Imposing points of zero displacements and zero slopes along any linear structure during harmonic excitations

Undamped oscillators are often employed as vibration absorbers to minimize excess vibration in structural systems. In this paper, undamped sprung masses and rotational oscillators are used to impose points of zero displacements and zero slopes for an arbitrarily supported linear structure during forced harmonic excitations. For convenience, such points are referred to as fixed nodes. When the sprung mass and rotational oscillator attachment locations and the fixed node locations coincide (or collocated), it is always possible to select the sprung mass and rotational oscillator parameters such that multiple fixed nodes are induced at any desired locations along the structure for any excitation frequency. When the attachment and the fixed node locations are not collocated (or non-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 fixed node locations are closely spaced, it is possible to specify a region of nearly zero amplitudes for a particular driving frequency, thus drastically reducing the vibrational level in that segment of the structure. An iterative scheme is proposed that quickly leads to a set of theoretically feasible oscillator parameters that can be used to induce fixed nodes anywhere along the linear structure. Numerical case studies are performed and they validated the proposed scheme of imposing points of zero displacements and zero slopes.