13 research outputs found
Fast Algorithms for the computation of Fourier Extensions of arbitrary length
Fourier series of smooth, non-periodic functions on are known to
exhibit the Gibbs phenomenon, and exhibit overall slow convergence. One way of
overcoming these problems is by using a Fourier series on a larger domain, say
with , a technique called Fourier extension or Fourier
continuation. When constructed as the discrete least squares minimizer in
equidistant points, the Fourier extension has been shown shown to converge
geometrically in the truncation parameter . A fast algorithm has been described to compute Fourier extensions for the case
where , compared to for solving the dense discrete
least squares problem. We present two algorithms for
the computation of these approximations for the case of general , made
possible by exploiting the connection between Fourier extensions and Prolate
Spheroidal Wave theory. The first algorithm is based on the explicit
computation of so-called periodic discrete prolate spheroidal sequences, while
the second algorithm is purely algebraic and only implicitly based on the
theory
Balancing of Flexible Rotors Supported on Fluid Film Bearings by Means of Influence Coefficients Calculated by the Numerical Assembly Technique
In this paper, a new method for the balancing of rotor-bearing systems supported on fluid film bearings is proposed. The influence coefficients necessary for balancing are calculated using a novel simulation method called the Numerical Assembly Technique. The advantages of this approach are quasi-analytical solutions for the equations of motion of complex rotor-bearing systems and very low computation times. The Numerical Assembly Technique is extended by speed-dependent stiffness and damping coefficients approximated by the short-bearing theory to model the behavior of rotor systems supported on fluid film bearings. The rotating circular shaft is modeled according to the Rayleigh beam theory. The Numerical Assembly Technique is used to calculate the steady-state harmonic response, influence coefficients, eigenvalues, and the Campbell diagram of the rotor. These values are compared to simulations with the Finite Element Method to show the accuracy of the procedure. Two numerical examples of rotor-bearing systems are successfully balanced by the proposed balancing method