Vibration and Dynamic Instability of a Beam-Plate in a Transverse Magnetic Field
01 Mar 1969-Journal of Applied Mechanics (American Society of Mechanical Engineers Digital Collection)-Vol. 36, Iss: 1, pp 92-100
About: This article is published in Journal of Applied Mechanics.The article was published on 1969-03-01. It has received 91 citations till now. The article focuses on the topics: Magnetic pressure & Magnetic energy.
TL;DR: In this paper, the authors presented experimental evidence for chaotic type non-periodic motions of a deterministic magnetoelastic oscillator, analogous to solutions in non-linear dynamic systems possessing what have been called "strange attractors".
Abstract: Experimental evidence is presented for chaotic type non-periodic motions of a deterministic magnetoelastic oscillator. These motions are analogous to solutions in non-linear dynamic systems possessing what have been called “strange attractors”. In the experiments described below a ferromagnetic beam buckled between two magnets undergoes forced oscillations. Although the applied force is sinusoidal, nevertheless bounded, non-periodic, apparently chaotic motions result due to jumps between two or three stable equilibrium positions. A frequency analysis of the motion shows a broad spectrum of frequencies below the driving frequency. Also the distribution of zero crossing times shows a broad spectrum of times greater than the forcing period. The driving amplitude and frequency parameters required for these non-periodic motions are determined experimentally. A continuum model based on linear elastic and non-linear magnetic forces is developed and it is shown that this can be reduced to a single degree of freedom oscillator which exhibits chaotic solutions very similar to those observed experimentally. Thus, both experimental and theoretical evidence for the existence of a strange attractor in a deterministic dynamical system is presented.
TL;DR: In this paper, a combination of electrostatic actuators is used to tune the linear and nonlinear stiffness coefficients of a uniaxial micromechanical device without affecting the resonant frequency or the linear stiffness.
Abstract: Using a combination of electrostatic actuators, we present a method to independently tune the linear and nonlinear stiffness coefficients of a uniaxial micromechanical device. To demonstrate the method's capability, we investigated the tuning of an oscillator with linear and cubic restoring forces. We successfully tuned the cubic stiffness from 0.31/spl times/10/sup 11/ to -5.1/spl times/10/sup 11/ N/m/sup 3/ without affecting the resonant frequency or the linear stiffness. Numerical results are presented which characterize the actuators and indicate important design parameters. Finally, issues such as actuator design, quadratic stiffness, and stability are discussed.
01 Jan 1978
TL;DR: A magnetic “stick–slip” model is proposed to explain the sudden bending transition of an elastic rod experiencing a uniform induction field applied at a normal angle with respect to its long axis and it is demonstrated that the magnetoelastic buckling corresponds to a classical Landau second-order transition.
Abstract: In its simplest form the magnetoelastic buckling instability refers to the sudden bending transition of an elastic rod experiencing a uniform induction field applied at a normal angle with respect to its long axis. This fundamental physics phenomenon was initially documented in 1968, and, surprisingly, despite many refinements, a gap has always remained between the observations and the theoretical expectations. Here, we first renew the theory with a simple model based on the assumption that the magnetization follows the rod axis as soon as it bends. We demonstrate that the magnetoelastic buckling corresponds to a classical Landau second-order transition. Our model yields a solution for the critical field as well as the shape of the deformed rods which we compare with experiments on flexible ferromagnetic nickel rods at the centimeter scale. We also report this instability at the micrometer scale with specially designed rods made of nanoparticles. We characterized our samples by determining all of the relevant parameters (radius, length, Young modulus, magnetic susceptibility) and, using these values, we found that the theory fits extremely well the experimental results for both systems without any adjustable parameter. The superparamagnetic feature of the microrods also highlights the fact that ferromagnetic systems break the symmetry before the buckling. We propose a magnetic “stick–slip” model to explain this peculiar feature, which was visible in past reports but never detailed.
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...In this latter case, the system may be studied only for its equilibrium configuration, or for its dynamic behavior (10)....
TL;DR: In this article, a lightweight damping device is proposed by utilizing eddy current damping, and it can be easily attached onto the workpiece surface by glue, which can be applied to damp multiple modes and attenuate machining vibration of a thin-walled frame.
Abstract: Machining vibrations are harmful to workpiece surface quality and tool life, especially for thin-walled parts. A lightweight damping device is proposed by utilizing eddy current damping, and it can be easily attached onto the workpiece surface by glue. The cylindrical device is mainly composed of a magnet, an aluminum cylindrical conductor, and two springs. An induced repulsive force due to the machining vibration is generated and transmitted to the workpiece and then contributed to the vibration attenuation. Dynamic response evaluation on a cantilever beam by hammer tests demonstrates that the device is able to damp vibration mode and the effect of additive mass on the beam dynamics is investigated by roving the attaching point. Moreover, the device is applied to damp multiple modes and attenuate machining vibration of a thin-walled frame. Machining tests under different configurations of cutting parameters are carried out, and its effectiveness of wide band and adaptability to the varying machining processes are validated.