Periodic Motions and Bifurcations of a Periodically Forced Spring Pendulum Varying With Excitation Amplitude

2021 ◽  
Author(s):  
Albert Luo ◽  
Yu Guo
Keyword(s):  
Excitation Amplitude ◽  
Periodic Motions

Periodic Motions and Bifurcations of a Periodically Forced Spring Pendulum Varying With Excitation Amplitude

2020 ◽  
Author(s):  
Yu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical Behavior ◽  
Excitation Amplitude ◽  
Periodic Motions ◽  
Pendulum System ◽  
Bifurcation Tree ◽  
Nonlinear Spring ◽  
Nonlinear Dynamical ◽  
Discrete Maps ◽  
Period 2 ◽  
Stability And Bifurcations

Abstract In this paper, the semi-analytical method of implicit discrete maps is employed to investigate the nonlinear dynamical behavior of a nonlinear spring pendulum. The implicit discrete maps are developed through the midpoint scheme of the corresponding differential equations of a nonlinear spring pendulum system. Using discrete mapping structures, different periodic motions are obtained for the bifurcation trees. With varying excitation amplitude, a bifurcation tree of period-1 motion to chaos is achieved through the bifurcation tree of period-1 to period-2 motions. The corresponding stability and bifurcations are studied through eigenvalue analysis. Finally, numerical illustrations of periodic motions are obtained numerically and analytically.

Investigation of the stability of periodic motions in a nonlinear automatic control system based on the fast fourier transform

2003 ◽  
Vol 3 ◽  
pp. 297-307
Author(s):  
V.V. Denisov
Keyword(s):  
Fourier Transform ◽  
Control System ◽  
Automatic Control ◽  
Fast Fourier Transform ◽  
Automatic Control System ◽  
Resonance Phenomenon ◽  
Periodic Motions ◽  
Multiply Connected ◽  
Non Linear ◽  
The Stability

An approach to the study of the stability of non-linear multiply connected systems of automatic control by means of a fast Fourier transform and the resonance phenomenon is considered.

Design and analysis of a vibration isolation system with cam–roller–spring–rod mechanism

2021 ◽  
pp. 107754632110005
Author(s):  
Yonglei Zhang ◽  
Guo Wei ◽  
Hao Wen ◽  
Dongping Jin ◽  
Haiyan Hu
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Experimental Studies ◽  
Excitation Amplitude ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Stiffness Characteristic ◽  
Negative Stiffness Mechanism ◽  
Isolation Systems ◽  
Vibration Isolation Performance

The vibration isolation system using a pair of oblique springs or a spring-rod mechanism as a negative stiffness mechanism exhibits a high-static low-dynamic stiffness characteristic and a nonlinear jump phenomenon when the system damping is light and the excitation amplitude is large. It is possible to remove the jump via adjusting the end trajectories of the above springs or rods. To realize this idea, the article presents a vibration isolation system with a cam–roller–spring–rod mechanism and gives the detailed numerical and experimental studies on the effects of the above mechanism on the vibration isolation performance. The comparative studies demonstrate that the vibration isolation system proposed works well and outperforms some other vibration isolation systems.

scholarly journals On excessive Transverse Coordinates for Orbital Stabilization of Periodic Motions

2020 ◽  
Vol 53 (2) ◽  
pp. 9250-9255
Author(s):  
Christian Fredrik Sætre ◽  
Anton Shiriaev
Keyword(s):  
Periodic Motions ◽  
Orbital Stabilization

On the Analysis of Hopf Bifurcation Associated with a Two-Fold Zero Eigenvalue, Part 1: Autonomous System

1999 ◽  
Vol 121 (1) ◽  
pp. 101-104 ◽  
Author(s):  
M. Moh’d ◽  
K. Huseyin
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycles ◽  
Autonomous System ◽  
Periodic Motions ◽  
Zero Eigenvalue ◽  
The Family ◽  
Dynamic Bifurcations ◽  
Formula Type

The static and dynamic bifurcations of an autonomous system associated with a twofold zero eigenvalue (of index one) are studied. Attention is focused on Hopf bifurcation solutions in the neighborhood of such a singularity. The family of limit cycles are analyzed fully by applying the formula type results of the Intrinsic Harmonic Balancing method. Thus, parameter-amplitude and amplitude-frequency relationships as well as an ordered form of approximations for the periodic motions are obtained explicitly. A verification technique, with the aid of MAPLE, is used to show the consistency of ordered approximations.

LSTM-based approach for predicting periodic motions of an impacting system via transient dynamics

2021 ◽  
Author(s):  
Kenneth Omokhagbo Afebu ◽  
Yang Liu ◽  
Evangelos Papatheou ◽  
Bingyong Guo
Keyword(s):  
Transient Dynamics ◽  
Periodic Motions

The analysis of TWI data for human being's periodic motions

2011 ◽  
Author(s):  
Zhaofa Zeng ◽  
Jiguang Sun ◽  
Jing Li ◽  
Fengshan Liu ◽  
Qi Lu ◽  
...  
Keyword(s):  
Periodic Motions

Active Control Comparison of Vibration in Flexible Spacecraft Using Different Active Friction Joints

2013 ◽  
Vol 446-447 ◽  
pp. 1160-1164
Author(s):  
Sahar Bakhtiari Mojaz ◽  
Hamed Kashani
Keyword(s):  
Energy Dissipation ◽  
Attitude Control ◽  
Vibration Suppression ◽  
Excitation Amplitude ◽  
Step Function ◽  
Flexible Spacecraft ◽  
Control Effort ◽  
Stick Slip ◽  
Control Comparison ◽  
Frictional Joints

Vibration properties of most assembled mechanical systems depend on frictional damping in joints. The nonlinear transfer behavior of the frictional interfaces often provides the dominant damping mechanism in structure and plays an important role in the vibratory response of it. For improving the performance of systems, many studies have been carried out to predict measure and enhance the energy dissipation of friction. This paper presents a new approach to vibration reduction of flexible spacecraft with enhancing the energy dissipation of frictional dampers. Spacecraft is modeled as a 3 degree of freedom mass-spring system which is controlled by a lead compensator and System responses to step function evaluated. Coulomb and Jenkins element has been used as vibration suppression mechanisms in joints and sensitivity of their performance to variations of spacecraft excitation amplitude and damper properties is analyzed. The relation between frictional force and displacement derived and used in optimization of control performance. Responses of system and control effort needed for the vibration control are compared for these two frictional joints. It is shown that attitude control effort reduces, significantly with coulomb dampers and response of system improves. On the other hand, due to stick-slip phenomena in Jenkins element, we couldn’t expect the same performance from Jenkins damper.

Bifurcation Trees of Periodic Motions to Chaos in a Parametric, Quadratic Nonlinear Oscillator

2014 ◽  
Vol 24 (05) ◽  
pp. 1450075 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Fourier Series ◽  
Nonlinear Systems ◽  
Analytical Solutions ◽  
Nonlinear Oscillator ◽  
Series Solution ◽  
Parametric Oscillator ◽  
Periodic Motions ◽  
Parametric Oscillators ◽  
Harmonic Term ◽  
Nonlinear Behaviors

In this paper, bifurcation trees of periodic motions to chaos in a parametric oscillator with quadratic nonlinearity are investigated analytically as one of the simplest parametric oscillators. The analytical solutions of periodic motions in such a parametric oscillator are determined through the finite Fourier series, and the corresponding stability and bifurcation analyses for periodic motions are completed. Nonlinear behaviors of such periodic motions are characterized through frequency–amplitude curves of each harmonic term in the finite Fourier series solution. From bifurcation analysis of the analytical solutions, the bifurcation trees of periodic motion to chaos are obtained analytically, and numerical illustrations of periodic motions are presented through phase trajectories and analytical spectrum. This investigation shows period-1 motions exist in parametric nonlinear systems and the corresponding bifurcation trees to chaos exist as well.

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