Periodic Motions in a Single-Degree-of-Freedom System Under Both an Aerodynamic Force and a Harmonic Excitation

2019 ◽  
Author(s):  
Bo Yu ◽  
Albert C. J. Luo
Keyword(s):  
Numerical Simulations ◽  
Analytical Approach ◽  
Aerodynamic Force ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stable Period

Abstract In this paper, a semi-analytical approach was used to predict periodic motions in a single-degree-of-freedom system under both aerodynamic force and harmonic excitation. Using the implicit mappings, the predictions of period-1 motions varying with excitation frequency are obtained. Stability of the period-1 motions are discussed, and the corresponding eigenvalues of period-1 motions are presented. Finally, numerical simulations of stable period-1 motions are illustrated.

Two Groups of Chaotic Vibrations in a Single-Degree-of-Freedom Maglev System

1997 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura
Keyword(s):  
Magnetic Levitation ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Period Doubling ◽  
Excitation Amplitude ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Moving Base ◽  
Period Doubling Bifurcations

Abstract In this paper, a single-degree-of-freedom magnetic levitation dynamic system, whose spring is composed of a magnetic repulsive force, is numerically analyzed. The numerical results indicate that a body levitated by magnetic force shows many kinds of vibrations upon adjusting the system parameters (viz., damping, excitation amplitude and excitation frequency) when the system is excited by the harmonically moving base. For a suitable combination of parameters, an aperiodic vibration occurs after a sequence of period-doubling bifurcations. Typical aperiodic vibrations that occurred after period-doubling bifurcations from several initial states are identified as chaotic vibration and classified into two groups by examining their power spectra, Poincare maps, fractal dimension analyses, etc.

The Dynamic Response of a System With Preloaded Compliance

1988 ◽  
Vol 110 (3) ◽  
pp. 278-283 ◽  
Author(s):  
S. W. Shaw ◽  
P. C. Tung
Keyword(s):  
Dynamic Response ◽  
Piecewise Linear ◽  
Harmonic Excitation ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Linear Features ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Stable Periodic ◽  
Model Equations

We consider the dynamic response of a single degree of freedom system with preloaded, or “setup,” springs. This is a simple model for systems where preload is used to suppress vibrations. The springs are taken to be linear and harmonic excitation is applied; damping is assumed to be of linear viscous type. Using the piecewise linear features of the model equations we determine the amplitude and stability of the periodic responses and carry out a bifurcation analysis for these motions. Some parameter regions which contain no simple stable periodic motions are shown to possess chaotic motions.

scholarly journals Shock Performance of Different Semiactive Damping Strategies

2010 ◽  
Vol 8 (02) ◽  
Author(s):  
D. F. Ledezma-Ramirez ◽  
N. Ferguson ◽  
M. Brennan
Keyword(s):  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Harmonic Vibration ◽  
Passive Stiffness ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Variable Damping ◽  
Stiffness And Damping ◽  
Shock Pulses

The problem of shock generated vibration is presented and analyzed. The fundamental background is explained based on the analysis of a single degree-of-freedom model with passive stiffness and damping. The advantages and limitations of such a shock mount are discussed. Afterwards, different semi-active strategies involving variable damping are presented. These strategies have been used for harmonic excitation but it is not clear how they will perform during a shock. This paper analyzes the different variable damping schemes already used for harmonic vibration in order to find any potential advantages or issues for theoretical shock pulses.

The Estimation of Viscous and Coulomb Damping in Harmonically Excited Oscillators

1999 ◽  
Author(s):  
J.-W. Liang ◽  
B. F. Feeny
Keyword(s):  
Free Vibration ◽  
Numerical Simulations ◽  
Dry Friction ◽  
Mechanical Vibration ◽  
Degree Of Freedom ◽  
Identification Algorithm ◽  
Single Degree Of Freedom ◽  
Coulomb Damping ◽  
Single Degree

Abstract This paper proposes a simple identification algorithm for estimating both viscous and dry friction in harmonically forced single-degree-of-freedom mechanical vibration systems. The method is especially suitable for the identification of systems for which the traditional free-vibration scheme is difficult to implement. Numerical simulations are included to show the effectiveness of the proposed algorithm. A numerical perturbation study is also included for insight on the robustness of the algorithm.

Effects of Clearance on Normal Mode Frequencies of a Nonsmooth System

1999 ◽  
Author(s):  
Eric A. Butcher
Keyword(s):  
Linear System ◽  
Numerical Simulations ◽  
Normal Mode ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Nonsmooth System ◽  
Single Degree ◽  
Equivalent Linear ◽  
Frequency Relation

Abstract The effects of a clearance or interference on the normal mode frequencies of a two-dof system with bilinear stiffness and without damping are investigated through various modifications of the bilinear frequency relation. First, the exact bilinear natural frequencies of a single degree-of-freedom system are analytically obtained in terms of the amount of clearance and the strength of nonlinearity, and an equivalent linear system is derived. These results are in turn used to construct three methods which approximate the bilinear frequencies for the 2-dof system in which the resulting approximate frequencies are compared with those obtained from numerical simulations. The results demonstrate how these bilinear normal mode frequencies vary with the magnitude of the clearance/interference and thus point toward the need of including such effects in methods which utilize the bilinear frequency relation.

Feedback Control of Grazing-Induced Chaos in the Single-Degree-of-Freedom Impact Oscillator

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Yongkang Shen ◽  
Shan Yin ◽  
Guilin Wen ◽  
Huidong Xu
Keyword(s):  
Feedback Control ◽  
Control Strategy ◽  
Dynamical Property ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
Impact Oscillator ◽  
Continuous Transition ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Existence And Stability

Based on the special dynamical property of continuous transition at certain degenerate grazing points in the single-degree-of-freedom impact oscillator, the control problem of the grazing-induced chaos is investigated in this paper. To design degenerate grazing bifurcations, we show how to obtain the degenerate grazing points of the 1/n impact periodic motions by the existence and stability analysis first. Then, a discrete-in-time feedback control strategy is used to suppress the grazing-induced chaos into the 1/n impact periodic motions precisely by the desired degenerate grazing bifurcation. The feasibility of the control strategy is verified by numerical simulations.

Categorization of Dynamic Loading Into Force-Controlled Loading and Displacement-Controlled Loading

2018 ◽  
Author(s):  
Ichiro Tamura ◽  
Shinichi Matsuura ◽  
Ryuya Shimazu ◽  
Koji Kimura
Keyword(s):  
Dynamic Loading ◽  
Kinematic Hardening ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Skeleton Curve ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Dynamic Loadings ◽  
Restoring Forces

To investigate the behavior of inelastic single-degree-of-freedom systems, the maximum restoring forces and maximum deformations of the systems due to a harmonic excitation are calculated and drawn as a diagram. These systems have restoring forces characterized by bilinear skeleton curve of the kinematic hardening type. The diagram shows two types of characteristics, and the dynamic loadings can be categorized into force-controlled loading and displacement-controlled loading.

Approximate Min-Max Equivalent Linearization

1971 ◽  
Vol 38 (4) ◽  
pp. 1070-1073
Author(s):  
R. E. Jonckheere
Keyword(s):  
Analytical Approach ◽  
Autonomous Systems ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Single Degree Of Freedom ◽  
Single Degree

A new analytical approach to approximate min-max equivalent linearization is presented for symmetrical autonomous systems with a single degree of freedom. It also serves as a foundation for previously suggested min-max methods.

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