Elastically Mounted Double Aerodynamic Pendulum

2019 ◽  
Vol 19 (05) ◽  
pp. 1941007 ◽  
Author(s):  
Yury D. Selyutskiy ◽  
Andrei P. Holub ◽  
Marat Z. Dosaev
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
State University ◽  
Periodic Motions ◽  
Aeroelastic System ◽  
Subsonic Wind Tunnel ◽  
Trivial Equilibrium ◽  
Rotational Degrees Of Freedom ◽  
Moscow State University

Elastically mounted double aerodynamic pendulum is an aeroelastic system with two rotational degrees of freedom. A wing is attached to the second link of the pendulum. It is shown that it is possible to select values of parameters in such a way as to make the trivial equilibrium (where both links of the pendulum are stretched along the flow) unstable. Numerical simulation of behavior of the system in such situations is performed, and arising limit cycles are studied. Experimental investigation of such aerodynamic pendulum is performed in the subsonic wind tunnel of the Institute of Mechanics of Lomonosov Moscow State University. Characteristics of periodic motions are registered for different values of parameters of the system. It is shown that experimental data are in qualitative agreement with results of numerical simulation.

Relaxation Effects in Small Critical Nozzles

2005 ◽  
Vol 128 (1) ◽  
pp. 170-176
Author(s):  
Aaron N. Johnson ◽  
Charles L. Merkle ◽  
Michael R. Moldover ◽  
John D. Wright
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Critical Flow ◽  
Worst Case ◽  
Relaxation Effects ◽  
Critical Nozzles ◽  
Rotational Degrees Of Freedom ◽  
Computational Fluid Dynamics Cfd ◽  
Flow Through ◽  
Throat Diameter

We computed the flow of four gases (He, N2, CO2, and SF6) through a critical flow venturi (CFV) by augmenting traditional computational fluid dynamics (CFD) with a rate equation that accounts for τrelax, a species-dependent relaxation time that characterizes the equilibration of the vibrational degrees of freedom with the translational and rotational degrees of freedom. Conventional CFD (τrelax=0) underpredicts the flow through small CFVs (throat diameter d=0.593mm) by up to 2.3% for CO2 and by up to 1.2% for SF6. When we used values of τrelax from the acoustics literature, the augmented CFD underpredicted the flow for SF6 by only 0.3%, in the worst case. The augmented predictions for CO2 were within the scatter of previously published experimental data (±0.1%). As expected, both conventional and augmented CFD agree with experiments for He and N2. Thus, augmented CFD enables one to calibrate a small CFV with one gas (e.g., N2) and to use these results as a flow standard with other gases (e.g., CO2) for which reliable values of τrelax and the relaxing heat capacity are available.

scholarly journals On Nonlinear Oscillations of a Near-Autonomous Hamiltonian System in the Case of Two Identical Integer or Half-Integer Frequencies

2021 ◽  
Vol 17 (1) ◽  
pp. 77-102
Author(s):  
O. V. Kholostova ◽  
Keyword(s):  
Hamiltonian System ◽  
Normal Form ◽  
Small Parameter ◽  
Degrees Of Freedom ◽  
Nonlinear Oscillations ◽  
Periodic Motions ◽  
Half Integer ◽  
Stability And Instability ◽  
Trivial Equilibrium ◽  
Two Parameters

This paper examines the motion of a time-periodic Hamiltonian system with two degrees of freedom in a neighborhood of trivial equilibrium. It is assumed that the system depends on three parameters, one of which is small; when it has zero value, the system is autonomous. Consideration is given to a set of values of the other two parameters for which, in the autonomous case, two frequencies of small oscillations of the linearized equations of perturbed motion are identical and are integer or half-integer numbers (the case of multiple parametric resonance). It is assumed that the normal form of the quadratic part of the Hamiltonian does not reduce to the sum of squares, i.e., the trivial equilibrium of the system is linearly unstable. Using a number of canonical transformations, the perturbed Hamiltonian of the system is reduced to normal form in terms through degree four in perturbations and up to various degrees in a small parameter (systems of first, second and third approximations). The structure of the regions of stability and instability of trivial equilibrium is investigated, and solutions are obtained to the problems of the existence, number, as well as (linear and nonlinear) stability of the system’s periodic motions analytic in fractional or integer powers of the small parameter. For some cases, conditionally periodic motions of the system are described. As an application, resonant periodic motions of a dynamically symmetric satellite modeled by a rigid body are constructed in a neighborhood of its steady rotation (cylindrical precession) on a weakly elliptic orbit and the problem of their stability is solved.

scholarly journals Stability Studies of a Coupled Model to Perturbation of Initial Data

2020 ◽  
Vol 23 (4) ◽  
pp. 615-633
Author(s):  
Konstantin Pavlovich Belyaev ◽  
Gury Mikhaylovich Mikhaylov ◽  
Alexey Nikolaevich Salnikov ◽  
Natalia Pavlovna Tuchkova
Keyword(s):  
Numerical Simulation ◽  
Stability Problem ◽  
Initial Conditions ◽  
Coupled Model ◽  
State University ◽  
Stability Studies ◽  
Time Periods ◽  
The Stability ◽  
Moscow State University ◽  
Ensemble Experiments

The stability problem is considered in terms of the classical Lyapunov definition. For this, a set of initial conditions is set, consisting of their preliminary calculations, and the spread of the trajectories obtained as a result of numerical simulation is analyzed. This procedure is implemented as a series of ensemble experiments with a joint MPI-ESM model of the Institute of Meteorology M. Planck (Germany). For numerical modeling, a series of different initial values of the characteristic fields was specified and the model was integrated, starting from each of these fields for different time periods. Изучались экстремальные характеристики уровня океана за период 30 лет. The statistical distribution was built, the parameters of this distribution were estimated, and the statistical forecast for 5 years in advance was studied. It is shown that the statistical forecast of the level corresponds to the calculated forecast obtained by the model. The localization of extreme level values was studied and an analysis of these results was carried out. Numerical calculations were performed on the Lomonosov-2 supercomputer of Lomonosov Moscow State University.

scholarly journals Singularities of integrable Liouville systems, reduction of integrals to lower degree and topological billiards: Recent results

2019 ◽  
Vol 46 (1) ◽  
pp. 47-63 ◽  
Author(s):  
A.T. Fomenko ◽  
V.V. Vedyushkina
Keyword(s):  
Differential Geometry ◽  
Hamiltonian Systems ◽  
Degrees Of Freedom ◽  
Lower Degree ◽  
State University ◽  
Integrable Hamiltonian Systems ◽  
Two Degrees Of Freedom ◽  
Moscow State University

In the paper we present the new results in the theory of integrable Hamiltonian systems with two degrees of freedom and topological billiards. The results are obtained by the authors, their students, and participants of scientific seminars of the Department of Differential Geometry and Applications, Faculty of Mathematics and Mechanics at Lomonosov Moscow State University.

On the Use of Quantum Thermal Bath in Unimolecular Fragmentation Simulations

2019 ◽  
Author(s):  
Riccardo Spezia ◽  
Hichem Dammak
Keyword(s):  
Degrees Of Freedom ◽  
Molecular Simulations ◽  
Zero Point ◽  
Thermal Bath ◽  
Unimolecular Dissociation ◽  
Point Energy ◽  
Rotational Degrees Of Freedom ◽  
The Difference ◽  
Nuclear Effects

<div> <div> <div> <p>In the present work we have investigated the possibility of using the Quantum Thermal Bath (QTB) method in molecular simulations of unimolecular dissociation processes. Notably, QTB is aimed in introducing quantum nuclear effects with a com- putational time which is basically the same as in newtonian simulations. At this end we have considered the model fragmentation of CH4 for which an analytical function is present in the literature. Moreover, based on the same model a microcanonical algorithm which monitor zero-point energy of products, and eventually modifies tra- jectories, was recently proposed. We have thus compared classical and quantum rate constant with these different models. QTB seems to correctly reproduce some quantum features, in particular the difference between classical and quantum activation energies, making it a promising method to study unimolecular fragmentation of much complex systems with molecular simulations. The role of QTB thermostat on rotational degrees of freedom is also analyzed and discussed. </p> </div> </div> </div>

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