Imposing points of zero displacement and zero slopes on a plate subjected to steady-state harmonic excitation

Abstract

In this paper, a simple and effective method to enforce fixed nodes, or points of zero displacement and zero slope, on an arbitrarily supported rectangular plate subjected to steady-state harmonic excitations is developed. This is achieved by attaching properly tuned translational and rotational oscillators at specified locations. The governing equations of the combined system are first derived using the assumed-modes method. By enforcing the conditions of zero displacements and zero slopes simultaneously, a set of constraint equations are formulated, from which the oscillator parameters can be determined. When the attachment locations coincide with the desired fixed node locations, it is always possible to select the oscillator parameters such that one or multiple fixed nodes are induced at any locations on the plate for any excitation frequency. When the attachment and the desired node locations are not collocated, it is only possible to induce nodes at certain locations on the plate. When the fixed node locations are judiciously chosen, a selected region of the plate can be made to remain nearly stationary. Thus, the proposed method provides a simple and yet effective means to passively control excessive vibrations.