Simultaneous assignment of resonances and antiresonances in vibrating systems through inverse dynamic structural modification

This paper proposes a method for the concurrent assignment of resonance and antiresonance frequencies in cross-receptances of undamped vibrating systems, by exploiting inverse dynamic structural modification. The technique also allows partially assigning the mode shapes of interest, which in turn makes it possible to perform pole-zero flipping in cross receptances. This is useful to shape receptances in the frequency range of interest. The method uses the inverse eigenvalue problem of the actual system and the adjunct one, by formulating it through the system matrices, to overcome the numerical issues of using the characteristic polynomials. Besides the theoretical formulation and the numerical application of the method, experimental validation is proposed through a laboratory cantilever beam, that shows the method effectiveness and ease of implementation.