How to find the rotational mode shapes using an accelerometer that can measure the translational mode shape only in the modal analysis experiment for a cantilever beam?
If two instruments are placed on opposite faces of cantilever, and accelaration is measured same time, it is possible. After getting the output, plot them on same time scale, and look for direction. Then process them about centreline (longitudinal axis), to get the rorational values. First, you may analyse the beam using solid elements, and rotational loads (time varying torsion at the end), to get the output as acceleration. Then you may process, and check for the expected output.
I would say that you need more than one sensing point to describe your shape; then you may derive the shape spatially. This is what I achieved with full-field measurements, please have a look to:
Conference Paper On the estimation of frequency response functions, dynamic r...
Conference Paper Accurate FRF estimation of derivative quantities from differ...
Article Chasing the high-resolution mapping of rotational and strain...
If the spatial description is too coarse, other authors have tried with closely spaced accereometers to get the same spatial derivation I did with non contacting measurements.
Best regards,
Alessandro
To find the rotational mode shapes of a cantilever beam using an accelerometer that can measure translational motion, you will need to perform a modal analysis experiment and use the measured translational mode shapes to determine the rotational mode shapes. Here are the general steps you can follow:
Phi_rotational(x) = -x * Phi_translational''(x) / L
where Phi_rotational(x) is the rotational mode shape at position x, Phi_translational''(x) is the second derivative of the translational mode shape at position x, and L is the length of the beam.
5. Repeat the above steps for each mode shape you want to measure.
By following these steps, you should be able to determine the rotational mode shapes of the cantilever beam using an accelerometer that can measure translational motion. It is important to note that the accuracy of the measured rotational mode shapes will depend on the accuracy of the measured translational mode shapes, as well as the accuracy of the excitation force.
Zubair R Wani Do you have experience in EMA for real data? I mean roving hammer method to obtain the mode shapes?
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