Tagged: cyclicmodalanalysis, structures


August 19, 2022 at 10:20 ambiao.zhouSubscriber
Hi, everybody.
I want to construct the massnormalized complexvalued cyclic modes based on the realvalued cyclic modes extracted from cyclic sysmetric modal analysis. But I have a problem about the massnormalization of the complex cyclic modes.
Below is the equation I used for expanding the reference sector mode (in complex
cyclic coordinates)
%
% Ux(n) = e^((n1)k*theta) + (Uxa + i*Uxb)
% Uy(n) = e^((n1)k*theta) + (Uya + i*Uyb)
% Uz(n) = e^((n1)k*theta) + (Uza + i*Uzb)
%
% Where:
% 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 complexvalued 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 complexvalued 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
Problem solved.

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