Computation of mode shape sensitivities

For each design variable change, the mode shape sensitivities, {ΔΦi}, are expressed in terms of frequency sensitivities, Δλi, as follows:

{ΔΦi} = – ([KR] – λi [MR])-1([ΔKR] – Δλi [MR] – λi [ΔMR]) {Φi}

This equation cannot be solved directly as ([KR] – λi [MR]) is a singular matrix. The Model Update solution process addresses this problem differently depending on the model reduction method that is used.

When the physical (Guyan) reduction method is specified, the eigenvalue solver uses the Nelson's method NOTE to calculate mode shape sensitivities. When the modal reduction method is specified, the eigenvalue solver uses the Fox and Kapoor method NOTE.

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Computation of mode shape sensitivities, Simcenter 3D 2021.1 Series

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Nelson R.B., “Simplified Calculation of Eigenvector Derivatives”, AIAA Journal, Vol. 14, No. 9, September 1976, pp. 1201–1205.

Fox R.L. and Kapoor M.P., “Rates of Change of Eigenvalues and Eigenvectors”, AIAA Journal, Vol. 6, No. 12, December 1968, pp. 2426–2429.

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