What are the units of displacement in the ModalStructuralResults returned by the solve function in PDE Toolbox

The 'solve' function in the PDE toolbox for solving structural analysis problems returns 'ModalStructuralResults':

https://www.mathworks.com/help/releases/R2019b/pde/ug/pde.thermalmodel.solve.html

https://www.mathworks.com/help/releases/R2019b/pde/ug/pde.modalstructuralresults.html

The documentation does not mention what are the units of the 'modal displacement values at nodes' stored in the 'ModeShapes' property of 'ModalStructuralResults'.

I was following the vibration of square plate tutorial at:

https://www.mathworks.com/help/releases/R2019b/pde/examples/vibration-of-a-square-plate.html

At the bottom of the tutorial the "The third component (z-component) of the solution for the seven lowest nonzero-frequency modes is being plotted" using the fields of 'ModeShapes'. I want to know what are the units of the values stored in "ModeShapes.uz"?

The legends of each of the figures show that the values go from 0 to -2 X 10^-3.

I want to know what are the units of these values?

Answer 1

[MathWorks Support Team]

Mode shapes have an arbitrary scale factor associated with them.

Hence, the magnitude of the numbers don't carry much meaning individually, its the relative displacement that shows the shapes of normal modes.

The main use-case for mode shapes is that the users can look at them and do other types of analysis (For example, transient, frequency response, etc.) so as to determine the actual magnitude.

Additionally, PDE Toolbox is unit-less and user's should set up the model in consistent units.

For example, if all inputs are in SI units, then output displacement would be in meters.