Passive modifications for partial assignment of natural frequencies of mass–spring systems

• Passive modification of mass–spring systems for partial eigenvalue assignment is proposed.
• The structure of the mass and stiffness matrices is maintained after modifications.
• The modifications are also physically realisable.

The inverse structural modification for assigning a subset of natural frequencies of a structure to some targeted values has been found to inevitably lead to undesired changes to the other natural frequencies of the original structure that should not have been modified, which is referred to as the frequency “spill-over” phenomenon. Passive structural modifications of mass–spring systems for partial assignment of natural frequencies without frequency “spill-over” are addressed in this paper. For two kinds of lumped mass–spring systems, i.e. simply connected in-line mass–spring systems and multiple-connected mass–spring systems, two solution methods are proposed to construct the required mass-normalised stiffness matrix, which satisfies the partial assignment requirement of natural frequencies and maintains the configuration of the original structure after modifications. The modifications are also physically realisable. Finally, some examples of lumped mass–spring systems are analysed to demonstrate the effectiveness and accuracy of the proposed methods.