The 'ms' calculated from 'modalfit' function is basically mode shape, which refers to the shape that a structure takes while vibrating at one of its natural frequencies. For a simple single-degree-of-freedom (SDOF) system, the mode shape is a measure of the relative displacement of the mass when the system vibrates at its natural frequency. The mode shapes returned by the modalfit are complex because they are derived by frequency response functions (frf) which are inherently complex. For interpreting complex mode shapes:
- Real part - The magnitude of the complex mode shape vector, i.e. the relative amplitude of motion at that point.
- Imaginary part - The phase angle of the complex mode shape vector, i.e. the phase relationship of the motion at that point relative to the input force.
When you calculate the mode shape by hand for a simple SDOF system, you consider only the amplitude of the displacement, which results in a real number. However, while experimentation with damped systems, the phase relationship is crucial for understanding how the structure deforms over time during vibration. Hence the imaginary part, which also represents the damped natural frequency.
An example for understanding the calculation for the same use case, spring-mass-damper system which has one mode (SDOF) is given in the following resource: https://www.mathworks.com/help/signal/ref/modalfrf.html?searchHighlight=modal%20analysis%20modalfit&s_tid=srchtitle_support_results_8_modal%20analysis%20modalfit#bvncuj_
You may also refer to this resource for visualization of mode shapes: https://www.mathworks.com/help/signal/ug/modal-analysis-of-a-simulated-system-and-a-wind-turbine-blade.html?searchHighlight=modal%20analysis%20modalfit&s_tid=srchtitle_support_results_5_modal%20analysis%20modalfit#d126e64632
Hope this helps!
