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Extra resources for A hp-discontinuous Galerkin method for the time-dependent Maxwell’s equation: a priori error estimate

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Muszynska [21] in the terms: A rotating machine is stable if its rotor performs a pure rotational motion around an appropriate axis at a required rotational speed and this motion is not accompanied by other modes of vibrations of the rotor, its elements or other stationary parts of the machine, or, if such vibrations take place, their amplitudes do not exceed admitted, acceptable values. , any random perturbation cannot drastically change its behavior. Such a perturbation causes only a transient decaying process leading to a previous regime of performance, or to a new one, which is included in the acceptable limits.

2 for its application to the undamped Jecott rotor). 1 In a similar way, complex coordinates for angular displacements can be defined (Chapter 3). In general, when using the complex-coordinates notation, the equation of motion of a multi-degrees-of-freedom axisymmetrical rotating system (Chapter 4) results in M0 q ¨0 (w)+ (C0 +lG0 ) q˙ 0 (w)+ (K0 +lH0 ) q0 (w)= f 0 (w) . 2) becomes ¸ µ· 0 ¸ · ¸¶ · C 0 G0 0 M0 0 q ¨ (w) + + q(w)+ ˙ 0 0 0 Mµ· 0 · C0 G 0 ¸ ¸¶ K0 0 0 H0 + + = f (w) . 2 The matrices that are symmetric when using the real coordinates approach are real in the equation written in terms of complex coordinates, whereas skew-symmetric matrices give way to symmetric, imaginary terms.

Amplitudes are independent of system axial symmetry. Given an infinitesimal deflection to an otherwise axisymmetric system, the amplitude will selfpropagate for whipping speeds above the threshold of instability. 1. Characterization of forced and self-excited rotor vibrations. 1 Linear rotordynamics Hydrodynamic bearings, labyrinth, or liquid seals Blade-tip clearance excitation Centrifugal pump and compressor whirl Propeller and turbomachinery whirl Ratio $@l 0> 2 ? $@l ? 1 ($@l = 0,5) $@l ? 0> 5 (0> 45 ?

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