Resonant Torques Research Articles

Locking of multiple resonant mode structures in the reversed-field pinch

Locking of a rotating mode by applying a resonant magnetic perturbation having the same helicity has been observed on various devices. Experiments have been carried out on the Madison Symmetric Torus reversed-field pinch (RFP) [Dexter et al., Fusion Technol. 19, 131 (1991)] which show that an externally applied magnetic perturbation can cause locking of the dominant magnetic modes (poloidal mode number m=1, toroidal mode numbers n=5–10) when the perturbation is resonant with them. A perturbation which is not resonant (m=0 or 2) produces no such effect. Thus, resonant torques may lock a stochastic magnetic structure arising from several modes, as likely exists in the RFP, as well as a distinct island as exists in tokamaks, although the details of the interaction are likely to be different.

Estimating induction motor shaft stress transients under shaft resonant and de-tuned conditions

When power to an induction motor is disconnected and then re-connected, the shaft experiences a potentially harmful transient torsional stress. The magnitude of the transient shaft stress depends on the electromagnetic torque of the motor and the resonant frequency of the system formed by the shaft and motor and load masses. To avoid resonance between transient electromagnetic torque frequencies and the mechanical natural frequency, the shaft may be de-tuned. This paper shows quantitatively the extent of worst-case resonant torques, the effect of an enforced reclosure time delay and the mitigating effects of altering the shaft resonant frequency to avoid high stresses. Peak shaft reclosure torque, when de-tuned, is independent of most motor parameters.

Dynamics of binary-disk interaction. 1: Resonances and disk gap sizes

We investigate the gravitational interaction of a generally eccentric binary star system with circumbinary and circumstellar gaseous disks. The disks are assumed to be coplanar with the binary, geometrically thin, and primarily governed by gas pressure and (turbulent) viscosity but not self-gravity. Both ordinary and eccentric Lindblad resonances are primarily responsible for truncating the disks in binaries with arbitrary eccentricity and nonextreme mass ratio. Starting from a smooth disk configuration, after the gravitational field of the binary truncates the disk on the dynamical timescale, a quasi-equilibrium is achieved, in which the resonant and viscous torques balance each other and any changes in the structure of the disk (e.g., due to global viscous evolution) occur slowly, preserving the average size of the gap. We analytically compute the approximate sizes of disks (or disk gaps) as a function of binary mass ratio and eccentricity in this quasi-equilibrium. Comparing the gap sizes with results of direct simulations using the smoothed particle hydrodynamics (SPH), we obtain a good agreement. As a by-product of the computations, we verify that standard SPH codes can adequately represent the dynamics of disks with moderate viscosity, Reynolds number R approximately 10(exp 3). For typical viscous disk parameters, and with a denoting the binary semimajor axis, the inner edge location of a circumbinary disk varies from 1.8a to 2.6a with binary eccentricity increasing from 0 to 0.25. For eccentricities 0 less than e less than 0.75, the minimum separation between a component star and the circumbinary disk inner edge is greater than a. Our calculations are relevant, among others, to protobinary stars and the recently discovered T Tau pre-main-sequence binaries. We briefly examine the case of a pre-main-sequence spectroscopic binary GW Ori and conclude that circumbinary disk truncation to the size required by one proposed spectroscopic model cannot be due to Linblad resonances, even if the disk is nonviscous.

Ring torque on janus and the melting of Enceladus

Voyager 2 images show parts of Enceladus' surface to be very smooth, lacking craters down to the resolution limit of 4 km. This absence of craters indicates geologically recent resurfacing, probably due to internal melting. However, calculations of current heating mechanisms, including radioactive decay and tidal heating due to Enceladus' resonance with Dione, yield heating rates too small to cause melting. The orbital mean motion of Janus (1980S1) is slightly less than twice that of Enceladus and, according to theoretical calculations, is currently decreasing as Janus' orbit evolves outward due to resonant torques from Saturn's rings. If Janus were ever locked into a stable 2:1 orbital commensurability with Enceladus, the resulting angular momentum transfer could have sufficiently enhanced the eccentricity of Enceladus' orbit for the ensuing tidal heating to have melted Enceladus' interior. The existence of a Laplace-like three-body resonance including Dione, although unlikely, would have increased heating. If Janus were indeed held in resonance with Enceladus until recently (10 7–10 8 years B.P.) when the lock was disrupted by an unspecified event (possibly a catastrophic collision which simultaneously created the coorbital pair, or by the influence of Dione) both the recent internal activity of Enceladus and the proximity of Janus to Saturn's rings may be explained. However, the predicted rapid time scale for ring evolution due to resonant torques from Saturn's inner moons remains a major problem.