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.

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.

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.

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.

Structural Design and Analysis of Aluminum Dome for Caofeidian Coal Storage

2016 ◽  
Vol 710 ◽  
pp. 396-401 ◽  
Author(s):  
Ze Chao Zhang ◽  
Hong Bo Liu ◽  
Xiao Dun Wang ◽  
Xiang Yu Yan ◽  
Jing Hai Yu ◽  
...  
Keyword(s):  
Finite Element ◽  
Aluminum Alloys ◽  
Three Dimensional ◽  
Single Layer ◽  
Element Model ◽  
Internal Force ◽  
Structural Deformation ◽  
Mode Analysis ◽  
Finite Element Software ◽  
The Stability

The upper part of Caofeidian coal storage was approximately hemispherical aluminum shell, covered with aluminum alloys plate. The capsule was made of aluminum alloys material, and its span was 125 meters. In the design, according to TEMCOR joint, we used the finite element software MIDAS to build the accurate geometry models and calculation models of aluminum alloys single layer latticed dome structures. By the combination of constant loads, live loads, snow load, wind load, temperature effect and other working conditions, we summarized the consumption of aluminum of the structures, and studied the structural internal force, structural deformation and structural stiffness. In addition, the X and Y two different direction seismic dynamic load was applied to the structure. The structural seismic performance under two kinds of modes were studied through the structure mode analysis of the vibration frequency. The vierendeel dome and single layer dome were controlled by the stability. ANSYS three-dimensional frame element model were set up, and the eigenvalue buckling analysis was carried out. By the geometrical nonlinear finite element method, combining with initial imperfections and material nonlinear, we found out the stability coefficient and the weak parts of the structure.

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.

Complex model ultra-short pulses in optical fibers via generalized third-order nonlinear Schrödinger dynamical equation

2020 ◽  
Vol 34 (17) ◽  
pp. 2050143
Author(s):  
Aly R. Seadawy ◽  
Naila Nasreen ◽  
Dianchen Lu
Keyword(s):  
Optical Fibers ◽  
Three Dimensional ◽  
Current Method ◽  
Dark Soliton ◽  
Complex Model ◽  
Contour Plot ◽  
Dynamical Equations ◽  
Third Order ◽  
Short Pulses ◽  
Nonlinear Schrödinger

In this paper, several types of solitons such as dark soliton, bright soliton, periodic soliton, kink soliton and solitary waves in three-dimensional and two-dimensional contour plot have been derived for the generalized third-order nonlinear Schrödinger dynamical equations (NLSEs). The generalized third-order NLSE is a significant model ultra-short pulses in optical fibers. The computational work and outcomes achieved show the influence and efficiency of current method. Furthermore, we can solve many other higher-order NLSEs with the help of simple and effective technique.

A Numerical Study of Flutter in a Transonic Fan

1998 ◽  
Vol 120 (3) ◽  
pp. 500-507 ◽  
Author(s):  
K. Isomura ◽  
M. B. Giles
Keyword(s):  
Cfd Simulation ◽  
Numerical Study ◽  
Three Dimensional ◽  
Third Order ◽  
Blade Vibration ◽  
Pressure Surface ◽  
Dominant Component ◽  
Bending Mode ◽  
The Stability ◽  
Transonic Fan

The bending mode Flutter of a modern transonic fan has been studied using a quasi-three-dimensional viscous unsteady CFD code. The type of flutter in this research is that of a highly loaded blade with a tip relative Mach number just above unity, commonly referred to as transonic stall flutter. This type of Flutter is often encountered in modern wide chord fans without a part span shroud. The CFD simulation uses an upwinding scheme with Roe’s third-order flux differencing, and Johnson and King’s turbulence model with the later modification due to Johnson and Coakley. A dynamic transition point model is developed using the en method and Schubauer and Klebanoff’s experimental data. The calculations of the flow in this fan reveal that the source of the flutter of IHI transonic fan is an oscillation of the passage shock, rather than a stall. As the blade loading increases, the passage shock moves forward. Just before the passage shock unstarts, the stability of the passage shock decreases, and a small blade vibration causes the shock to oscillate with a large amplitude between unstarted and started positions. The dominant component of the blade excitation force is due to the foot of the oscillating passage shock on the blade pressure surface.

ON THE ONSET OF QUASI-PERIODIC SOLUTIONS IN THIRD-ORDER NONLINEAR DYNAMICAL SYSTEMS

2005 ◽  
Vol 15 (10) ◽  
pp. 3165-3180 ◽  
Author(s):  
R. GENESIO ◽  
C. GHILARDI
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Nonlinear Dynamical Systems ◽  
General Relation ◽  
Three Dimensional ◽  
Third Order ◽  
Van Der Pol ◽  
Nonlinear Dynamical ◽  
Classical Systems

The paper considers the existence of quasi-periodic solutions in three-dimensional systems. Since these solutions commonly arise as a consequence of a Neimark–Sacker bifurcation of a limit cycle, a fairly general relation connected to this phenomenon is pointed out as the main result of the paper. Then, the application of harmonic balance techniques makes possible to exploit such a relation. In particular, a simplified condition denoting the quasi-periodicity onset can be derived, in making evident the main elements for this transition in terms of structure and parameters, and hence some remarks on the features of the interested systems. Several examples show the application of the above condition to detect "tori" in the state space in a qualitative (not simply numerical) way. They consider classical systems — Rössler, where such behavior seems to be unknown, Chua, forced Van der Pol — and new quadratic systems.

scholarly journals Coupled Nonlinear Dynamics in the Three-Mode Integrable System on a Regular Chain

2021 ◽  
Vol 66 (7) ◽  
pp. 601
Author(s):  
O.O. Vakhnenko
Keyword(s):  
Linear Problem ◽  
Hamiltonian Formulation ◽  
Dynamical Equations ◽  
Third Order ◽  
Nonlinear Dynamical ◽  
One Dimensional ◽  
Zero Curvature Representation ◽  
Coupled Subsystems ◽  
Regular Chain ◽  
Auxiliary Linear Problem

The article suggests the nonlinear lattice system of three dynamical subsystems coupled both in their potential and kinetic parts. Due to its essentially multicomponent structure the system is capable to model nonlinear dynamical excitations on regular quasi-one-dimensional lattices of various physical origins. The system admits a clear Hamiltonian formulation with the standard Poisson structure. The alternative Lagrangian formulation of system’s dynamics is also presented. The set of dynamical equations is integrable in the Lax sense, inasmuch as it possesses a zero-curvature representation. Though the relevant auxiliary linear problem involves a spectral third-order operator, we have managed to develop an appropriate two-fold Darboux–Backlund dressing technique allowing one to generate the nontrivial crop solution embracing all three coupled subsystems in a rather unusual way.

Characterization of a monolayer graphitic structure

1994 ◽  
Vol 52 ◽  
pp. 760-761
Author(s):  
X. Lin ◽  
X. K. Wang ◽  
V. P. Dravid ◽  
J. B. Ketterson ◽  
R. P. H. Chang
Keyword(s):  
Three Dimensional ◽  
Single Layer ◽  
Synthesis Process ◽  
Graphitic Structure ◽  
Positive Gaussian Curvature ◽  
Graphitic Sheet ◽  
Structural And Electronic Properties ◽  
New Material ◽  
Hexagonal Network

For small curvatures of a graphitic sheet, carbon atoms can maintain their preferred sp2 bonding while allowing the sheet to have various three-dimensional geometries, which may have exotic structural and electronic properties. In addition the fivefold rings will lead to a positive Gaussian curvature in the hexagonal network, and the sevenfold rings cause a negative one. By combining these sevenfold and fivefold rings with sixfold rings, it is possible to construct complicated carbon sp2 networks. Because it is much easier to introduce pentagons and heptagons into the single-layer hexagonal network than into the multilayer network, the complicated morphologies would be more common in the single-layer graphite structures. In this contribution, we report the observation and characterization of a new material of monolayer graphitic structure by electron diffraction, HREM, EELS.The synthesis process used in this study is reported early. We utilized a composite anode of graphite and copper for arc evaporation in helium.

Sign in / Sign up

Export Citation Format

Share Document