Experimental Modal Analysis (vibration_toolbox.ema)

ema – Experimental Modal Analysis

ema.frf(x, f, dt)

Return the frequency response function.

Calculates \(H(i\\omega)\), and coherance of the sampled data.

Parameters

x: array

Array with the displacement data

f: array

Array with the force data

dt: float

Time step of the sampled data

n: int

Number of points in the fft

Returns

freq: array

Driving frequencies

mag: array

Magnitude of the frequency response function

ang: array

Phase of the frequency response function

coh: array

Coherence function

Plot with the frf magnitude, phase and coherence.

Examples

>>> # First we need to load the sampled data which in a .mat file
>>> import vibration_toolbox as vtb
>>> import scipy.io as sio
>>> data = sio.loadmat(vtb.__path__[0] + '/data/frf_data1.mat')
>>> #print(data)
>>> # Data is imported as arrays. Modify then to fit our function
>>> x = data['x']
>>> x = x.reshape(len(x))
>>> f = data['f']
>>> f = f.reshape(len(f))
>>> dt = data['dt']
>>> dt = float(dt)
>>> # Now we are able to call the function
>>> freq, mag, ang, coh = vtb.frf(x, f, dt)
>>> mag[10]
1.018394853080...

ema.mdof_cf(f, TF, Fmin=None, Fmax=None)

Curve fit to multiple degree of freedom FRF.

If Fmin and Fmax are not entered, the first and last elements of TF are used.

If the first column of TF is a collocated (input and output location are the same), then the mode shape returned is the mass normalized mode shape. This can then be used to generate an identified mass, damping, and stiffness matrix as shown in the following example.

Parameters

f: array

The frequency vector in Hz. Does not have to start at 0 Hz.

TF: array

The complex transfer function

Fmin: int

The minimum frequency to be used for curve fitting in the FRF

Fmax: int

The maximum frequency to be used for curve fitting in the FRF

Returns

z: double

The damping ratio

nf: double

Natural frequency (Hz)

u: array

The mode shape

Notes

FRF are columns comprised of the FRFs presuming single input, multiple output z and nf are the damping ratio and natural frequency (Hz) u is the mode shape. Only one peak may exist in the segment of the FRF passed to sdofcf. No zeros may exist within this segment. If so, curve fitting becomes unreliable.

Examples

>>> # First we need to load the sampled data which is in a .mat file
>>> import vibration_toolbox as vtb
>>> import scipy.io as sio
>>> data = sio.loadmat(vtb.__path__[0] + '/data/case2.mat')
>>> #print(data)
>>> # Data is imported as arrays. Modify then to fit our function
>>> TF = data['Hf_chan_2']
>>> f = data['Freq_domain']
>>> # Now we are able to call the function
>>> z, nf, a = vtb.mdof_cf(f,TF,500,1000)
>>> nf
192.59382330...

ema.plot_fft(t, time_response, ax=None, **kwargs)

Plot fft ot time response.

Parameters

tarray

Time array.

time_responsearray

Array with the system’s time response.

axmatplotlib.axes, optional

Matplotlib axes where the amplitude will be plotted. If None creates a new.

Returns

axarray with matplotlib.axes, optional

Matplotlib axes array created with plt.subplots. Plot has frequency in rad/s and magnitude in meters peak to peak.

Examples

>>> import vibration_toolbox as vtb
>>> t = np.linspace(0, 10, 1000)
>>> time_response = 2 * np.sin(40*t)
>>> vtb.plot_fft(t, time_response)
<matplotlib.axes...

ema.sdof_cf(f, TF, Fmin=None, Fmax=None)

Curve fit to a single degree of freedom FRF.

Only one peak may exist in the segment of the FRF passed to sdofcf. No zeros may exist within this segment. If so, curve fitting becomes unreliable.

If Fmin and Fmax are not entered, the first and last elements of TF are used.

Parameters

f: array

The frequency vector in Hz. Does not have to start at 0 Hz.

TF: array

The complex transfer function

Fmin: int

The minimum frequency to be used for curve fitting in the FRF

Fmax: int

The maximum frequency to be used for curve fitting in the FRF

Returns

z: double

The damping ratio

nf: double

Natural frequency (Hz)

a: double

The numerator of the identified transfer functions

Plot of the FRF magnitude and phase.

Examples

>>> # First we need to load the sampled data which is in a .mat file
>>> import vibration_toolbox as vtb
>>> import scipy.io as sio
>>> data = sio.loadmat(vtb.__path__[0] + '/data/case1.mat')
>>> #print(data)
>>> # Data is imported as arrays. Modify then to fit our function.
>>> TF = data['Hf_chan_2']
>>> f = data['Freq_domain']
>>> # Now we are able to call the function
>>> z, nf, a = vtb.sdof_cf(f,TF,500,1000)
>>> nf
212.092530551...