Structural modification. Part 2: assignment of natural frequencies and antiresonances by an added beam

In this paper the inverse structural modification problem is solved in order to determine the dimensions of the cross-section of a beam that when added to an original structure will assign natural frequencies or antiresonances as specified. In order for this to be accomplished rotational receptances must be measured as presented in the companion paper. When the modification is cast as an additional forcing term on the original structure a system of multivariate polynomials in the parameters of the beam cross-section are revealed. The solution of this system yields the beam parameters that assign the specified vibration behaviour.