Inverse problem of imposing nodes to suppress vibration for a structure subjected to multiple harmonic excitations

Abstract Undamped oscillators are frequently used as a means to minimize excess vibration in flexible structures. In this paper, parallel vibration absorbers are employed to solve the inverse problem of dictating a node location, i.e., a point of zero vibration, for an arbitrarily supported linear structure subjected to multiple harmonic excitations. When the attachment location for the oscillators and the desired node location coincide (or collocated), it is always possible to select a set of spring–mass parameters such that a node is induced at the desired location for an input consisting of multiple harmonics. When the attachment and the specified node locations are not collocated, however, it is only possible to induce a node at certain locations along the elastic structure for the same input. When the input consists of two harmonics with closely spaced frequencies, it is possible to induce a point of nearly zero amplitude for frequencies in the range between the two driving frequencies. Moreover, when the specified node locations are in the vicinity of one another, a region of nearly zero deflections can be enforced, effectively quenching vibration in that segment of the structure. Finally, the proposed algorithm can be easily modified and extended to enforcing more than one node when the structure is being excited by multiple harmonics, for both the collocated and non-collocated cases. A procedure to guide the proper selection of the spring–mass parameters is outlined in detail, and numerical case studies are presented to verify the utility of the proposed scheme of imposing one or multiple nodes for an arbitrarily supported linear structure subjected to an input consisting of multiple harmonics.

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