Harmonic Balance computations


Several specific treatments for Harmonic Balance computations are available such as:

Specific function

antares.prepare4tsm(nharm, list_omega, list_nbblade)

Initialize the HbComputations for a TSM computation with two rows.

  • nharm – the number of harmonics of the computation

  • list_omega – rotation speed of both rows expressed in radians per second

  • list_nbblade – the number of blades of both rows


the two HbComputations

HbComputation object

Defines an Almost-Periodic Computation.

The HbComputation object can ease setting up the Harmonic Balance computations.


  • frequencies: numpy.ndarray

    List of frequencies considered. For TSM, put also the harmonics, not only the fundamental frequency.

  • timelevels: numpy.ndarray

    List of timelevels. Default is evenly spaced timelevels on the smallest frequency.

  • phaselag: numpy.ndarray

    List of phaselags associated to each frequency.

Main functions

class antares.HbComputation

Define an Almost-Periodic Computation.

The IDFT and DFT Almost-Periodic Matrix can be computed. All the definitions are based on the following article

ap_dft_matrix(frequencies=None, timelevels=None)

Compute the Almost-Periodic DFT matrix

ap_idft_matrix(frequencies=None, timelevels=None)

Compute the Almost-Periodic IDFT matrix

ap_source_term(frequencies=None, timelevels=None)

Compute the Almost-Periodic source term which is to \(D_t[\cdot] = i A^{-1} P A\), where \(A\) denotes the DFT matrix, \(A^{-1}\) the IDFT matrix and \(P = diag(-\omega_N,\cdots,\omega_0,\cdots,\omega_N )\)


Returns the condition number of the almost periodic IDFT matrix


Set the timelevels vector as evenly spaced over the base frequency period.


Optimization of the timelevels using gradient-based algorithm. See HbAlgoOPT for more infos.

p_source_term(frequencies=None, timelevels=None)

Compute the analytical mono-frequential source term