Hi,
I carried out successfully an eigenfrequency analysis of a piezoelectric structure and now I need some help in understanding the meaning of the results.
These are the six eigenfrequencies that I found:
2968.3458428909757-1.8095493631772506i
13608.900380896357+915.4349497985088i
15335.000591497948+424.2799489321054i
40886.81667544398+7309.84485583443i
44541.79244857697+162.59187825549208i
80139.68435108368-3760.1058813209215i
and these are the six eigenvalues (= lambda):
-11.369733971331478-18650.666986680182i
5751.847426252672-85507.24292011866i
2665.82954126111-96352.65040209018i
45929.10979594117-256899.4457924949i
1021.5949005216398-279864.33586834144i
-23625.442026955163-503532.4872367387i
According to the COMSOL documentantion, I found the following relations to post-process these data (please, correct me, if I am wrong):
1. eigenfrequency = -1*lambda / (2*pi*i)
2. mode_frequency = abs( imag(-1*lambda) / (2*pi) )
3. Quality_factor = imag(lambda) / (2*real(lambda) )
4. decay_factor = real(lambda) (also named elesewhere "damping in time")
By applying these formulas: I am finding, correctly, positive values for "mode_frequencies" but I am getting some "quality_factors" and "decay_factors" that are positive and others that are negative.
What does it physically mean? Have I found stable (positive eigenvalues) and unstable (negative eigenvalues) modes for my structure? Or simply is there anything wrong with my simulations/results?
Thank you very much.
PS: I applied no loads to structure (only the constraints for the fixed end of the beam and the ground and the terminal conditions for the piezo).
I carried out successfully an eigenfrequency analysis of a piezoelectric structure and now I need some help in understanding the meaning of the results.
These are the six eigenfrequencies that I found:
2968.3458428909757-1.8095493631772506i
13608.900380896357+915.4349497985088i
15335.000591497948+424.2799489321054i
40886.81667544398+7309.84485583443i
44541.79244857697+162.59187825549208i
80139.68435108368-3760.1058813209215i
and these are the six eigenvalues (= lambda):
-11.369733971331478-18650.666986680182i
5751.847426252672-85507.24292011866i
2665.82954126111-96352.65040209018i
45929.10979594117-256899.4457924949i
1021.5949005216398-279864.33586834144i
-23625.442026955163-503532.4872367387i
According to the COMSOL documentantion, I found the following relations to post-process these data (please, correct me, if I am wrong):
1. eigenfrequency = -1*lambda / (2*pi*i)
2. mode_frequency = abs( imag(-1*lambda) / (2*pi) )
3. Quality_factor = imag(lambda) / (2*real(lambda) )
4. decay_factor = real(lambda) (also named elesewhere "damping in time")
By applying these formulas: I am finding, correctly, positive values for "mode_frequencies" but I am getting some "quality_factors" and "decay_factors" that are positive and others that are negative.
What does it physically mean? Have I found stable (positive eigenvalues) and unstable (negative eigenvalues) modes for my structure? Or simply is there anything wrong with my simulations/results?
Thank you very much.
PS: I applied no loads to structure (only the constraints for the fixed end of the beam and the ground and the terminal conditions for the piezo).