Ranking criterion for modal contribution factors

• $\alpha$ = mode number

• $P_{\alpha }$ = partial response for mode $\alpha$

• $P_{\alpha R}$ = real portion of partial response for mode $\alpha$

• $P_{\alpha I}$ = imaginary portion of partial response for mode $\alpha$

• $P_{\alpha M}$ = magnitude of partial response for mode $\alpha$

• $P_{\alpha P}$ = phase of partial response for mode $\alpha$

• T = total response P

• $TR={\sum }_{\alpha }{P}_{\alpha R}$ = real portion of total response

• $TI={\sum }_{\alpha }{P}_{\alpha I}$ = imaginary portion of total response

• $TM=\sqrt{T{R}^2+T{I}^2}$ magnitude of total response

• $TP=$ phase of total response

• ${\delta }_{\alpha }=\sqrt{{\left(TR+{0.1}^{\ast }{p}_{\alpha R}\right)}^2+{\left(TI+{0.1}^{\ast }{p}_{\alpha I}\right)}^2}-TM$ = delta in total response magnitude for 10% increase in any given partial response (i.e. sensitivity)

You can determine the top n modes based on the absolute value of ${\delta }_{\alpha }$ and output $p_{\alpha M}$ and $p_{\alpha P}$ for these modes.