On discontinuous dynamics of a 2-DOF oscillator with an one-sided rigid obstacle

Fan, Jinjun; Li, Chun-Liang; Yang, Zhichao; Chen, Shoulian; Cao, Jing; Dou, Chenjing

doi:10.1016/j.ijnonlinmec.2019.103261

Cited by 10 publications

(3 citation statements)

References 68 publications

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“…The expected direction of the system motion can be obtained by applying a position feedback controller [23] or reversing the impact side [24]. A rich and complex dynamic response of the vibroimpact system was confirmed, as a result of the co-existence of non-smooth friction and the impact force [25,26]. The system response has been found to be either periodic, quasiperiodic and chaotic response, and thus required a careful design [21] and/or parameter selection [27] to make the system work stable.…”

Section: Introductionmentioning

confidence: 89%

A comparative study on the two vibration driven locomotion systems in various friction levels

Nguyen

2021

Vietnam J. Mech.

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This paper presented comparison results of two locomotion models: a pure-vibration driven and a vibro-impact driven system. In experiments, the friction force can be varied without changing the internal and the body masses. The mathematical models of the two systems were developed and experimentally verified. Using dimensionless models, the results can be expanded to other sizes in practice. The two models were compared in the following aspects: the progression rate, the motion direction and the dynamics response. The effect of friction as an important variable on the dynamic response of the two scaled models were examined and compared by means of bifurcation analysis and basin of attraction. It has been found that, the pure-vibration can provide forward motion better than the vibro-impact does. The highest progression rate of the vibro-impact was less than that of the pure-vibration system in the investigated ranges of input parameters. Besides, the pure-vibration always has period-1 motion, whereas the vibro-impact system has a rich and complex dynamic response, including period-1, period-2 as well as chaotic motions. The results obtained would be useful for design and operating the self-propelled locomotion systems.

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Section: Introductionmentioning

confidence: 89%

A comparative study on the two vibration driven locomotion systems in various friction levels

Nguyen

2021

Vietnam J. Mech.

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“…Early researches of collision dynamics concentrate on single-degree linear collision system [35][36][37][38] , which demonstrates period doubling bifurcation, chaos and chattering. In recent years, Dou, and et al studied dynamical behaviours of single-degree-of-freedom and two-degree-of-freedom systems with bilateral rigid constraints and one-side rigid obstacle, considering the nonlinear friction and external force, seen in [39][40][41]. With the help of Melnikov method, numerical calculation and experiment, Li et al [42] investigated the rich dynamics of SD oscillator with a pair of extra bilateral rigid constraints, verifying the thresholds of parameters for the global bifurcations and chaotic oscillations.…”

Section: Introductionmentioning

confidence: 99%

The complicated dynamical behaviours of a geometrical oscillator with a mass parameter

Huang

Cao

2023

Preprint

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In this paper, we consider a special kind of geometrical nonlinear oscillator with a mass parameter admitting two different dynamical states leading to a double-valued potential energy. A cylindrical manifold is introduced to formulate the equation of motion to describe the distinguished dynamical behaviours. With the help of Hamiltonian, the complex bifurcations are demonstrated with the varying of parameters including periodic solutions, the steady states and the blowing up phenomenon near θ = ± π/2 to infinity. A toroidal manifold is introduced to map the infinities into (0, ±2, 0) on the torus exhibiting saddle-node-like behaviour, where the uniqueness of solution is failed, for which a special ‘collision’ parameter is introduced to define the possible motion leaving from the infinities. A numerical method which is proposed to get solution near the infinity where Runge-Kutta method fails, is employed to get the bifurcation diagrams using Poincaré sections for the perturbed system to exhibit the complex dynamics including the co-existence of periodic solutions, the chaos from the coexisted periodic doubling and also the instant chaos from the coexisted periodic solutions. The results demonstrated herein this paper provide a brand new insight into the understanding of enriched nonlinear dynamics and an essential explanation about ‘collision’ of mechanical system with both the geometrical and mass parameters.

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“…One configuration with best plane enforcement is then evaluated for mechanism variable output sensitivity and parasite error, thereby providing details about the design area. Rotational rigidity is determined based on numerical simulation in the in-plane rotational axis and tension [5][6][7][8]. In view of the linearity and nonlinearity method of the mechanism, a passive control system was tested.…”

Section: Introductionmentioning

confidence: 99%

Performance Improvement of Suspension Characteristics by Implementation of Active Suspension System in Two Wheelers

Backiyaraj

Parthasarathy

Nachippan

et al. 2021

IJAME

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New and better two-wheel models have increased demand today, with increased protection, comfort and performance. The human body gets exhausted, which contributes to back pain and neck pain because of the excessive use of bikes, wrong riding positions, poor weather and suspension system issues. The systems engineer would focus on the design of the vehicle suspension mechanism to minimise human discomfort. This research aims to study the feasibility of implementing a suspension system with active suspension for a two-wheeler by way of numerical modelling, simulation and analysis. First of all, the active suspension system for a 2 DOF system is modelled and analysed. The analysis done is frequency response analysis and time-domain analysis. The time-domain analysis is done using two road inputs; one is a bump input, which is designed according to the standards, and the other is a random road input. Then the two-wheelers were modelled as a 4 DOF model. The controller is modelled using optimal control theory. A linear quadratic regulator (LQR) controller is used because the system is assumed to have linear characteristics and the cost function of the system is quadratic. It is observed that suspension characteristics are improved by using the active suspension system in two-wheelers.

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On discontinuous dynamics of a 2-DOF oscillator with an one-sided rigid obstacle

Cited by 10 publications

References 68 publications

A comparative study on the two vibration driven locomotion systems in various friction levels

A comparative study on the two vibration driven locomotion systems in various friction levels

The complicated dynamical behaviours of a geometrical oscillator with a mass parameter

Performance Improvement of Suspension Characteristics by Implementation of Active Suspension System in Two Wheelers

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