AsymptoticStability

class sharpy.postproc.asymptoticstability.AsymptoticStability

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
folder	str	Output folder	./output
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()

Displays root locus diagrams.

Returns the fig and ax handles for further editing.

Returns:ax: Return type:fig

export_eigenvalues(num_evals)

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)

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()

Warning

Under development

Plot the aeroelastic mode shapes for the first n_modes_to_plot

print_eigenvalues()

Prints the eigenvalues to a table with the corresponding natural frequency, period and damping ratios

run()

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)

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: