Efficient and accurate calculation of sensitivity of damped eigensystems

• Eigensensitivity of non-classically viscously damped systems is studied.
• A correction modal method for eigensensitivity calculation is presented.
• The method maintains original-space without involving state-space formulas.
• The modal truncation error is expressed as the available modes and system matrices.
• The proposed method yields good trade-off between accuracy and efficiency.

The exact methods (the algebraic method and Nelson’s method) to calculate eigensensitivities need a matrix decomposition for each eigensensitivity, and therefore are time-consuming. The modal method may be the most efficient method for eigensensitivity analysis, but suffers from modal truncation error. A method is presented by exactly expressing the modal truncation error as a sum of available modes and system matrices. The proposed method maintains original space without having to use the state-space form. It is shown that the proposed method yields good trade-off between accuracy and computational complexity in terms of the theoretical analysis and numerical studies.