Reciprocity (engineering)

Reciprocity in linear systems is the principle that a response Rab, measured at a ___location (and direction if applicable) a, when the system has an excitation signal applied at a ___location (and direction if applicable) b, is exactly equal to Rba which is the response at ___location b, when that same excitation is applied at a. This applies for all frequencies of the excitation signal. If Hab is the transfer function between a and b then Hab = Hba, if the system is linear.

In the special case of a modal analysis this is known as Maxwell's reciprocity theorem.^[1] In electromagnetism the concept is known as Lorentz reciprocity, a special case of which is the reciprocity theorem of electrical networks.

The reciprocity principle is also used in the analysis of structures.^[2] When combined with superposition, symmetry and anti-symmetry, it can be used to resolve complex load conditions.

References

1. "Experimental modal analysis" (PDF). Archived from the original (PDF) on 2008-09-07.
2. Benaroya, Haym (2004). Mechanical Vibration: Analysis, Uncertainties, and Control. CRC Press. ISBN 9780824753801.