Nonlinear Dynamics

Items from 1 to 20 out of 7,023 results

article

Chaotic Motion in a Spinning Spacecraft with Circumferential Nutational Damper

P. A. Meehan, S. F. Asokanthan

Nonlinear Dynamics > 1997 > 12 > 1 > 69-87

The dynamics of a simplified model of a spinning spacecraft with a circumferential nutational damper is investigated using numerical simulations for nonlinear phenomena. A realistic spacecraft parameter configuration is investigated and is found to exhibit chaotic motion when a sinusoidally varying torque is applied to the spacecraft for a range of forcing amplitude and frequency. Such a torque, in...

article

Secondary System Analysis for Space Pay-Load

M. Battaini, F. Casciati, L. Faravelli

Nonlinear Dynamics > 1997 > 12 > 1 > 89-106

The paper deals with the response of a secondary system carried on by a space vehicle during its orbital flight, i.e. when subjected to gravitational and fluid dynamical actions. The vibrations of the inner load are passively controlled using an adequate base isolation device whose behaviour can be represented by a nonlinear endochronic hysteretic model. The possibility of an efficient analysis of...

article

Nonstationary Vibrations of a String with Time-Varying Length and a Mass-Spring Attached at the Lower End

Y. Terumichi, M. Ohtsuka, M. Yoshizawa, Y. Fukawa, more

Nonlinear Dynamics > 1997 > 12 > 1 > 39-55

The purpose of this paper is to study the nonstationary vibration of a string with time-varying length and a mass-spring system attached at the lower end. The string is hung vertically and excited sinusoidally by a horizontal displacement at its upper end. The mass is supported by a guide spring horizontally and has two-degrees-of-freedom, vertical and horizontal. It is shown analytically that axial...

article

Chaotic Oscillation of Saddle Form Cable-Suspended Roofs under Vertical Excitation Action

Jiashen Fan, Fusheng He, Zhengrong Liu

Nonlinear Dynamics > 1997 > 12 > 1 > 57-68

The purpose of this paper is to investigate the dynamic behaviour of saddle form cable-suspended roofs under vertical excitation action. The governing equations of this problem are system of nonlinear partial differential and integral equations. We first establish a spectral equation, and then consider a model with one coefficient, i.e., a perturbed Duffing equation. The analytical solution is derived...

article

Slow Periodic Crossing of a Pitchfork Bifurcation in an Oscillating System

G. J. M. Maree

Nonlinear Dynamics > 1997 > 12 > 1 > 1-37

A study is made of the dynamics of oscillating systems with a slowly varying parameter. A slowly varying forcing periodically crosses a critical value corresponding to a pitchfork bifurcation. The instantaneous phase portrait exhibits a centre when the forcing does not exceed the critical value, and a saddle and two centres with an associated double homoclinic loop separatrix beyond this value. The...

article

Nonlinear Random Response of Ocean Structures Using First- and Second-Order Stochastic Averaging

M. Hijawi, R. A. Ibrahim, N. Moshchuk

Nonlinear Dynamics > 1997 > 12 > 2 > 155-197

This paper deals with the dynamic response of nonlinear elastic structure subjected to random hydrodynamic forces and parametric excitation using a first- and second-order stochastic averaging method. The governing equation of motion is derived by using Hamilton's principle, taking into account inertia and curvature nonlinearities and work done due to hydrodynamic forces. Within the framework of first-order...

article

Free Vibration in a Class of Self-Excited Oscillators with 1:3 Internal Resonance

S. Natsiavas, K. D. Bouzakis, P. Aichouh

Nonlinear Dynamics > 1997 > 12 > 2 > 109-128

Free vibration of a two degree of freedom weakly nonlinear oscillator is investigated. The type of nonlinearity considered is symmetric, it involves displacement as well as velocity terms and gives rise to self-excited oscillations in many engineering applications. After presenting the equations of motion in a general form, a perturbation methodology is applied for the case of 1:3 internal resonance...

article

Three-to-One Internal Resonances in Hinged-Clamped Beams

Char-Ming Chin, Ali H. Nayfeh

Nonlinear Dynamics > 1997 > 12 > 2 > 129-154

The nonlinear planar response of a hinged-clamped beam to a primary excitation of either its first mode or its second mode is investigated. The analysis accounts for mid-plane stretching, a static axial load and a restraining spring at one end, and modal damping. For a range of axial loads, the second natural frequency is approximately three times the first natural frequency and hence the first and...

article

Bifurcation Control of Parametrically Excited Duffing System by a Combined Linear-Plus-Nonlinear Feedback Control

Hiroshi Yabuno

Nonlinear Dynamics > 1997 > 12 > 3 > 263-274

For a parametrically excited Duffing system we propose a bifurcation control method in order to stabilize the trivial steady state in the frequency response and in order to eliminate jump in the force response, by employing a combined linear-plus-nonlinear feedback control. Because the bifurcation of the system is characterized by its modulation equations, we first determine the order of the feedback...

article

Multiple Internal Resonance in Suspended Cables under Random In-Plane Loading

W. K. Chang, R. A. Ibrahim

Nonlinear Dynamics > 1997 > 12 > 3 > 275-303

The random excitation of a suspended cable with simultaneous internal resonances is considered. The internal resonances can take place among the first in-plane and the first two out-of-plane modes. The external loading is represented by a wide-band random process. The response statistics are estimated using the Fokker-Planck-Kolmogorov (FPK) equation, together with Gaussian and non-Gaussian closures...

article

Nonlinear Dynamic Stability of Normal and Arthritic Greyhounds

Dan B. Marghitu, Prasad Nalluri

Nonlinear Dynamics > 1997 > 12 > 3 > 237-250

In this paper the dynamic stability of greyhound gait was analyzed within the framework of nonlinear dynamics theory. A video based motion analysis system was utilized to obtain the kinematic data of the hindlimb joints of greyhounds at trot. Phase plane portraits and first return maps for the coxofemoral, femorotibial, and the tarsal joints were calculated from averaged kinematic data for each dog...

article

Analysis of Nonlinear Oscillations by Gabor Spectrograms

H. Franco, R. M. O. Pauletti

Nonlinear Dynamics > 1997 > 12 > 3 > 215-236

We examine the potential of the Gabor spectrogram as a tool for the study of the temporal behavior of nonlinear oscillators. Numerical simulations of a snap-through system and homogeneous Duffing equation are analyzed by this method. Gabor spectrograms show dynamic properties of nonlinear oscillators in situations where the conventional Fourier analysis is not appropriate.

article

Bifurcation and Chaos in the Duffing Oscillator with a PID Controller

Fangsen Cui, C. H. Chew, Jianxue Xu, Yuanli Cai

Nonlinear Dynamics > 1997 > 12 > 3 > 251-262

We discuss in this paper the bifurcation, stability and chaos of the non-linear Duffing oscillator with a PID controller. Hopf bifurcation can occur and we show that there is a global stable fixed point. The PID controller works well in some fields of the parameter space, but in other fields of the parameter space, or if the reference input is not equal to zero, chaos is common for hard spring type...

article

An Elliptic Lindstedt--Poincaré Method for Certain Strongly Non-Linear Oscillators

S. H. Chen, Y. K. Cheung

Nonlinear Dynamics > 1997 > 12 > 3 > 199-213

An elliptic Lindstedt--Poincaré (L--P) method is presented for the steady-state analysis of strongly non-linear oscillators of the form $$\ddot x + c_1 x + c_3 x^3 = \varepsilon f(x,\dot x)$$ , in which the Jacobian elliptic functions are employed instead of the usual circular functions in the classical L--P perturbation procedure. This method can be viewed as a generalization of the L--P method...

article

Analysis of Stability and Instability Regions in Parametrically Excited Hamiltonian Systems

A. A. Zevin

Nonlinear Dynamics > 1997 > 12 > 4 > 327-341

Qualitative analysis of parametrically excited linear Hamiltonian systems is carried out. It is proved that the stability and instability regions are convex in the excitation frequency. Lower bounds for the boundaries of some instability regions are obtained expressed in the natural frequencies of the system in the absence of a parametric excitation. It is shown that a dominant high-frequency excitation...

article

Comparison of Various Techniques for Modelling Flexible Beams in Multibody Dynamics

R. E. Valembois, P. Fisette, J. C. Samin

Nonlinear Dynamics > 1997 > 12 > 4 > 367-397

The modelling of flexible elements in mechanical systems has been widely investigated through several methods issuing from both the area of structural mechanics and the field of multibody dynamics. As regards the latter discipline, beside the problem of the generation of the multibody equations of motion, the choice of a spatial discretization method for modelling flexible elements has always been...

article

A Bifurcation Analysis of the Dynamics of a Simplified Shell Model

R. Baumgarten, E. Kreuzer, A. A. Popov

Nonlinear Dynamics > 1997 > 12 > 4 > 307-317

We study parametrically excited vibrations of a shallow cylindrical panel. The mathematical model is a system of two partial differential equations based on Donnell's shallow shell theory. The original equations are discretised using Galerkin approximations and all calculations are performed through symbolic manipulations. A bifurcation analysis of a system model with two degrees of freedom is accomplished...

article

Unilaterality and Dry Friction: A Geometric Formulation for Two-Dimensional Rigid Body Dynamics

Anna Sinopoli

Nonlinear Dynamics > 1997 > 12 > 4 > 343-366

The dynamics of a rigid body simply supported on a moving rigid ground in the presence of dry friction is investigated. Rigid body kinematics, in terms of generalized coordinates, and features of contact are discussed. According to the contact laws, a variational formulation is adopted to describe the dynamics and to analyze, in the case of contact, the connection between dynamically possible motions...

article

Long Asymptotic Correlation Time for Non-Linear Autonomous Itô's Stochastic Differential Equation

Yevgeny V. Mamontov, Magnus Willander

Nonlinear Dynamics > 1997 > 12 > 4 > 399-411

Itô's stochastic differential equations theory is a common approach to analysis of stochastic phenomena in various systems. In many applications, an important feature of the systems is the flicker effect. It is well known that it cannot be described with linear autonomous scalar equations of the above kind. The reason is that the flicker effect is usually associated with a correlation time which is...

article

Is There Chaotic Synchronization in Space Extend Systems?

Liu Zengrong, Zhang Wei, Huang Xin

Nonlinear Dynamics > 1997 > 12 > 4 > 319-326

Based on coupled map lattice (CML), the chaotic synchronous pattern in space extend systems is discussed. Making use of the criterion for the existence and the conditions of stability, we find an important difference between chaotic and nonchaotic movements in synchronization. A few numerical results are presented.

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Keywords

CHAOS (396)
STABILITY (278)
BIFURCATION (255)
SYNCHRONIZATION (224)
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NONLINEAR DYNAMICS (161)
TIME DELAY (144)
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NONLINEAR (48)
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DYNAMICS (47)
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OPTIMAL CONTROL (46)
SYMBOLIC COMPUTATION (46)
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PARAMETER ESTIMATION (42)
ENERGY HARVESTING (41)
LYAPUNOV FUNCTION (40)
NONLINEAR ENERGY SINK (40)
SOLITONS (39)
DARBOUX TRANSFORMATION (38)
NONLINEAR CONTROL (38)
NONLINEAR NORMAL MODES (38)
PERIODIC SOLUTIONS (38)
HYPERCHAOS (36)
MULTIBODY DYNAMICS (36)
PARAMETER IDENTIFICATION (36)
FRACTIONAL DERIVATIVE (35)
MEMRISTOR (35)
PRIMARY RESONANCE (35)
ABSOLUTE NODAL COORDINATE FORMULATION (33)
COMPLEX NETWORKS (33)
CONSERVATION LAWS (33)
POINCARÉ MAP (33)
COMPLEX NETWORK (32)
MEMS (32)
MULTIPLE SCALES (32)
STABILIZATION (32)
BIFURCATION ANALYSIS (31)
HARMONIC BALANCE METHOD (31)
RESONANCE (31)
FRICTION (30)
LINEAR MATRIX INEQUALITY (30)
NONLINEARITY (30)
ROBUSTNESS (30)
VIBRATION (30)
BACKSTEPPING (29)
SYSTEM IDENTIFICATION (29)
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CRYPTOGRAPHY (28)
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DUFFING OSCILLATOR (27)
GLOBAL STABILITY (27)
LYAPUNOV STABILITY (27)
MULTIPLE SCALES METHOD (27)
NONLINEAR ANALYSIS (27)
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NONLINEAR SCHRÖDINGER EQUATION (26)
NUMERICAL SIMULATION (26)
PERTURBATION METHODS (26)
SOLITON (26)
TIME-VARYING DELAY (26)
CRYPTANALYSIS (25)
EXACT SOLUTIONS (25)
NOISE (25)
HYSTERESIS (24)
IMPULSIVE CONTROL (24)
MODELING (24)
MULTI-AGENT SYSTEMS (24)
PINNING CONTROL (24)
STOCHASTIC AVERAGING (24)
TIME DELAYS (24)
ASYMPTOTIC STABILITY (23)
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INFONA - science communication portal

Nonlinear Dynamics

Chaotic Motion in a Spinning Spacecraft with Circumferential Nutational Damper

Secondary System Analysis for Space Pay-Load

Nonstationary Vibrations of a String with Time-Varying Length and a Mass-Spring Attached at the Lower End

Chaotic Oscillation of Saddle Form Cable-Suspended Roofs under Vertical Excitation Action

Slow Periodic Crossing of a Pitchfork Bifurcation in an Oscillating System

Nonlinear Random Response of Ocean Structures Using First- and Second-Order Stochastic Averaging

Free Vibration in a Class of Self-Excited Oscillators with 1:3 Internal Resonance

Three-to-One Internal Resonances in Hinged-Clamped Beams

Bifurcation Control of Parametrically Excited Duffing System by a Combined Linear-Plus-Nonlinear Feedback Control

Multiple Internal Resonance in Suspended Cables under Random In-Plane Loading

Nonlinear Dynamic Stability of Normal and Arthritic Greyhounds

Analysis of Nonlinear Oscillations by Gabor Spectrograms

Bifurcation and Chaos in the Duffing Oscillator with a PID Controller

An Elliptic Lindstedt--Poincaré Method for Certain Strongly Non-Linear Oscillators

Analysis of Stability and Instability Regions in Parametrically Excited Hamiltonian Systems

Comparison of Various Techniques for Modelling Flexible Beams in Multibody Dynamics

A Bifurcation Analysis of the Dynamics of a Simplified Shell Model

Unilaterality and Dry Friction: A Geometric Formulation for Two-Dimensional Rigid Body Dynamics

Long Asymptotic Correlation Time for Non-Linear Autonomous Itô's Stochastic Differential Equation

Is There Chaotic Synchronization in Space Extend Systems?

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