in case of non-proportional structural damping, our mode shapes of a mdof system becomes complex according to the attached photo in case 1(c) from "Modal Testing: Theory, Practice and Application" by D.J.Ewins.
what's the physical interpretation of complex mode shapes?
Dear Mr. Mohamad
May be this be helpful
http://lpsa.swarthmore.edu/MtrxVibe/Anims/VibrationAnimations.html
Thanks Mr. Muhannad Husain
There was no interpretation of complex mode shapes just normal mode shape animations which was very useful indeed.
In the dynamics of damped mechanical systems we can face generally two complex objects: complex frequency and complex mode.
Real part of the complex frequency usually (not always) is negative and represents the exponential damping (attenuation) of the amplitude, when the imaginary part is the frequency of corresponding wave function.
Complex mode results in the complex amplitude in the given point of a structure (beam, plate etc.). In this case absolute value of this complex number represents amplitude of the vibration and the argument represents the phase.
This article contains some relevant information about this approach.
https://en.wikipedia.org/wiki/Phasor
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