Imposing nodes at arbitrary locations for general elastic structures during harmonic excitations

Spring–mass systems are frequently used as vibration absorbers to minimize excess vibration in structural systems. In this paper, sprung masses are used to impose the points of zero vibration for general elastic structures during forced harmonic excitations. For convenience, such points are referred to as nodes. When the oscillator attachment locations and the node locations coincide (or are collocated), it is always possible to select the spring–mass parameters such that multiple nodes are induced at any desired locations along the structure for any excitation frequency. When the oscillators and the node locations are not collocated, however, it is only possible to induce nodes at certain locations along the elastic structure for a given driving frequency. Moreover, when the desired node locations are closely spaced, it is possible to specify a region of nearly zero amplitudes for a particular driving frequency, effectively quenching vibration in that region. A procedure to guide the proper selection of the spring–mass parameters in order to induce multiple nodes is outlined in detail, and numerical experiments are performed to verify the utility of the proposed scheme of imposing nodes at multiple locations during harmonic excitations.