August 19, 2022 at 10:20 ambiao.zhouSubscriber
I want to construct the mass-normalized complex-valued cyclic modes based on the real-valued cyclic modes extracted from cyclic sysmetric modal analysis. But I have a problem about the mass-normalization of the complex cyclic modes.
Below is the equation I used for expanding the reference sector mode (in complex
% Ux(n) = e^((n-1)k*theta) + (Uxa + i*Uxb)
% Uy(n) = e^((n-1)k*theta) + (Uya + i*Uyb)
% Uz(n) = e^((n-1)k*theta) + (Uza + i*Uzb)
% Uxa: the value from base sector in Ansys
% Uxb: the value from duplicate sector in Ansys
% k: is the Harmonic Index
% theta: is the sector angle
% n = sector number(1 to N total number of sectors)
Afterwards, in order to normalize the modes with repect to the mass matrix of the full structure, Ux(n),Uy(n),Uz(n) for are divided by:
% sqrt(N) if k = 0 or k = N/2,
% sqrt(N/2) : for all other Harmonic Indices
At this point, these Ux,Uy,Uz are in the complex form.
It has been verified that either the real part or the imaginary part of U = [Ux;Uy;Uz] is normalized with repect to the mass matrix of the full structure.
However, these complex-valued cyclic modes gives the following product:
U^H*M*U = [2, 2i; -2i, 2 ] (only for harmonic index with double modes. For harmonic index 0 with a single mode, the results are correct. See the image below).
So my problem is how to get the complex-valued cyclic modes normalized to the mass matrix of the full structure?
Any comments and help will be highly appreciated.
August 21, 2022 at 2:53 pmbiao.zhouSubscriber
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