Enforcing nodes at required locations in a harmonically excited structure using simple oscillators

With a suitably chosen set of spring-mass parameters, a single or multiple points of zero vibration (or otherwise referred to as nodes) can be induced anywhere along a general elastic structure during forced harmonic excitations. In application, however, the actual selection of the oscillator parameters also depends on the tolerable vibration amplitudes of the absorber masses, because if the vibration amplitudes of these masses are large, then theoretically feasible solutions could not be implemented in practice. In this paper, spring-mass systems are used as a means to impose single or multiple nodes anywhere along a harmonically forced structure, subjected to the constraints of tolerable vibration amplitudes for the masses. When the node locations are chosen so that they are closely spaced, a region of nearly zero amplitudes can be induced, effectively quenching vibration in that segment of the structure. Numerical experiments show that the required mass and its vibration amplitude for each oscillator are inversely related. This observation serves as a guide for the proper selection of the oscillator parameters in order to induce multiple nodes and to meet the tolerable vibration amplitudes of the oscillator masses. An efficient procedure for choosing the required oscillator parameters is outlined in detail, and numerical experiments are performed to verify the proposed methodology of imposing nodes at multiple locations along any arbitrary structure during harmonic excitations.