Numerical and experimental study of a double physical pendulum with magnetic interaction

Wojna, Mateusz; Wijata, Adam; Wasilewski, Grzegorz; Awrejcewicz, Jan

doi:10.1016/j.jsv.2018.05.032

Cited by 41 publications

(23 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Saeed and Kamel [43] gave an active magnetic bearing-based tuned controller to suppress lateral vibrations of a nonlinear Jeffcott rotor system. Wojna et al [44] gave the numerical and experimental study of a double physical pendulum with the magnetic interaction. Sun et al [45] investigated the nonlinear dynamic characteristics of the active magnetic bearing system based on the cell-mapping method with a case study.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

Zhang

2020

Shock and Vibration

View full text Add to dashboard Cite

The asymptotic perturbation method is used to analyze the nonlinear vibrations and chaotic dynamics of a rotor-active magnetic bearing (AMB) system with 16-pole legs and the time-varying stiffness. Based on the expressions of the electromagnetic force resultants, the influences of some parameters, such as the cross-sectional area Aα of one electromagnet and the number N of windings in each electromagnet coil, on the electromagnetic force resultants are considered for the rotor-AMB system with 16-pole legs. Based on the Newton law, the governing equation of motion for the rotor-AMB system with 16-pole legs is obtained and expressed as a two-degree-of-freedom system with the parametric excitation and the quadratic and cubic nonlinearities. According to the asymptotic perturbation method, the four-dimensional averaged equation of the rotor-AMB system is derived under the case of 1 : 1 internal resonance and 1 : 2 subharmonic resonances. Then, the frequency-response curves are employed to study the steady-state solutions of the modal amplitudes. From the analysis of the frequency responses, both the hardening-type nonlinearity and the softening-type nonlinearity are observed in the rotor-AMB system. Based on the numerical solutions of the averaged equation, the changed procedure of the nonlinear dynamic behaviors of the rotor-AMB system with the control parameter is described by the bifurcation diagram. From the numerical simulations, the periodic, quasiperiodic, and chaotic motions are observed in the rotor-active magnetic bearing (AMB) system with 16-pole legs, the time-varying stiffness, and the quadratic and cubic nonlinearities.

show abstract

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

Zhang

2020

Shock and Vibration

View full text Add to dashboard Cite

show abstract

“…This article extends our previous investigation 46,47 and includes a more detailed theoretical analysis and numerical investigation. It is organized in the following way.…”

Section: Introductionmentioning

confidence: 52%

Numerical and experimental study of dynamics of two pendulums under a magnetic field

Polczyński

Wijata

Awrejcewicz

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part I:

Self Cite

View full text Add to dashboard Cite

In this article, a two-degree-of-freedom system consisting of two pendulums with magnets embedded in a variable magnetic field is investigated experimentally and numerically. Pivots of the pendulums are coupled by an elastic element. The magnetic interaction originates from permanent magnets, mounted at free ends of the pendulums and current-powered air coils underneath. A novel model for the magnetic force is proposed and verified experimentally. Nonlinear dynamics of the system is examined by means of time series, bifurcation diagrams, phase portraits, and Poincaré sections. Regions of chaotic and regular motion are predicted numerically and justified experimentally. Multiperiodic motion and coexisting solutions are detected, and pictures in basins of their attraction are reported, among other.

show abstract

“…Moreover, when k 1 0, k 2 0, k 1 p 1 − m 1 n 1 0, k 2 p 2 − m 2 n 2 0 are not held, (29) has an infinite number of solutions or no solutions, which leads to many periodic or no periodic solutions in the original system (6). For example, if k 1 0, k 2 0, k 1 p 1 − m 1 n 1 0, k 2 p 2 − m 2 n 2 = 0, (31) is equivalent to…”

Section: Periodic Solutionmentioning

confidence: 99%

“…When ϕ 11 u 2 − ϕ 21 u 1 0 or u 1 0 is true, Equation (37) has no solution. Hence, system (6) has no collision periodic solution. Note 1 Conditions (20) and (32) are sufficient and unnecessary conditions for system (6) with the first kind of collision periodic solution.…”

Section: Periodic Solutionmentioning

confidence: 99%

“…The researches were focused on the drive system, sensing system, shape design of the mechanical arm, and inertial impact influence on the dynamic response at the link [3,4]. Many results showed that the impact double pendulum could be used to simulate the bionic manipulator [5][6][7]. In fact, with the motion refinement of the manipulator and the installation requirements of the external drive, the gap and damping at the link of the manipulator should be considered, as well as the type and installation mode of the external drive, which can be simplified as a collision double pendulum with external simple harmonic excitation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Periodic Solution of a Non-Smooth Double Pendulum with Unilateral Rigid Constrain

2019

View full text Add to dashboard Cite

In this paper, a double pendulum model is presented with unilateral rigid constraint under harmonic excitation, which leads to be an asymmetric and non-smooth system. By introducing impact recovery matrix, modal analysis, and matrix theory, the analytical expressions of the periodic solutions for unilateral double-collision will be discussed in high-dimensional non-smooth asymmetric system. Firstly, the impact laws are classified in order to detect the existence of periodic solutions of the system. The impact recovery matrix is introduced to transform the impact laws of high-dimensional system into matrix. Furthermore, by use of modal analysis and matrix theory, an invertible transformation is constructed to obtain the parameter conditions for the existence of the impact periodic solution, which simplifies the calculation and can be easily extended to high-dimensional non-smooth system. Hence, the range of physical parameters and the restitution coefficients is calculated theoretically and non-smooth analytic expression of the periodic solution is given, which provides ideas for the study of approximate analytical solutions of high-dimensional non-smooth system. Finally, numerical simulation is carried out to obtain the impact periodic solution of the system with small angle motion.

show abstract

Numerical and experimental study of a double physical pendulum with magnetic interaction

Cited by 41 publications

References 45 publications

Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

Numerical and experimental study of dynamics of two pendulums under a magnetic field

Periodic Solution of a Non-Smooth Double Pendulum with Unilateral Rigid Constrain

Contact Info

Product

Resources

About