Discrete mass and stiffness modifications for the inverse eigenstructure assignment in vibrating systems: Theory and experimental validation

The inverse eigenstructure assignment in structural dynamics and control aims at determining the mass and stiffness parameters to ensure the desired dynamic behavior expressed in terms of the prescribed eigenstructure. Several methods have been developed for the solution of this problem in the past. However, in the techniques proposed so far, all the design variables are assumed to be continuous. In practice, some design variables can only be changed through discrete modifications since either standard mass modules or springs are available. The determination of the discrete optimal solution of the structural modification problem cannot be performed by simply rounding the continuous optimal solution to the “nearest” integer, since rounded solutions can be considerably far from the optimality. On the other hand, the total enumeration as a solution method is infeasible for medium and large scale problems. To overcome this limitation, in this work, the eigenstructure assignment is formulated firstly as an inverse eigenvalue problem within the frame of constrained nonlinear integer programming, and then is solved by means of a partial enumeration technique with a reduced number of iterations. The experimental validation of the method on a five-degree-of-freedom lumped-parameter rig demonstrates its capability to compute effective modifications meeting the prescribed requirements and satisfying all the constraints.