**Abstract**: The inverse structural modification problem of a multi-degree-of-freedom system aims at computing the necessary mass and stiffness changes leading to a desired optimized dynamics, i.e. to a prescribed eigenstructure. Such a problem is often formulated as an unconstrained inverse eigenvalue problem, which leads to interesting solutions but does not always ensure their feasibility.
In this work the structural modification problem is instead formulated as an inverse eigenvalue problem within the frame of convex constrained quadratic optimization, which ensures that an unique, and hence global, optimal and feasible solution does exist and that it can be efficiently computed by means of numerical algorithms.
In particular the method proposed is addressed to the optimization of multibody systems under single and constant frequency harmonic excitation, which is often a practical need. There are in fact several examples of industrial devices operating under a single harmonic oscillatory forced motion. Popular examples are sieves, conveyors and linear feeders. In these cases structural optimization should be performed in a narrow range of frequencies, by assigning the desired eigenstructure of the modes with the most significant modal participation factors at the excitation frequency.
The proposed approach is validated numerically with reference to two different test cases, involving both lumped and distributed parameter systems.
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