scholarly journals Regular and Chaotic Dynamics of Flexible Plates

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
J. Awrejcewicz ◽  
E. Yu. Krylova ◽  
I.V. Papkova ◽  
V. A. Krysko
Keyword(s):  
Nonlinear Dynamics ◽  
Hopf Bifurcation ◽  
Chaotic Dynamics ◽  
Rectangular Plates ◽  
Control Parameters ◽  
Periodic Load ◽  
Chaotic Vibrations ◽  
Flexible Plates ◽  
Independent Variable ◽  
Time Periodic

Nonlinear dynamics of flexible rectangular plates subjected to the action of longitudinal and time periodic load distributed on the plate perimeter is investigated. Applying both the classical Fourier and wavelet analysis we illustrate three different Feigenbaum type scenarios of transition from a regular to chaotic dynamics. We show that the system vibrations change with respect not only to the change of control parameters, but also to all fixed parameters (system dynamics changes when the independent variable, time, increases). In addition, we show that chaotic dynamics may appear also after the second Hopf bifurcation. Curves of equal deflections (isoclines) lose their previous symmetry while transiting into chaotic vibrations.

Chaotic Vibrations of Sector-Type Spherical Shells

2008 ◽  
Vol 3 (4) ◽  
Author(s):  
A. V. Krysko ◽  
J. Awrejcewicz ◽  
I. V. Papkova
Keyword(s):  
Nonlinear Dynamics ◽  
Chaotic Dynamics ◽  
Static Stability ◽  
Control Parameters ◽  
Spherical Shells ◽  
Spherical Cap ◽  
Chaotic Vibrations ◽  
Novel Method ◽  
Sector Type ◽  
Mechanical Objects

In this work, chaotic vibrations of shallow sector-type spherical shells are studied. A sector-type shallow shell is understood as a shell defined by a sector with associated boundary conditions and obtained by cutting a spherical shell for a given angle θk, or it is a sector of a shallow spherical cap associated with the mentioned angle. Both static stability and complex nonlinear dynamics of the mentioned mechanical objects subjected to transversal uniformly distributed sign-changeable load are analyzed, and the so-called vibration charts and scales regarding the chosen control parameters are reported. In particular, scenarios of transition from regular to chaotic dynamics of the mentioned shells are investigated. A novel method to control chaotic dynamics of the studied flexible spherical shells driven by transversal sign-changeable load via synchronized action of the sign-changeable antitorque is proposed and applied. All investigations are carried out within the fields of qualitative theory of differential equations and nonlinear dynamics.

scholarly journals Wavelet-Based Analysis of the Regular and Chaotic Dynamics of Rectangular Flexible Plates Subjected to Shear-Harmonic Loading

2012 ◽  
Vol 19 (5) ◽  
pp. 979-994 ◽  
Author(s):  
J. Awrejcewicz ◽  
I.V. Papkova ◽  
E.U. Krylova ◽  
V.A. Krysko
Keyword(s):  
Chaotic Dynamics ◽  
Time Instant ◽  
Vibration Characteristics ◽  
Harmonic Load ◽  
Rectangular Plates ◽  
Harmonic Loading ◽  
Linear Dynamics ◽  
Flexible Plates ◽  
Load Action ◽  
Real Picture

We investigate non-linear dynamics of flexible rectangular plates subjected to external shear harmonic load action. We show that an application of the classical and widely used Fourier analysis does not allow to obtain real picture of the frequency vibration characteristics in each time instant. On the other hand, we show that application of the wavelets approach allows to follow frequency time evolutions. Our numerical results indicate that vibrations in different plate points occur with the same frequencies set although their power is different. Hence, the vibration characteristics can be represented by one arbitrary taken plate point. Furthermore, using wavelets scenarios of transitions from regular to chaotic dynamics are illustrated and discussed including two novel scenarios not reported so far in the existing literature.

scholarly journals Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations

2013 ◽  
Vol 225 (1) ◽  
pp. 213-232 ◽  
Author(s):  
Michele Ducceschi ◽  
Cyril Touzé ◽  
Stefan Bilbao ◽  
Craig J. Webb
Keyword(s):  
Nonlinear Dynamics ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Modal Interaction ◽  
Free And Forced Vibrations

scholarly journals Investigation of the Effect of Additive White Noise on the Dynamics of Contact Interaction of the Beam Structure

2019 ◽  
Author(s):  
Ольга Салтыкова ◽  
Olga Saltykova ◽  
Александр Кречин ◽  
Alexander Krechin
Keyword(s):  
Nonlinear Dynamics ◽  
White Noise ◽  
Contact Interaction ◽  
Geometric Nonlinearity ◽  
Chaotic Dynamics ◽  
Kutta Method ◽  
Beam Structure ◽  
Runge Kutta Method ◽  
Additive White Noise ◽  
The Finite Difference Method

The purpose of this work is to study and scientific visualization the effect of additive white noise on the nonlinear dynamics of beam structure contact interaction, where beams obey the kinematic hypotheses of the first and second approximation. When constructing a mathematical model, geometric nonlinearity according to the T. von Karman model and constructive nonlinearity are taken into account. The beam structure is under the influence of an external alternating load, as well as in the field of additive white noise. The chaotic dynamics and synchronization of the contact interaction of two beams is investigated. The resulting system of partial differential equations is reduced to a Cauchy problem by the finite difference method and then solved by the fourth order Runge-Kutta method.

A Mechanical Filter Concept to Suppress Crane Load Oscillations

1997 ◽  
Author(s):  
B. Balachandran ◽  
Y.-Y. Li
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Control Parameters ◽  
Pivot Point ◽  
Preliminary Results ◽  
Scalar Control ◽  
Load Response ◽  
Mechanical Filter ◽  
Circular Track ◽  
Ship Roll

Abstract In this article, preliminary results obtained in the exploration of a mechanical filter concept for suppressing crane-load oscillations on a ship vessel are presented. The pivot point about which the load oscillates is constrained to follow a circular track in the considered filter. The governing dynamical systems for the cases with and without the filter are presented, and the nonlinear dynamics of these systems is studied with respect to quasi-static variation of different scalar control parameters. It is shown that the presence of the filter helps in eliminating some of the sub-critical bifurcations that may arise in the crane-load response during periodic ship-roll excitations.

scholarly journals Multiconsensus of Nonlinear Multiagent Systems with Intermittent Communication

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jie Chen ◽  
Guang-Hui Xu ◽  
Liang Geng
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Function ◽  
Multiagent Systems ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Control Parameters ◽  
Numerical Examples ◽  
Relative Information ◽  
Loop Dynamics ◽  
Intermittent Communication

Compared with single consensus, the multiconsensus of multiagent systems with nonlinear dynamics can reflect some real-world cases. This paper proposes a novel distributed law based only on intermittent relative information to achieve the multiconsensus. By constructing an appropriate Lyapunov function, sufficient conditions on control parameters are derived to undertake the reliability of closed-loop dynamics. Ultimately, the availability of results is completely validated by these numerical examples.

scholarly journals Hopf Bifurcation and Dynamic Analysis of an Improved Financial System with Two Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
G. Kai ◽  
W. Zhang ◽  
Z. Jin ◽  
C. Z. Wang
Keyword(s):  
Nonlinear Dynamics ◽  
Hopf Bifurcation ◽  
Equilibrium Point ◽  
Chaotic System ◽  
Financial System ◽  
Two Delays ◽  
Normal Form Method ◽  
The Stability ◽  
Manifold Theory ◽  
Theoretical Results

The complex chaotic dynamics and multistability of financial system are some important problems in micro- and macroeconomic fields. In this paper, we study the influence of two-delay feedback on the nonlinear dynamics behavior of financial system, considering the linear stability of equilibrium point under the condition of single delay and two delays. The system undergoes Hopf bifurcation near the equilibrium point. The stability and bifurcation directions of Hopf bifurcation are studied by using the normal form method and central manifold theory. The theoretical results are verified by numerical simulation. Furthermore, one feature of the proposed financial chaotic system is that its multistability depends extremely on the memristor initial condition and the system parameters. It is shown that the nonlinear dynamics of financial chaotic system can be significantly changed by changing the values of time delays.

Time-periodic spatially periodic planforms in Euclidean equivariant partial differential equations

1995 ◽  
Vol 352 (1698) ◽  
pp. 125-168 ◽  
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Pattern ◽  
Invariant Equilibrium ◽  
Periodic Patterns ◽  
Planar Lattice ◽  
Diffusive Convection ◽  
Spatially Periodic ◽  
Spatio Temporal ◽  
Boussinesq Fluid ◽  
Time Periodic

In Rayleigh-Bénard convection, the spatially uniform motionless state of a fluid loses stability as the Rayleigh number is increased beyond a critical value. In the simplest case of convection in a pure Boussinesq fluid, the instability is a symmetry-breaking steady-state bifurcation that leads to the formation of spatially periodic patterns. However, in many double-diffusive convection systems the heat-conduction solution actually loses stability via Hopf bifurcation. These hydrodynamic systems provide motivation for the present study of spatiotemporally periodic pattern formation in Euclidean equivariant systems. We call such patterns planforms . We classify, according to spatio-temporal symmetries and spatial periodicity, many of the time-periodic solutions that may be obtained through equivariant Hopf bifurcation from a group-invariant equilibrium. Instead of focusing on plan- forms periodic with respect to a specified planar lattice, as has been done in previous investigations, we consider all planforms that are spatially periodic with respect to some planar lattice. Our classification results rely only on the existence of Hopf bifurcation and planar Euclidean symmetry and not on the particular dif­ferential equation.

Nonlinear dynamics at a Hopf bifurcation with axisymmetry breaking in a jet

1998 ◽  
Vol 57 (4) ◽  
pp. R3695-R3698 ◽  
Author(s):  
Ionut Danaila ◽  
Jan Dušek ◽  
Fabien Anselmet
Keyword(s):  
Nonlinear Dynamics ◽  
Hopf Bifurcation
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