AsymptoticStability¶

class sharpy.postproc.asymptoticstability.AsymptoticStability[source]¶

Calculates the asymptotic stability properties of the linearised aeroelastic system by computing the corresponding eigenvalues.

To use an iterative eigenvalue solver, the setting iterative_eigvals should be set to on. This will be beneficial when deailing with very large systems. However, the direct method is preferred and more efficient when the system is of a relatively small size (typically around 5000 states).

Warning

The setting modes_to_plot to plot the eigenvectors in Paraview is currently under development.

The settings that this solver accepts are given by a dictionary, with the following key-value pairs:

Name	Type	Description	Default
`print_info`	`bool`	Print information and table of eigenvalues	`False`
`reference_velocity`	`float`	Reference velocity at which to compute eigenvalues for scaled systems	`1.0`
`frequency_cutoff`	`float`	Truncate higher frequency modes. If zero none are truncated	`0`
`export_eigenvalues`	`bool`	Save eigenvalues and eigenvectors to file.	`False`
`display_root_locus`	`bool`	Show plot with eigenvalues on Argand diagram	`False`
`velocity_analysis`	`list(float)`	List containing min, max and number of velocities to analyse the system	`[]`
`iterative_eigvals`	`bool`	Calculate the first `num_evals` using an iterative solver.	`False`
`num_evals`	`int`	Number of eigenvalues to retain.	`200`
`modes_to_plot`	`list(int)`	List of mode numbers to simulate and plot	`[]`
`postprocessors`	`list(str)`	To be used with `modes_to_plot`. Under development.	`[]`
`postprocessors_settings`	`dict`	To be used with `modes_to_plot`. Under development.	`{}`

display_root_locus()[source]¶

Displays root locus diagrams.

Returns the fig and ax handles for further editing.

Returns: ax:
Return type: fig

export_eigenvalues(num_evals)[source]¶

Saves a num_evals number of eigenvalues and eigenvectors to file. The files are saved in the output directoy and include:

eigenvectors.dat: (num_dof, num_evals) array of eigenvectors

eigenvalues_r.dat: (num_evals, 1) array of the real part of the eigenvalues

eigenvalues_i.dat: (num_evals, 1) array of the imaginary part of the eigenvalues.

The units of the eigenvalues are rad/s

References

Loading and saving complex arrays: https://stackoverflow.com/questions/6494102/how-to-save-and-load-an-array-of-complex-numbers-using-numpy-savetxt/6522396

Parameters: num_evals – Number of eigenvalues to save

mode_time_domain(fact, fact_rbm, mode_num, cycles=2)[source]¶

Returns a single, scaled mode shape in time domain.

Parameters

fact – Structural deformation scaling
fact_rbm – Rigid body motion scaling
mode_num – Number of mode to plot
cycles – Number of periods/cycles to plot

Returns

Time domain array and scaled eigenvector in time.

Return type

tuple

plot_modes()[source]¶: Warning

Under development

Plot the aeroelastic mode shapes for the first n_modes_to_plot

print_eigenvalues()[source]¶: Prints the eigenvalues to a table with the corresponding natural frequency, period and damping ratios

run(online=False)[source]¶

Computes the eigenvalues and eigenvectors

Returns: Eigenvalues sorted and frequency truncated eigenvectors (np.ndarray): Corresponding mode shapes
Return type: eigenvalues (np.ndarray)

static sort_eigenvalues(eigenvalues, eigenvectors, frequency_cutoff=0)[source]¶

Sort continuous-time eigenvalues by order of magnitude.

The conjugate of complex eigenvalues is removed, then if specified, high frequency modes are truncated. Finally, the eigenvalues are sorted by largest to smallest real part.

Parameters

eigenvalues (np.ndarray) – Continuous-time eigenvalues
eigenvectors (np.ndarray) – Corresponding right eigenvectors
frequency_cutoff (float) – Cutoff frequency for truncation [rad/s]

Returns: