Experimental and Numerical Analyses for Auto-Parametric Internal Resonance of a Framed Structure

2020 ◽  
pp. 2150012
Author(s):  
Yuchun Li ◽  
Wei Liu ◽  
Chao Shen ◽  
Xiaojun Yang
Keyword(s):  
Internal Resonance ◽  
Vibration Exciter ◽  
Engineering Structures ◽  
Periodic Force ◽  
Stability Boundaries ◽  
Horizontal Beam ◽  
Resonance Response ◽  
Vertical Beam ◽  
The Common ◽  
The Stability

The auto-parametric internal resonance experiment of a [Formula: see text]-shaped frame is first conducted in this research. A non-contact electromagnetic vibration exciter is used to exert a periodic force on the vertical beam of the frame. The phenomena of internal resonance and non-internal resonance are observed and measured in this test. A common resonance of the vertical beam is excited by the external electromagnetic force, and the auto-parametric internal resonance of the horizontal beam is subsequently induced by the common resonance. The numerical method is also used to simulate the internal resonance and non-internal resonance. The stability boundaries of internal resonance and non-internal resonance are numerically and experimentally determined and compared. The numerical stability boundaries are in agreement with the experimental results. The results indicate that a small external excitation can excite a strong internal resonance response of a framed structure. The unstable domain of the internal resonance is much bigger than that of the non-internal resonance. The auto-parametric internal resonance is much more dangerous than the non-internal resonance. The risk of auto-parametric internal resonance should be emphasized and avoided in the designs of engineering structures.

Dynamic Stability of Poroelastic Columns

1999 ◽  
Vol 67 (2) ◽  
pp. 360-362 ◽  
Author(s):  
G. Cederbaum
Keyword(s):  
Dynamic Stability ◽  
Multiple Scales ◽  
Transversely Isotropic ◽  
Axial Direction ◽  
Periodic Force ◽  
Stability Boundaries ◽  
Coupled Equations ◽  
Column Material ◽  
The Stability ◽  
Fluid Diffusion

The dynamic stability of a poroelastic column subjected to a longitudinal periodic force is investigated. The column material is assumed to be transversely isotropic with respect to the column axis, and the pore fluid flow is possible in the axial direction only. The motion of the column is governed by two coupled equations, for which the stability boundaries are determined analytically by using the multiple-scales method. It is shown that due to the fluid diffusion the stability regions are expanded, relative to the elastic (drained) case. The critical (minimum) loading amplitude, for which instability occurs, is also given. [S0021-8936(00)00902-8]

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

Soil Strength Reduction Method Induced by Variation of Water Content

2012 ◽  
Vol 170-173 ◽  
pp. 847-852
Author(s):  
Peng Ming Jiang ◽  
Zhong Lei Yan ◽  
Peng Li
Keyword(s):  
Slope Stability ◽  
Unsaturated Soil ◽  
Unsaturated Soils ◽  
Characteristic Curve ◽  
Strength Reduction ◽  
Actual State ◽  
Soil Slope ◽  
Simple Method ◽  
The Common ◽  
The Stability

As the complexity of unsaturated soil theory, and it must have a long test period when we study the unsaturated soils, so the conventional design analysis software does not provide such analysis, so we can imagine that such a slope stability analysis does not accurately reflect the actual state of the slope. Based on the known soil moisture content，this paper use the soil water characteristic curve and strength theory of unsaturated soil to calculate the strength reduction parameters of soil which can calculate the stability of the soil slope when using the common calculation method. It is noticeable that this method can be extended and applied if we establish regional databases for this simple method, and these databases can improve the accuracy of the calculation of slope stability.

scholarly journals The Stability of the Aggregate Loss Distribution

Risks ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 91 ◽  
Author(s):  
Riccardo Gatto
Keyword(s):  
Stability Analysis ◽  
Survival Function ◽  
Saddlepoint Approximation ◽  
Computational Formula ◽  
Important Indicator ◽  
The Common ◽  
Infinitesimal Perturbation ◽  
Aggregate Loss ◽  
Aggregate Loss Distribution ◽  
The Stability

In this article we introduce the stability analysis of a compound sum: it consists of computing the standardized variation of the survival function of the sum resulting from an infinitesimal perturbation of the common distribution of the summands. Stability analysis is complementary to the classical sensitivity analysis, which consists of computing the derivative of an important indicator of the model, with respect to a model parameter. We obtain a computational formula for this stability from the saddlepoint approximation. We apply the formula to the compound Poisson insurer loss with gamma individual claim amounts and to the compound geometric loss with Weibull individual claim amounts.

scholarly journals Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

2021 ◽  
Vol 11 (11) ◽  
pp. 4833
Author(s):  
Afroja Akter ◽  
Md. Jahedul Islam ◽  
Javid Atai
Keyword(s):  
Numerical Stability ◽  
Bragg Gratings ◽  
Stability Boundaries ◽  
Quintic Nonlinearity ◽  
Numerical Stability Analysis ◽  
Gap Solitons ◽  
The Stability ◽  
Dual Core

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

DRY TURBULENCE FROM A TIME-DELAYED CHUA'S CIRCUIT

1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA
Keyword(s):  
Difference Equation ◽  
Stability Region ◽  
Nonlinear Difference Equation ◽  
Chua’S Circuit ◽  
Stability Boundaries ◽  
Chua's Circuit ◽  
Infinite Dimensional ◽  
Chaotic Region ◽  
The Stability ◽  
Left Portion

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.

scholarly journals Parametric and Internal Resonances of an Axially Moving Beam with Time-Dependent Velocity

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Bamadev Sahoo ◽  
L. N. Panda ◽  
G. Pohit
Keyword(s):  
Internal Resonance ◽  
Multiple Scales ◽  
Time History ◽  
Mean Value ◽  
Phase Portraits ◽  
Axially Moving Beam ◽  
Internal Resonances ◽  
Moving Beam ◽  
Axially Moving ◽  
The Stability

The nonlinear vibration of a travelling beam subjected to principal parametric resonance in presence of internal resonance is investigated. The beam velocity is assumed to be comprised of a constant mean value along with a harmonically varying component. The stretching of neutral axis introduces geometric cubic nonlinearity in the equation of motion of the beam. The natural frequency of second mode is approximately three times that of first mode; a three-to-one internal resonance is possible. The method of multiple scales (MMS) is directly applied to the governing nonlinear equations and the associated boundary conditions. The nonlinear steady state response along with the stability and bifurcation of the beam is investigated. The system exhibits pitchfork, Hopf, and saddle node bifurcations under different control parameters. The dynamic solutions in the periodic, quasiperiodic, and chaotic forms are captured with the help of time history, phase portraits, and Poincare maps showing the influence of internal resonance.

Zambia's Second Republic —the Establishment of a One-Party State

1974 ◽  
Vol 12 (2) ◽  
pp. 231-244 ◽  
Author(s):  
Jan Pettman
Keyword(s):  
Political Development ◽  
Political System ◽  
The State ◽  
Second Republic ◽  
National Unity ◽  
Common Enemy ◽  
The Common ◽  
The Government ◽  
The Stability ◽  
Party State

Zambia inherited a system of government and administration in 1964 which was ill-suited to the tasks of political development to which her new leaders were dedicated. What little national unity and mobilisation had been achieved in the independence struggle declined with the removal of the common enemy. The Government rested on a fragile base, without the support of agreed rules and practices to limit and contain conflict, and without adequate instruments available for the implementation of its policies. So the search began for a more suitable political system, which could cope with the new needs of independence, and provide for the stability of the state and the survival of the Government.

Influence of Axial Excitations and of Boundary Conditions on the Parametric Instability of a Beam

1995 ◽  
Author(s):  
Régis Dufour ◽  
Alain Berlioz ◽  
Thomas Streule
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Time Varying ◽  
Periodic Force ◽  
Modal Reduction ◽  
Time Varying Parameter ◽  
The Stability

Abstract In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It shows that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

Ba-, Si- and vacancy-rich phlogopites from the talc-bearing sulfide ore deposit of La Creuse, Beaujolais, France

2018 ◽  
Vol 82 (5) ◽  
pp. 1187-1210
Author(s):  
Marie-Lola Pascal ◽  
Michel Fonteilles ◽  
Véronique Tournis ◽  
Benoît Baptiste ◽  
Jean-Louis Robert ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Monoclinic Space Group ◽  
Excess Charge ◽  
Formula Unit ◽  
X Ray Diffraction ◽  
Ore Deposit ◽  
Sulfide Ore ◽  
The Common ◽  
The Stability ◽  
High Level

ABSTRACTBa-rich and Si-rich phlogopites occur in the talc-bearing rocks of the La Creuse sulfide ore deposit in Beaujolais, France. They form a group of compositions completely separated from the common Al-rich phlogopites that occur in the surrounding talc-free metasiltites and metarhyolites, with higher Ba and Mg and lower Al contents. The Ba-rich phlogopites have a relatively narrow compositional range (0.24 to 0.80 Ba per formula unit, for 44 valencies) with high and constant Si (5.8 atoms per formula unit, apfu) and Mg + Fe (5.6 apfu), probably buffered by the presence of talc. Compared to low-Al phlogopites from talc-free rocks, the excess charge introduced by the BaK–1 substitution is compensated by interlayer vacancies. Such a high level of interlayer vacancy (0.56 pfu), related to the talc-producing metasomatic conditions, is essential for the stability of this special group of Ba-rich and Si-rich phlogopites.Single crystal X-ray diffraction analyses were performed. Ba-rich and Si-rich phlogopite is monoclinic, space group C2/m, (R = 5.31%) with a = 5.3185(5), b = 9.2136(9), c = 10.1349(11) Å and β = 100.131(11)°. The occupancies of Mg/Fe and K/Ba were refined exploring different vacancies. The solutions giving the best R factor (4.77%) and goodness-of-fit (1.06) are obtained with 15% < vacancy < 40% at the interlayer site.

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