nass-micro-station-measurements/2018-01-12 - Marc/index.org

Measurements

• Experimental conditions
• Measurements procedure
• Measurement Channels
• Experiments
• Data Analysis
  • Loading and pre-processing of the data
  • X-direction FRF
  • Y-direction FRF
  • Z-direction FRF
  • Save the processed data
• Results

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.

Measurements procedure

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

• Marle
• Tilt Stage
• Top of Hexapod

Natural Frequency [Hz]	4.5
Weight [g]	140
Sensitivity [V/(m/s)]	31.3

L-28LB Geophone characteristics

The structure is excited using an instrumented hammer with impacts on

• Marble X-Y-Z
• Hexapod X-Y-Z

Measurement Channels

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

Description of each measurement channel

Experiments

Meas. nb	Location	Direction
1	Marble	X
2	Hexapod	X
3	Marble	Y
4	Hexapod	Y
5	Marble	Z
6	Hexapod	Z

Description of the location of direction of the excitation for each measurement

Data Analysis

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

X-direction FRF

  <<plt-matlab>>

Response to a force applied on the marble in the X direction

  <<plt-matlab>>

Response to a force applied on the hexa in the X direction

Y-direction FRF

  <<plt-matlab>>

Response to a force applied on the marble in the Y direction

  <<plt-matlab>>

Response to a force applied on the hexa in the Y direction

Z-direction FRF

  <<plt-matlab>>

Response to a force applied on the marble in the Z direction

  <<plt-matlab>>

Response to a force applied on the hexa in the Z direction

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');

Results

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