that value's rate of change). Beyond this, a compound mapping cross-coupling several controls and synthesis parameters can surprisingly increase the performer's intuitive understanding of the instrument.

Sign in / Sign up

Export Citation Format

Share Document