^ ` ^ ` > @ > @ > @ > @ ^ ` ^ ` AB AB AB AB cc ci c c AB AB AB AB ic ii i i H H u f H H u f ª º ½ ½ ° ° ° ° « » ® ¾ ® ¾ « » ° ° ° ° ¯ ¿ ¯ ¿ ¬ ¼ (1) and for the known component A, ^ ` ^ ` > @ > @ > @ > @ ^ ` ^ ` A A A A cc ci c c A A A A ic ii i i u H H f u H H f ª º ½ ½ ° ° ° ° « » ® ¾ ® ¾ « » ° ° ° ° ¯ ¿ ¯ ¿ ¬ ¼ (2) The coupling conditions at connection DOF are: ^ ` ^ ` ^ ` AB A B c c c u u u (3) ^ ` ^ ` ^ ` AB A B c c c f f f (4) and at internal DOFs on component B: ^ ` ^ ` AB B i i u u (5) ^ ` ^ ` AB B i i f f (6) Impedance Approach For the Impedance based approach, subtracting the inverse of (2) by the inverse of (1) and introducing the conditions (3), (4), (5) and (6), with some algebraic manipulation one can obtain, > @ > @ > @ > @ > @ AB B cc cc cc AB cc ic N H H N H ª º ª º « » « » « » « » ¬ ¼ ¬ ¼ (7) with, > @ > @ > @ > @ > @ > @ 1 1 AB A AB A cc cc cc cc ci ic N I H H H H (8) > @ > @ > @ > @ > @ 1 1 AB A AB A ic ic cc ii ic N H H H H (9) If only connection DOF are measured, then (7) simplifies to > @ > @ > @ > @ > @ 1 1 B AB A AB cc cc cc cc cc H I H H H (9) Mobility Approach For the Mobility based approach, subtracting (2) from (1) and introducing the coupling conditions (3), (4), (5) and (6), with some algebraic manipulation one can obtain > @ > @ > @ > @ > @ > @ > @ > @ > @ > @ > @ > @ > @ A AB AB A B AB AB cc cc ci ci cc cc ci cc ci A AB AB A ic ic ii ii H H H H H H H I 0 H H H H § · ª º ª º ¨ ¸ ª º « » « » ª º ¬ ¼ ¨ ¸ ¬ ¼ « » « » ¨ ¸ ¬ ¼ ¬ ¼ © ¹ (10) If only connection DOF are measured, then (10) simplifies to 174
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