Dynamic Behaviors of an Impact Oscillator in Harmonic Excitation

2013 ◽  
Vol 04 (04) ◽  
pp. 543
Author(s):  
Jianlian Cheng ◽  
Xinxin Xu ◽  
Yitian Chen ◽  
Bei Xia
Keyword(s):  
Harmonic Excitation ◽  
Impact Oscillator ◽  
Dynamic Behaviors

Numerical Study of an Impact Oscillator

1995 ◽  
Author(s):  
Kannan Marudachalam ◽  
Faruk H. Bursal
Keyword(s):  
Dynamical Systems ◽  
Numerical Algorithm ◽  
Initial Conditions ◽  
Numerical Study ◽  
Harmonic Excitation ◽  
General Purpose ◽  
Constrained Systems ◽  
Global Dynamics ◽  
Impact Oscillator ◽  
Stick Slip

Abstract Systems with discontinuous dynamics can be found in diverse disciplines. Meshing gears with backlash, impact dampers, relative motion of components that exhibit stick-slip phenomena axe but a few examples from mechanical systems. These form a class of dynamical systems where the nonlinearity is so severe that analysis becomes formidable, especially when global behavior needs to be known. Only recently have researchers attempted to investigate such systems in terms of modern dynamical systems theory. In this work, an impact oscillator with two-sided rigid constraints is used as a paradigm for studying the characteristics of discontinuous dynamical systems. The oscillator has zero stiffness and is subjected to harmonic excitation. The system is linear without impacts. However, the impacts introduce nonlinearity and dissipation (assuming inelastic impacts). A numerical algorithm is developed for studying the global dynamics of the system. A peculiar type of solution in which the trajectories in phase space from a certain set of initial conditions merge in finite time, making the dynamics non-invertible, is investigated. Also, the effect of “grazing,” a behavior common to constrained systems, on the dynamics of the system is studied. Based on the experience gained in studying this system, the need for an efficient general-purpose numerical algorithm for solving discontinuous dynamical systems is motivated. Investigation of stress, vibration, wear, noise, etc. that are associated with impact phenomena can benefit greatly from such an algorithm.

Feed-Back Numerical Implementations of an Optimal Procedure for Chaos Control in a Two-Well Impact Oscillator

1997 ◽  
Author(s):  
Stefano Lenci ◽  
Giuseppe Rega
Keyword(s):  
Phase Space ◽  
Numerical Simulations ◽  
Chaotic Dynamics ◽  
Chaos Control ◽  
Inverted Pendulum ◽  
Harmonic Excitation ◽  
Impact Oscillator ◽  
Potential Wells ◽  
Optimal Procedure ◽  
Optimal Excitation

Abstract The problem of controlling the chaotic dynamics of an inverted pendulum is addressed. Starting from the optimal excitation obtained in previous works, which gives satisfactory results but only on one side of the phase space, two different implementations have been developed in order to improve the controlled feature of the system. The implementations consist in a shrewd alternation of one-side optimal and of harmonic excitation, and in an alternation of right and left optimal excitations. They are aimed at reducing the scattered nature of the response, which has been synthetized by the number of jumps between the two potential wells. Some numerical simulations have been performed, showing the effectiveness of the proposed procedure. Furthermore, the comparison between the two cases has been discussed on both a local and a global basis.

scholarly journals Dynamic Behaviors of a Two-Degree-of-Freedom Impact Oscillator with Two-Sided Constraints

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Songtao Li ◽  
Qunhong Li ◽  
Zhongchuan Meng
Keyword(s):  
Bifurcation Point ◽  
Period Doubling ◽  
Harmonic Excitation ◽  
Impact Oscillator ◽  
Grazing Bifurcation ◽  
Constraint System ◽  
Codimension Two ◽  
Codimension One ◽  
Discontinuity Mapping ◽  
Elastic Constraints

The dynamic model of a vibroimpact system subjected to harmonic excitation with symmetric elastic constraints is investigated with analytical and numerical methods. The codimension-one bifurcation diagrams with respect to frequency of the excitation are obtained by means of the continuation technique, and the different types of bifurcations are detected, such as grazing bifurcation, saddle-node bifurcation, and period-doubling bifurcation, which predicts the complexity of the system considered. Based on the grazing phenomenon obtained, the zero-time-discontinuity mapping is extended from the single constraint system presented in the literature to the two-sided elastic constraint system discussed in this paper. The Poincare mapping of double grazing periodic motion is derived, and this compound mapping is applied to obtain the existence conditions of codimension-two grazing bifurcation point of the system. According to the deduced theoretical result, the grazing curve and the codimension-two grazing bifurcation points are validated by numerical simulation. Finally, various types of periodic-impact motions near the codimension-two grazing bifurcation point are illustrated through the unfolding diagram and phase diagrams.

Drifting Impact Oscillator With a New Model of the Progression Phase

2012 ◽  
Vol 79 (6) ◽  
Author(s):  
Olusegun K. Ajibose ◽  
Marian Wiercigroch ◽  
Ekaterina Pavlovskaia ◽  
Alfred R. Akisanya ◽  
Györygy Károlyi
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic Analysis ◽  
Harmonic Excitation ◽  
Plastic Medium ◽  
Impact Oscillator ◽  
Static Loads ◽  
New Model ◽  
Topological Similarity ◽  
Time Histories ◽  
Loading And Unloading

In this paper, a new model of the progression phase of a drifting oscillator is proposed. This is to account more accurately for the penetration of an impactor through elasto-plastic solids under a combination of a static and a harmonic excitation. First, the dynamic response of the semi-infinite elasto-plastic medium subjected to repeated impacts by a rigid impactor with conical or spherical contacting surfaces is considered in order to formulate the relevant force-penetration relationship during the loading and unloading phases of the contact. These relationships are then used to develop a physical and mathematical model of a new drifting oscillator, where the time histories of the progression through the medium include both the loading and unloading phases. A nonlinear dynamic analysis of the system was performed and it confirms that the maximum progressive motion of the oscillator occurs when the system exhibits period one motion. The dynamic response for both contact geometries (conical or spherical) show a topological similarity for a range of the static loads.

A Periodically Forced Impact Oscillator With Large Dissipation

1983 ◽  
Vol 50 (4a) ◽  
pp. 849-857 ◽  
Author(s):  
S. W. Shaw ◽  
P. J. Holmes
Keyword(s):  
Harmonic Excitation ◽  
Coefficient Of Restitution ◽  
Periodic Motions ◽  
Impact Oscillator ◽  
Chaotic Motions ◽  
One Dimensional ◽  
Mapping Analysis ◽  
Stable Periodic ◽  
Almost All ◽  
Dimensional Mapping

We consider the simple harmonic oscillator with harmonic excitation and a constraint that restricts motions to one side of the equilibrium position. Thus, on the achievement of a specified displacement, the direction of motion is reversed using the simple impact rule. The coefficient of restitution for this impact, r, is taken to be small. For r = 0 the motions of the system can be studied using a one-dimensional mapping. Analysis of this map shows that stable periodic orbits exist at almost all forcing frequencies but that transient nonperiodic or chaotic motions can also occur. Moreover, over certain (narrow) frequency windows arbitrarily long stable periodic motions exist. These results are then extended to the case r ≠ 0, small.

scholarly journals DYNAMIC CHARACTERISTICS OF NON-SMOOTH SUSPENSION SYSTEM UNDER FRACTIONAL-ORDER DISPLACEMENT FEEDBACK

10.6036/10125 ◽  
2021 ◽  
Vol 96 (3) ◽  
pp. 322-328
Author(s):  
JIANCHAO ZHANG ◽  
Zhan Chen ◽  
Jun Wang ◽  
Yufei Hu
Keyword(s):  
Feedback Control ◽  
Analytical Solution ◽  
Fractional Order ◽  
Dynamic Characteristics ◽  
Harmonic Excitation ◽  
Suspension System ◽  
Vehicle Body ◽  
Dynamic Behaviors ◽  
Integer Order ◽  
Suspension Systems

Vehicle suspension systems generally have non-smooth factors, such as clearances, collision, and constraint. The bad dynamic behaviors caused by these non-smooth factors have not been controlled effectively, thus influencing the driving performance and riding comfort of vehicles. To explore the dynamic characteristics of non-smooth suspension systems for controlling the bad dynamic behaviors, an approximate analytical solution to the response of a two-degree of freedom nonlinear suspension system, which has a fractional-order displacement feedback under harmonic excitation, was deduced by the Krylov–Bogoliubov (KB) method. This analytical solution was verified by the numerical solution of the suspension system. Moreover, the response of the suspension system with fractional-order displacement feedback control was compared with those of the systems without feedback control and traditional integer-order control. The influences of the main parameters of the system on the dynamic suspension characteristics were analyzed thoroughly. Finally, the stability of the suspension system was analyzed by plotting the maximum Lyapunov index diagram. Results show that compared with the systems without feedback control and with traditional integer-order control, the nonlinear suspension system with fractional-order displacement feedback control can significantly improve vehicle acceleration, the dynamic deflection of the suspension, and the displacement of the vehicle body. Controlling the nonlinear stiffness coefficient of the suspension system within 103–106 is conducive to decreasing the dynamic deflection of the suspension system of vehicles, while increasing the fractional-order control coefficient and the fractional order is beneficial to controlling the dynamic deflection of the suspension system and the displacement of the vehicle body. Conclusions obtained in the study can provide unique references for the optimal design and control of nonlinear suspension systems with fractional-order displacement feedback control. Keywords: suspension; non-smooth; fractional order; dynamics; analytical solution; nonlinear.

INVESTIGATION ON BUBBLE DYNAMIC BEHAVIORS UNDER PULSE HEATING

2018 ◽  
Author(s):  
S.C. Wu ◽  
Xiangdong Liu ◽  
Chengbin Zhang ◽  
Yongping Chen
Keyword(s):  
Pulse Heating ◽  
Bubble Dynamic ◽  
Dynamic Behaviors

scholarly journals Robust Position Control of a Two-Sided 1-DoF Impacting Mechanical Oscillator Subject to an External Persistent Disturbance by Means of a State-Feedback Controller

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Firas Turki ◽  
Hassène Gritli ◽  
Safya Belghith
Keyword(s):  
State Feedback ◽  
Position Control ◽  
External Disturbance ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Mechanical Oscillator ◽  
Impact Oscillator ◽  
State Feedback Controller ◽  
The Impact

This paper proposes a state-feedback controller using the linear matrix inequality (LMI) approach for the robust position control of a 1-DoF, periodically forced, impact mechanical oscillator subject to asymmetric two-sided rigid end-stops. The periodic forcing input is considered as a persistent external disturbance. The motion of the impacting oscillator is modeled by an impulsive hybrid dynamics. Thus, the control problem of the impact oscillator is recast as a problem of the robust control of such disturbed impulsive hybrid system. To synthesize stability conditions, we introduce the S-procedure and the Finsler lemmas by only considering the region within which the state evolves. We show that the stability conditions are first expressed in terms of bilinear matrix inequalities (BMIs). Using some technical lemmas, we convert these BMIs into LMIs. Finally, some numerical results and simulations are given. We show the effectiveness of the designed state-feedback controller in the robust stabilization of the position of the impact mechanical oscillator under the disturbance.

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