mdof.modal module

This module implements functions that extract modal information from a state space realization or transfer function.

mdof.modal.system_modes(realization, dt, n_peaks=None, sorted_by=None, sort_descending=True, filter_by=None, filter_lim=None, **options)

Modal identification from a state space system realization.

Parameters:

• realization (tuple of arrays) – realization in the form of state space coefficients (A,B,C,D)

• dt (float) – timestep.

• n_peaks (int) – (optional) number of peaks to return. By default, all peaks are returned.

• sorted_by (string) – (optional) characteristic by which to sort peaks. choose out of the following: ‘period’, ‘MPC’, ‘EMAC’, … sorting order is highest to lowest (descending), unless sort_descending is set to False.

• sort_descending (boolean) – (optional) sort from highest to lowest default: True

• filter_by (list of strings) – (optional) list of characteristics by which to filter peaks. example: [‘MPC’, ‘EMAC’]. choose out of the following: ‘period’, ‘MPC’, ‘EMAC’, ‘frequency’, ‘damping’, ‘condition_number’, …

• filter_lim (list of tuples of floats) – (optional) list of lower and upper limits by which to filter. example: [(0.5,1.0), (0.5,1.0)]

• decimation (int) – (optional) decimation factor. default: 1

• Observability (array) – (optional) Observability matrix; can be reused from mdof.realize.srim(). default: None

Returns:

system modes, including natural frequencies, damping ratios, mode shapes, condition numbers, and modal validation metrics EMAC and MPC.

Return type:

dictionary

mdof.modal.spectrum_modes(periods, amplitudes, n_peaks=None, sorted_by=None, **options)

Modal identification from a transfer function.

Parameters:

• periods (array) – transfer function periods

• amplitudes (array) – transfer function amplitudes

• n_peaks (int) – (optional) number of peaks to return. By default, all peaks are returned.

• sorted_by (string) – (optional) characteristic by which to sort peaks. choose out of the following: ‘height’, … sorting order is highest to lowest (descending).

• prominence (float) – (optional) prominence of selected peaks

Returns:

(fundamental_periods, fundamental_amplitudes)

Return type:

tuple