I have measured the mode shapes using rowing hammer method, but I have only 15 data points for 450 mm length of the beam. It is insufficient to find higher order mode shapes. My question is '' is to correct to use cubic spline interpolation method? If not, which one is a more appropriate one?
Your spatial representation of the mode shapes is limited by the number of degrees of freedom that you really measure. Obviously, you can interpolate the spatial representation as long as you have physical meaning of the real mode shapes (I.e. you cannot guess a set of higher order modes from a limited set of measured dofs that only able to represent the low order modes ... Except if you assume a predefined order of modes and the particular shape of each misrepresented mode.
Any extrapolation made is an assumption on the mode shape itself. If you have a good idea of your modes, you can build up an extrapolation technique that will provide relevant result. If you do not know what the mode shape will be no, extrapolation method can be true on the sole basis of its principle.
A common application is called modal expansion and requires a Finite Element Model to expand the measured mode shapes on the mesh. If the FEM topology and properties are representative, you can get good results and also an indication to where you may miss information.
If you want more information on shape expansion methods, I suggest you check the
"Test/analysis correlation" section of the publication page
http://www.sdtools.com/Publications.html
I hope this helps.
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