Theoretical and numerical analysis of regular one-side oscillations in a single pendulum system driven by a magnetic field

Wijata, Adam; Polczyński, Krystian; Awrejcewicz, Jan

doi:10.1016/j.ymssp.2020.107229

Cited by 30 publications

(5 citation statements)

References 53 publications

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“…has coils and the linear track installs the permanent magnet. Owing to the electromagnetic principle, the coil current 𝑖 can produce the actuation force 𝐹 = 𝜃𝑖 (𝜃 is the electromagnetic coupling constant that is related to the coil length and magnetic field strength [30][31][32]), which drives the mover 𝑚 ! to vibrate.…”

Section: Problem Statementmentioning

confidence: 99%

Active vibration isolation performance of the bistable nonlinear electromagnetic actuator with the elastic boundary

Yang

Tong

Lin

et al. 2022

Journal of Sound and Vibration

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Section: Problem Statementmentioning

confidence: 99%

Active vibration isolation performance of the bistable nonlinear electromagnetic actuator with the elastic boundary

Yang

Tong

Lin

et al. 2022

Journal of Sound and Vibration

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“…( 12) for f 1 and f 2 . The representation (15) excludes odd multiples of t since these decouple from the even multiples as for the classical Mathieu equation. The order of f 1 and f 2 in Eq.…”

Section: Condition For Harmonic Instabilitymentioning

confidence: 99%

“…Without the plate, the vertical oscillations of the pivot can stabilize the inverted pendulum [20]. The limit of the stable region is found from the same representation (15) as for harmonic instability. For C = 0, the leading terms of the determinant in A and B near i.e., the stability boundary is B = √ −2 A.…”

Section: Stability For Negative Amentioning

confidence: 99%

“…Numerical solu-tions reveal numerous interesting bifurcation phenomena in such systems at subharmonic frequency ratios [13]. Moreover, magnetic pendulums that are excited by time-dependent fields were recently studied experimentally [14,15]. The corresponding mathematical models, which can reproduce the fully nonlinear behavior successfully, include additional terms for a damping element with elasticity and friction.…”

Section: Introductionmentioning

confidence: 99%

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Parametric instability of a vertically driven magnetic pendulum with eddy-current braking by a flat plate

2022

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The vertically driven pendulum is one of the classical systems where parametric instability occurs. We study its behavior with an additional electromagnetic interaction caused by eddy currents in a nearby thick conducting plate that are induced when the bob is a magnetic dipole. The known analytical expressions of the induced electromagnetic force and torque acting on the dipole are valid in the quasistatic limit, i.e., when magnetic diffusivity of the plate is sufficiently high to ensure an equilibrium between magnetic field advection and diffusion. The equation of motion of the vertically driven pendulum is derived assuming that its magnetic dipole moment is aligned with the axis of rotation and that the conducting plate is horizontal. The vertical position of the pendulum remains an equilibrium with the electromagnetic interaction. Conditions for instability of this equilibrium are derived analytically by the harmonic balance method for the subharmonic and harmonic resonances in the limit of weak electromagnetic interaction. The analytical stability boundaries agree with the results of numerical Floquet analysis for these conditions but differ substantially when the electromagnetic interaction is strong. The numerical analysis demonstrates that the area of harmonic instability can become doubly connected. Bifurcation diagrams obtained numerically show the co-existence of stable periodic orbits in such conditions. For moderately strong driving, chaotic motions can be maintained for the subharmonic instability.

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“…Many numerical methods have been applied for solving linear and non-linear differential equations [13][14][15][16]. One of the most popular physical models encountered in undergraduate courses is the simple pendulum and the differential equation describing its motion [14,15,[17][18][19][20][21][22][23][24][25]. Historically, the equation arises when studying the oscillations of a pendulum clock, but also appears in various other areas of physics, since problems often can be reduced to a differential equation similar to that describing the pendulum [16,21,22,26,27].…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution for Time Period of Simple Pendulum Under Magnetic Field

et al. 2023

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In the present study, the numerical solution of the time period of a Simple Pendulum under a magnetic field investigated. The analytical solution presented for the given problem. The numerical solution for the problem achieved by using two numerical quadrature methods, namely, Simpson’s 3/8 and Boole’s method. The period of a simple pendulum with a large angle is presented. The results of the numerical quadrature have been compared to the exact solution. Absolute and relative mistakes of the problem have been presented. The Matlab program 2013R has created a numerical method to analyze the outcome. Moreover, it is established that the comparison results guarantee the present method's ability and accuracy.

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Theoretical and numerical analysis of regular one-side oscillations in a single pendulum system driven by a magnetic field

Cited by 30 publications

References 53 publications

Active vibration isolation performance of the bistable nonlinear electromagnetic actuator with the elastic boundary

Active vibration isolation performance of the bistable nonlinear electromagnetic actuator with the elastic boundary

Parametric instability of a vertically driven magnetic pendulum with eddy-current braking by a flat plate

Numerical Solution for Time Period of Simple Pendulum Under Magnetic Field

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