Measurements

1. Experimental conditions
2. Measurements procedure
3. Measurement Channels
4. Experiments
5. Data Analysis
6. Results

1 Experimental conditions

Date	2018-01-12
Sensors	Geophones
Excitation	Instrumented Hammer
Location	Laboratory
Notes	Unglued Granite

The granite is not glued to the floor
FS = 512Hz
Made by Marc Lesourd on the 12 of January 2018

Goal: Obtain better coherence at low frequency.

2 Measurements procedure

Geophones L-28LB geophones (table 1) are placed on

Marle
Tilt Stage
Top of Hexapod

Table 1: L-28LB Geophone characteristics
Natural Frequency [Hz]	4.5
Weight [g]	140
Sensitivity [V/(m/s)]	31.3

The structure is excited using an instrumented hammer with impacts on

Marble X-Y-Z
Hexapod X-Y-Z

3 Measurement Channels

Table 2: Description of each measurement channel
Ch. nb	Element	Location	Direction
1	Hammer	variable
2	Geophone	Marble	X-Y-Z
3	Geophone	Tilt stage	X-Y-Z
4	Geophone	Top of Hexapod	X-Y-Z

4 Experiments

Table 3: Description of the location of direction of the excitation for each measurement
Meas. nb	Location	Direction
1	Marble	X
2	Hexapod	X
3	Marble	Y
4	Hexapod	Y
5	Marble	Z
6	Hexapod	Z

5 Data Analysis

5.1 Loading and pre-processing of the data

The Geophone sensitivity is defined below:

w0 = 4.5*2*pi; % [rad/s]
ksi = 0.38;
G0 = 31.3; % [V/(m/s)]
G = G0*(s/w0)^2/((s/w0)^2 + 2*ksi*(s/w0) + 1); % [V/(m/s)]

We then:

load the data
add a minus sign when needed
integrate the signal to have displacement instead of velocity
scaled with the sensitivity of the Geophone

load('./raw_data/freq_frf.mat') % freq_frf

w = j*2*pi*freq_frf; % j.omega in [rad/s]

scaling = squeeze(freqresp(G, 2*pi*freq_frf))/G0;

load('./raw_data/frf_marble_x.mat') % ReIm1
frf_marble_x = zeros(size(ReIm1, 1), 3);
frf_marble_x(:, 1) = -ReIm1(:, 2)./w./scaling; % marble_x
frf_marble_x(:, 2) = -ReIm1(:, 3)./w./scaling; % tilt_x
frf_marble_x(:, 3) = -ReIm1(:, 4)./w./scaling; % hexa_x

load('./raw_data/frf_hexa_x.mat') % ReIm2
frf_hexa_x = zeros(size(ReIm2, 1), 3);
frf_hexa_x(:, 1) = -ReIm2(:, 2)./w./scaling; % marble_x
frf_hexa_x(:, 2) = -ReIm2(:, 3)./w./scaling; % tilt_x
frf_hexa_x(:, 3) = -ReIm2(:, 4)./w./scaling; % hexa_x

load('./raw_data/frf_marble_y.mat') % ReIm3
frf_marble_y = zeros(size(ReIm3, 1), 3);
frf_marble_y(:, 1) = -ReIm3(:, 2)./w./scaling; % marble_y
frf_marble_y(:, 2) = -ReIm3(:, 3)./w./scaling; % tilt_y
frf_marble_y(:, 3) = -ReIm3(:, 4)./w./scaling; % hexa_y

load('./raw_data/frf_hexa_y.mat') % ReIm4
frf_hexa_y = zeros(size(ReIm4, 1), 3);
frf_hexa_y(:, 1) = ReIm4(:, 2)./w./scaling; % marble_y
frf_hexa_y(:, 2) = ReIm4(:, 3)./w./scaling; % tilt_y
frf_hexa_y(:, 3) = ReIm4(:, 4)./w./scaling; % hexa_y

load('./raw_data/frf_marble_z.mat') % ReIm5
frf_marble_z = zeros(size(ReIm5, 1), 3);
frf_marble_z(:, 1) = ReIm5(:, 2)./w./scaling; % marble_z
frf_marble_z(:, 2) = ReIm5(:, 3)./w./scaling; % tilt_z
frf_marble_z(:, 3) = ReIm5(:, 4)./w./scaling; % hexa_z

load('./raw_data/frf_hexa_z.mat') % ReIm6
frf_hexa_z = zeros(size(ReIm6, 1), 3);
frf_hexa_z(:, 1) = ReIm6(:, 2)./w./scaling; % marble_z
frf_hexa_z(:, 2) = ReIm6(:, 3)./w./scaling; % tilt_z
frf_hexa_z(:, 3) = ReIm6(:, 4)./w./scaling; % hexa_z

load('./raw_data/coher_marble_x.mat') % coh1
coh_marble_x = zeros(size(coh1, 1), 3);
coh_marble_x(:, 1) = coh1(:, 2); % marble_x
coh_marble_x(:, 2) = coh1(:, 3); % tilt_x
coh_marble_x(:, 3) = coh1(:, 4); % hexa_x

load('./raw_data/coher_hexa_x.mat') % coh2
coh_hexa_x = zeros(size(coh2, 1), 3);
coh_hexa_x(:, 1) = coh2(:, 2); % marble_x
coh_hexa_x(:, 2) = coh2(:, 3); % tilt_x
coh_hexa_x(:, 3) = coh2(:, 4); % hexa_x

load('./raw_data/coher_marble_y.mat') % coh3
coh_marble_y = zeros(size(coh3, 1), 3);
coh_marble_y(:, 1) = coh3(:, 2); % marble_y
coh_marble_y(:, 2) = coh3(:, 3); % tilt_y
coh_marble_y(:, 3) = coh3(:, 4); % hexa_y

load('./raw_data/coher_hexa_y.mat') % coh4
coh_hexa_y = zeros(size(coh4, 1), 3);
coh_hexa_y(:, 1) = coh4(:, 2); % marble_y
coh_hexa_y(:, 2) = coh4(:, 3); % tilt_y
coh_hexa_y(:, 3) = coh4(:, 4); % hexa_y

load('./raw_data/coher_marble_z.mat') % coh5
coh_marble_z = zeros(size(coh5, 1), 3);
coh_marble_z(:, 1) = coh5(:, 2); % marble_z
coh_marble_z(:, 2) = coh5(:, 3); % tilt_z
coh_marble_z(:, 3) = coh5(:, 4); % hexa_z

load('./raw_data/coher_hexa_z.mat') % coh6
coh_hexa_z = zeros(size(coh6, 1), 3);
coh_hexa_z(:, 1) = coh6(:, 2); % marble_z
coh_hexa_z(:, 2) = coh6(:, 3); % tilt_z
coh_hexa_z(:, 3) = coh6(:, 4); % hexa_z

5.2 X-direction FRF

Figure 1: Response to a force applied on the marble in the X direction

Figure 2: Response to a force applied on the hexa in the X direction

5.3 Y-direction FRF

Figure 3: Response to a force applied on the marble in the Y direction

Figure 4: Response to a force applied on the hexa in the Y direction

5.4 Z-direction FRF

Figure 5: Response to a force applied on the marble in the Z direction

Figure 6: Response to a force applied on the hexa in the Z direction

5.5 Save the processed data

Finally, we save the processed data.

save('./data/id31_microstation_2018_01_12_frf.mat', ...
       'freq_frf', ...
       'frf_marble_x', ...
       'frf_marble_y', ...
       'frf_marble_z', ...
       'frf_hexa_x', ...
       'frf_hexa_y', ...
       'frf_hexa_z');
save('./data/id31_microstation_2018_01_12_coh.mat', ...
       'freq_frf', ...
       'coh_marble_x', ...
       'coh_marble_y', ...
       'coh_marble_z', ...
       'coh_hexa_x', ...
       'coh_hexa_y', ...
       'coh_hexa_z');

6 Results

Resonances at 42Hz, 70Hz and 125Hz have been identified
The coherence is much better than when using accelerometers