I want to use Buckinghum Pi Theorem to relate a similitude of the blade to the prototype blade.
I began as stating the natural frequency is function of ( Young's Modulus, Length of the blade, Cross Section area,Moment of inertia,Density)
Fn (fn,E,L,A,I,Rho) ,then I got the dimensionless pi groups that relate natural frequency of similitude to the prototype !!!
Is this correct procedure or should I derive the natural frequencies equations first ?
Ahmed,
You do not need to derive the natural frequencies if you are just scaling them between a prototype and full-scaled model. Please also check the attached files. Check page 16 of "6-scaleeffects.pdf"; the other two files give helpful tips as well. I hope these help.
Hello Mr. Hesham,
the Pi-Theorem of Buckingham is a formalism for data reduction and scaling. It is applicable, when all influential quantities and their dimensions are known. If more quatities than necessary are included, non-dimensional groups with no impact are generated. You do not have to know the mathematical equations in order to apply the Pi theorem. Thus, you could scale the results from measurements even when dimensional equations are unknown or unsolvable. Therefore, usually a 5 point list is used in order to identify physical quantities of impact. However, the a priori knowledge of the respective equations or first principles might be useful in order to identify the influential quantities.
Best regards
Bastian
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