Non-Linear Dynamic Stability of Shallow Reticulated Spherical Shells

2011 ◽  
Vol 142 ◽  
pp. 107-110
Author(s):  
Ming Jun Han ◽  
You Tang Li ◽  
Ping Qiu ◽  
Xin Zhi Wang
Keyword(s):  
Three Dimensional ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Linear Dynamic ◽  
The Third ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

Non-Linear Dynamic Characteristics of Single-Layer Shallow Reticulated Spherical Shells

2013 ◽  
Vol 303-306 ◽  
pp. 2794-2797
Author(s):  
Zhen Yang ◽  
Yu Lian Chen ◽  
Ming Jun Han
Keyword(s):  
Three Dimensional ◽  
Single Layer ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Floquet Exponent ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

Equilibrium and Stability of a Three-Dimensional Toroidal MHD Configuration Near its Magnetic Axis

1976 ◽  
Vol 31 (11) ◽  
pp. 1277-1288 ◽  
Author(s):  
D. Lortz ◽  
J. Nührenberg
Keyword(s):  
Three Dimensional ◽  
Magnetic Axis ◽  
Stability Criteria ◽  
Sufficient Criterion ◽  
Third Order ◽  
Stagnation Points ◽  
The Third ◽  
Longitudinal Current ◽  
The Stability

Abstract The expansion of a three-dimensional toroidal magnetohydrostatic equilibrium around its magnetic axis is reconsidered. Equilibrium and stability plasma-β estimates are obtained in connection with a discussion of stagnation points occurring in the third-order flux surfaces. The stability criteria entering the β-estimates are: (i) a necessary criterion for localized disturbances, (ii) a new sufficient criterion for configurations without longitudinal current. Hamada coordinates are used to evaluate these criteria.

Synthesis and third-order nonlinear optical properties of novel ethynyl-linked heteropentamer composed of four porphyrins and one pyrene

2009 ◽  
Vol 13 (02) ◽  
pp. 275-282 ◽  
Author(s):  
Ning Sheng ◽  
Jing Sun ◽  
Yongzhong Bian ◽  
Jianzhuang Jiang ◽  
Dong Xu
Keyword(s):  
Optical Properties ◽  
Nonlinear Optical ◽  
Three Dimensional ◽  
Spectroscopic Methods ◽  
Third Order ◽  
Zinc Compounds ◽  
Nlo Properties ◽  
Metal Free ◽  
The Third ◽  
Wide Range

Novel heteropentameric porphyrins-pyrene arrays, in which four meso-tetraphenyl porphyrins are linked to the center unit of pyrene by four acetylenyl bonds, were designed and synthesized. The newly synthesized heteropentameric compounds have been characterized by a wide range of spectroscopic methods. The third-order nonlinear optical (NLO) properties of both the metal-free and zinc compounds of the three-dimensional arrays were investigated by Z-scan experiments, showing enhanced NLO properties compared with that of the porphyrin and pyrene monomers.

scholarly journals Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yingguo Li
Keyword(s):  
Neural Network ◽  
Time Delay ◽  
Recurrent Neural Network ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Nonlinear Dynamical ◽  
Bifurcation Direction ◽  
The Stability ◽  
Manifold Theory

We consider the nonlinear dynamical behavior of a three-dimensional recurrent neural network with time delay. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Applying the nor- mal form method and center manifold theory, we obtain some local bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution. Some numerical examples are also presented to verify the theoretical analysis.

MODULATION STABILITY OF WAVE PACKETS IN A THREE-LAYER HYDRODYNAMIC SYSTEM

2019 ◽  
pp. 30-35
Author(s):  
O. Avramenko ◽  
M. Lunyova
Keyword(s):  
Order Approximation ◽  
Wave Packets ◽  
Stability Diagram ◽  
Third Order ◽  
Weakly Nonlinear ◽  
The Third ◽  
Hydrodynamic System ◽  
Contact Surfaces ◽  
The Stability ◽  
Third Order Approximation

The article is devoted to the problem of propagation of weakly nonlinear wave-packets along contact surfaces in a three-layer hydrodynamic system "half space – layer – layer with rigid lid". The condition of solvability of the problem in the third-order approximation is obtained, the evolution equation is derived in the form of a nonlinear Schrodinger equation and the modulation stability condition for its solutions is obtained. The stability diagram and its analysis are presented for the solution which takes place in the case of the balance between dispersion and non-linearity.

Stability of the High-Speed Journal Bearing Under Steady Load: 2—The Compressible Film

1963 ◽  
Vol 85 (3) ◽  
pp. 274-279 ◽  
Author(s):  
H. S. Cheng ◽  
P. R. Trumpler
Keyword(s):  
Equilibrium Position ◽  
High Speed ◽  
Equilibrium Solution ◽  
Journal Bearing ◽  
Analog Computer ◽  
Dynamical Equations ◽  
Nonlinear Dynamical ◽  
Linearized Equations ◽  
Stability Chart ◽  
The Stability

The governing equations for the dynamical system of a self-acting gas-lubricated journal bearing are formulated. An approximate solution for the equilibrium position of the journal center is obtained by use of Galerkin’s method. The equilibrium solution shows close agreement with the exact numerical computer solution obtained by Elrod. The stability of the equilibrium solution is investigated by solving the linearized equations on an analog computer. The solution of the set of linearized equations shows that there exists a threshold speed of instability for each equilibrium position. The value of this threshold speed is presented in a stability chart. In addition, approximate particular solutions for the nonlinear dynamical equations are obtained by use of the analog computer. The results are shown as trajectories of the journal center when it is displaced arbitrarily from the equilibrium position.

scholarly journals Детально-сравнительный анализ взаимодействия сверхзвукового потока с поперечной газовой струей при больших параметрах нерасчетности

2019 ◽  
Vol 89 (10) ◽  
pp. 1513
Author(s):  
А.О. Бекетаева ◽  
P. Bruel ◽  
А.Ж. Найманова
Keyword(s):  
Gas Flow ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Mach Disk ◽  
Navier Stokes ◽  
Third Order ◽  
Navier Stokes Equations ◽  
The Third ◽  
Eno Scheme

The interaction of the spatial supersonic turbulent gas flow with a sound jet injected perpendicularly was widely studied both numerically and experimentally. However, there are only a few studies of the detail analysis of the formation and distribution of vortex structures from moderate till high pressure ratio (the ratio of pressure in the jet to pressure in the main flow).The aim of this paper is the study and identify the system of the vortex forming behind the injected sound jet in a transverse supersonic flow from the point of view of the mixing efficiency. For that the three-dimensional Favre-averaged Navier-Stokes equations, coupled with the turbulence model are solved numerically on the basis of the third-order ENO scheme. The three-dimensional Favre-averaged Navier-Stokes equations, coupled with the turbulence model are solved numerically on the basis of the third-order ENO scheme. The presence of well known vortex structures are shown: two oppositely rotating vortices in front of the jet; horseshoe vortex; two pairs of the vortex in the mixing zone of the jet and the main flow, where one of them is located in the wake behind the jet and other in the lateral line of the jet. Also, the pressure ratio parameters are determined at which the additional pairs of vortices appear. Where, the first of them is formed on the edge of the Mach disk as a result of the interaction of the decelerated jet flow behind the Mach disk with the high-speed ascending flow behind the barrel. And, the second is due to the interaction of the ascending jet flow with the main gas flow. As a result of comparative analysis the criterion of the pressure ratio parameters are found under which a clear picture of additional horn vortices is observed near the wall in the region behind the jet. The graph of the dependence of the angle of inclination of the bow shock wave on the parameter of pressure ratio is obtained. Satisfactory agreement of the pressure distribution on the wall in front of the jet in the symmetry plane with experimental data is established.

scholarly journals Economical factorized schemes for third-order pseudoparabolic equations

2021 ◽  
pp. 44-57
Author(s):  
Мурат Хамидбиевич Бештоков
Keyword(s):  
General Theory ◽  
Parabolic Equations ◽  
Difference Schemes ◽  
Stability And Convergence ◽  
Third Order ◽  
The Third ◽  
Stability Of Difference Schemes ◽  
The Stability ◽  
Pseudoparabolic Equations

Изучены экономичные факторизованные схемы для псевдопараболических уравнений третьего порядка. На основе общей теории устойчивости разностных схем доказаны устойчивость и сходимость разностных схем. Economical factorized schemes for pseudo-parabolic equations of the third order are studied. On the basis of the general theory of stability of difference schemes, the stability and convergence of difference schemes are proved.

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